diff --git a/worlds/yachtdice/Rules.py b/worlds/yachtdice/Rules.py index 1eb7487254..b4984ca56a 100644 --- a/worlds/yachtdice/Rules.py +++ b/worlds/yachtdice/Rules.py @@ -159,6 +159,7 @@ def dice_simulation_strings(categories, num_dice, num_rolls, fixed_mult, step_mu for val1, prob1 in c.items(): for val2, prob2 in dist1.items(): new_val = int(max(val1, val2 * mult)) + new_val = new_val - new_val % 2 new_prob = prob1 * prob2 # Update the probability for the new value diff --git a/worlds/yachtdice/YachtWeights.py b/worlds/yachtdice/YachtWeights.py index 3b788d5c88..99f9489477 100644 --- a/worlds/yachtdice/YachtWeights.py +++ b/worlds/yachtdice/YachtWeights.py @@ -7904,3 +7904,28 @@ yacht_weights = { ("FourAndFiveFullHouse", 8, 7): {50: 97782, 0: 2218}, ("FourAndFiveFullHouse", 8, 8): {50: 98916, 0: 1084}, } + +def round_down_to_nearest(n, k): + return n - (n % k) + +def combine_rounded_keys(yacht_weights, change_category): + new_yacht_weights = {} + for main_key, sub_dict in yacht_weights.items(): + if main_key[0] in change_category: + new_sub_dict = {} + for key, value in sub_dict.items(): + rounded_key = round_down_to_nearest(key, 2) + if rounded_key in new_sub_dict: + new_sub_dict[rounded_key] += value + else: + new_sub_dict[rounded_key] = value + new_yacht_weights[main_key] = new_sub_dict + else: + new_yacht_weights[main_key] = sub_dict + return new_yacht_weights + +change_category = ['SumOfEvens', 'DoubleThreesAndFours', 'TinyStraight', 'MicroStraight', 'TwosAndThrees', 'TwoOneTwoConsecutive', 'TwoPair', 'FiveDistinctDice', 'Threes', 'ThreeOdds', 'Ones', 'FourAndFiveFullHouse', 'Pair', 'OneTwoOneConsecutive', 'Distincts', 'SmallStraight', 'Yacht', 'QuadrupleOnesAndTwos', 'Fours', 'LargeStraight', 'Fives', 'FullHouse', 'SumOfOdds', 'Sixes', 'ThreeOfAKind', 'Twos', 'FourOfAKind', 'Choice', 'ThreeDistinctDice'] + + + +yacht_weights = combine_rounded_keys(yacht_weights, change_category) diff --git a/worlds/yachtdice/temp_YachtWeights_make_small.py b/worlds/yachtdice/temp_YachtWeights_make_small.py new file mode 100644 index 0000000000..228b4da3bf --- /dev/null +++ b/worlds/yachtdice/temp_YachtWeights_make_small.py @@ -0,0 +1,7978 @@ +# A file containing the results of our simulations. +# Every entry consists of a key. This key has input category, number of dice, and number of rolls. +# The value then shows a list of all possible scores to get, and how many times of 100000 it achieved. + +# example: ("Choice", 2, 2): +# {8: 13639, 9: 12220, 10: 13755, 5: 4889, 6: 9840, 7: 14772, 12: 7780, 11: 15622, 2: 1269, 3: 2445, 4: 3769} +# this example shows the outcomes for the category "Choice", with 2 dice and 2 rolls. +# 13639 out of 100000 times, a score of 8 was achieved for example. +yacht_weights = { + ("Ones", 0, 0): {0: 100000}, + ("Ones", 0, 1): {0: 100000}, + ("Ones", 0, 2): {0: 100000}, + ("Ones", 0, 3): {0: 100000}, + ("Ones", 0, 4): {0: 100000}, + ("Ones", 0, 5): {0: 100000}, + ("Ones", 0, 6): {0: 100000}, + ("Ones", 0, 7): {0: 100000}, + ("Ones", 0, 8): {0: 100000}, + ("Ones", 1, 0): {0: 100000}, + ("Ones", 1, 1): {0: 83416, 1: 16584}, + ("Ones", 1, 2): {0: 69346, 1: 30654}, + ("Ones", 1, 3): {0: 57756, 1: 42244}, + ("Ones", 1, 4): {0: 48709, 1: 51291}, + ("Ones", 1, 5): {1: 59786, 0: 40214}, + ("Ones", 1, 6): {1: 66509, 0: 33491}, + ("Ones", 1, 7): {1: 72162, 0: 27838}, + ("Ones", 1, 8): {0: 23094, 1: 76906}, + ("Ones", 2, 0): {0: 100000}, + ("Ones", 2, 1): {0: 69715, 1: 27502, 2: 2783}, + ("Ones", 2, 2): {0: 48066, 1: 42669, 2: 9265}, + ("Ones", 2, 3): {1: 48585, 0: 33544, 2: 17871}, + ("Ones", 2, 4): {1: 50092, 2: 26566, 0: 23342}, + ("Ones", 2, 5): {1: 48250, 2: 35714, 0: 16036}, + ("Ones", 2, 6): {1: 44545, 0: 11355, 2: 44100}, + ("Ones", 2, 7): {2: 51940, 0: 7812, 1: 40248}, + ("Ones", 2, 8): {1: 35484, 2: 59121, 0: 5395}, + ("Ones", 3, 0): {0: 100000}, + ("Ones", 3, 1): {0: 57462, 1: 35151, 2: 6907, 3: 480}, + ("Ones", 3, 2): {1: 44253, 2: 19531, 3: 2889, 0: 33327}, + ("Ones", 3, 3): {1: 42237, 3: 7510, 2: 30821, 0: 19432}, + ("Ones", 3, 4): {0: 11191, 1: 36208, 2: 38606, 3: 13995}, + ("Ones", 3, 5): {3: 21443, 2: 43130, 1: 28891, 0: 6536}, + ("Ones", 3, 6): {2: 44196, 1: 22501, 3: 29606, 0: 3697}, + ("Ones", 3, 7): {1: 16717, 2: 43782, 3: 37367, 0: 2134}, + ("Ones", 3, 8): {1: 12567, 2: 40951, 3: 45202, 0: 1280}, + ("Ones", 4, 0): {0: 100000}, + ("Ones", 4, 1): {0: 48178, 1: 38635, 3: 1534, 2: 11592, 4: 61}, + ("Ones", 4, 2): {1: 40775, 3: 8051, 0: 23349, 2: 26967, 4: 858}, + ("Ones", 4, 3): {1: 32547, 2: 35556, 0: 11366, 3: 17371, 4: 3160}, + ("Ones", 4, 4): {2: 37271, 1: 23241, 3: 26943, 4: 7214, 0: 5331}, + ("Ones", 4, 5): {2: 34536, 3: 34496, 1: 15336, 4: 12992, 0: 2640}, + ("Ones", 4, 6): {2: 29743, 3: 39298, 4: 19633, 1: 10073, 0: 1253}, + ("Ones", 4, 7): {2: 24313, 3: 41680, 1: 6304, 4: 27092, 0: 611}, + ("Ones", 4, 8): {4: 34460, 3: 42267, 0: 313, 1: 3915, 2: 19045}, + ("Ones", 5, 0): {0: 100000}, + ("Ones", 5, 1): {1: 40202, 0: 40042, 3: 3249, 2: 16165, 4: 331, 5: 11}, + ("Ones", 5, 2): {1: 35432, 3: 13849, 2: 31231, 0: 16212, 4: 3032, 5: 244}, + ("Ones", 5, 3): {3: 24952, 2: 34509, 1: 23548, 0: 6556, 4: 9117, 5: 1318}, + ("Ones", 5, 4): {3: 32048, 2: 30176, 1: 14157, 4: 17403, 5: 3664, 0: 2552}, + ("Ones", 5, 5): {4: 25625, 0: 1079, 3: 34614, 2: 23245, 5: 7733, 1: 7704}, + ("Ones", 5, 6): {1: 4104, 5: 13068, 4: 32816, 2: 16702, 3: 32901, 0: 409}, + ("Ones", 5, 7): {4: 37869, 3: 28973, 5: 19366, 0: 175, 2: 11497, 1: 2120}, + ("Ones", 5, 8): {1: 1094, 5: 26646, 3: 24639, 2: 7382, 4: 40166, 0: 73}, + ("Ones", 6, 0): {0: 100000}, + ("Ones", 6, 1): {2: 20320, 0: 33501, 1: 40042, 3: 5295, 4: 773, 5: 69}, + ("Ones", 6, 2): {1: 29379, 3: 19350, 2: 32368, 5: 1141, 0: 11326, 4: 6344, 6: 92}, + ("Ones", 6, 3): {4: 15450, 3: 28928, 5: 4634, 1: 16463, 2: 30197, 0: 3764, 6: 564}, + ("Ones", 6, 4): {3: 31038, 4: 25136, 2: 21790, 1: 8093, 0: 1231, 5: 10779, 6: 1933}, + ("Ones", 6, 5): {3: 27868, 4: 30878, 5: 18389, 2: 14029, 1: 3790, 6: 4628, 0: 418}, + ("Ones", 6, 6): {2: 8389, 4: 33022, 3: 22007, 6: 8599, 5: 26133, 1: 1692, 0: 158}, + ("Ones", 6, 7): {5: 32432, 3: 16397, 6: 13966, 4: 31702, 2: 4749, 1: 707, 0: 47}, + ("Ones", 6, 8): {6: 20483, 5: 37005, 4: 28116, 3: 11500, 2: 2575, 1: 304, 0: 17}, + ("Ones", 7, 0): {0: 100000}, + ("Ones", 7, 1): {2: 23331, 0: 27838, 1: 39224, 3: 7827, 4: 1536, 5: 235, 6: 9}, + ("Ones", 7, 2): {3: 23224, 2: 31678, 1: 23850, 4: 10350, 5: 2696, 0: 7796, 6: 387, 7: 19}, + ("Ones", 7, 3): {6: 2239, 2: 24317, 1: 11142, 3: 29131, 5: 9405, 4: 21297, 0: 2247, 7: 222}, + ("Ones", 7, 4): {4: 28065, 5: 17986, 2: 14787, 1: 4647, 3: 26420, 6: 6464, 7: 1026, 0: 605}, + ("Ones", 7, 5): {5: 26190, 4: 28867, 6: 12698, 3: 19667, 2: 7907, 1: 1773, 7: 2724, 0: 174}, + ("Ones", 7, 6): {4: 25653, 3: 12915, 6: 20371, 5: 30596, 7: 5840, 2: 3905, 1: 669, 0: 51}, + ("Ones", 7, 7): {5: 32077, 4: 20364, 6: 27540, 3: 7943, 7: 10044, 2: 1802, 1: 213, 0: 17}, + ("Ones", 7, 8): {6: 33357, 4: 15425, 5: 30293, 7: 15406, 3: 4579, 2: 856, 1: 78, 0: 6}, + ("Ones", 8, 0): {0: 100000}, + ("Ones", 8, 1): {4: 2620, 2: 26136, 0: 23156, 1: 37295, 3: 10332, 5: 417, 6: 39, 7: 4, 8: 1}, + ("Ones", 8, 2): {4: 14130, 3: 25847, 0: 5472, 2: 29314, 1: 19058, 5: 5000, 6: 1038, 7: 133, 8: 8}, + ("Ones", 8, 3): {1: 7452, 6: 5203, 3: 27032, 5: 14360, 4: 24664, 2: 18864, 7: 1114, 0: 1209, 8: 102}, + ("Ones", 8, 4): {4: 27157, 2: 9318, 6: 12536, 3: 20389, 5: 23430, 7: 3804, 1: 2540, 8: 559, 0: 267}, + ("Ones", 8, 5): {6: 20582, 3: 12395, 4: 23638, 5: 27792, 1: 817, 7: 8765, 2: 4298, 8: 1655, 0: 58}, + ("Ones", 8, 6): {6: 27112, 7: 15535, 5: 27508, 4: 17025, 3: 6901, 8: 3948, 2: 1716, 1: 242, 0: 13}, + ("Ones", 8, 7): {5: 23980, 4: 11343, 7: 22673, 6: 30438, 8: 7330, 3: 3508, 2: 643, 1: 82, 0: 3}, + ("Ones", 8, 8): {6: 30830, 4: 7029, 7: 29143, 8: 12025, 5: 18895, 3: 1768, 2: 286, 1: 23, 0: 1}, + ("Twos", 0, 0): {0: 100000}, + ("Twos", 0, 1): {0: 100000}, + ("Twos", 0, 2): {0: 100000}, + ("Twos", 0, 3): {0: 100000}, + ("Twos", 0, 4): {0: 100000}, + ("Twos", 0, 5): {0: 100000}, + ("Twos", 0, 6): {0: 100000}, + ("Twos", 0, 7): {0: 100000}, + ("Twos", 0, 8): {0: 100000}, + ("Twos", 1, 0): {0: 100000}, + ("Twos", 1, 1): {0: 83475, 2: 16525}, + ("Twos", 1, 2): {0: 69690, 2: 30310}, + ("Twos", 1, 3): {0: 57818, 2: 42182}, + ("Twos", 1, 4): {0: 48418, 2: 51582}, + ("Twos", 1, 5): {2: 59699, 0: 40301}, + ("Twos", 1, 6): {2: 66442, 0: 33558}, + ("Twos", 1, 7): {2: 71818, 0: 28182}, + ("Twos", 1, 8): {0: 23406, 2: 76594}, + ("Twos", 2, 0): {0: 100000}, + ("Twos", 2, 1): {0: 69724, 2: 27485, 4: 2791}, + ("Twos", 2, 2): {0: 48238, 2: 42479, 4: 9283}, + ("Twos", 2, 3): {0: 33290, 2: 48819, 4: 17891}, + ("Twos", 2, 4): {2: 49957, 4: 26907, 0: 23136}, + ("Twos", 2, 5): {4: 35654, 2: 48200, 0: 16146}, + ("Twos", 2, 6): {4: 44420, 2: 44497, 0: 11083}, + ("Twos", 2, 7): {4: 51995, 2: 40343, 0: 7662}, + ("Twos", 2, 8): {4: 59120, 2: 35526, 0: 5354}, + ("Twos", 3, 0): {0: 100000}, + ("Twos", 3, 1): {2: 34522, 0: 58021, 4: 6995, 6: 462}, + ("Twos", 3, 2): {0: 33548, 2: 44261, 4: 19358, 6: 2833}, + ("Twos", 3, 3): {2: 42372, 4: 30748, 0: 19375, 6: 7505}, + ("Twos", 3, 4): {6: 13998, 4: 38569, 2: 36435, 0: 10998}, + ("Twos", 3, 5): {4: 43283, 2: 28838, 6: 21360, 0: 6519}, + ("Twos", 3, 6): {6: 29650, 4: 44233, 2: 22498, 0: 3619}, + ("Twos", 3, 7): {6: 37142, 2: 16979, 4: 43684, 0: 2195}, + ("Twos", 3, 8): {6: 45405, 4: 40920, 2: 12420, 0: 1255}, + ("Twos", 4, 0): {0: 100000}, + ("Twos", 4, 1): {4: 11628, 0: 48235, 2: 38602, 6: 1463, 8: 72}, + ("Twos", 4, 2): {2: 40678, 0: 23289, 6: 8032, 4: 27102, 8: 899}, + ("Twos", 4, 3): {6: 17263, 2: 32677, 0: 11177, 4: 35702, 8: 3181}, + ("Twos", 4, 4): {6: 26867, 4: 37240, 8: 7169, 2: 23225, 0: 5499}, + ("Twos", 4, 5): {4: 34605, 6: 34268, 8: 12771, 2: 15782, 0: 2574}, + ("Twos", 4, 6): {8: 19602, 4: 29706, 2: 9910, 6: 39523, 0: 1259}, + ("Twos", 4, 7): {2: 6323, 4: 24103, 6: 41894, 8: 27058, 0: 622}, + ("Twos", 4, 8): {6: 42309, 4: 18855, 2: 3813, 8: 34745, 0: 278}, + ("Twos", 5, 0): {0: 100000}, + ("Twos", 5, 1): {0: 40028, 2: 40241, 6: 3383, 4: 16003, 8: 334, 10: 11}, + ("Twos", 5, 2): {0: 16009, 6: 13797, 4: 31024, 8: 2985, 2: 35901, 10: 284}, + ("Twos", 5, 3): {8: 9087, 2: 23477, 4: 34349, 10: 1328, 6: 25270, 0: 6489}, + ("Twos", 5, 4): {4: 30199, 2: 14032, 8: 17149, 10: 3748, 6: 32214, 0: 2658}, + ("Twos", 5, 5): {4: 23643, 8: 25853, 10: 7495, 6: 33993, 0: 1032, 2: 7984}, + ("Twos", 5, 6): {6: 32774, 2: 4152, 8: 32900, 10: 13183, 0: 450, 4: 16541}, + ("Twos", 5, 7): {6: 29481, 8: 37636, 10: 19256, 4: 11231, 2: 2226, 0: 170}, + ("Twos", 5, 8): {10: 26467, 8: 40798, 6: 23993, 4: 7571, 2: 1108, 0: 63}, + ("Twos", 6, 0): {0: 100000}, + ("Twos", 6, 1): {0: 33502, 4: 19717, 2: 40413, 6: 5481, 8: 815, 10: 68, 12: 4}, + ("Twos", 6, 2): {2: 29638, 8: 6339, 4: 32701, 0: 11210, 6: 18988, 10: 1046, 12: 78}, + ("Twos", 6, 3): {6: 29102, 2: 16459, 8: 15825, 4: 29795, 0: 3673, 10: 4581, 12: 565}, + ("Twos", 6, 4): {2: 8048, 8: 25066, 4: 21977, 6: 31053, 10: 10654, 12: 1959, 0: 1243}, + ("Twos", 6, 5): {10: 18355, 4: 13949, 6: 28142, 8: 30723, 2: 3753, 12: 4637, 0: 441}, + ("Twos", 6, 6): {10: 26213, 6: 22222, 4: 8455, 8: 32692, 12: 8618, 2: 1679, 0: 121}, + ("Twos", 6, 7): {10: 32532, 8: 31410, 6: 16142, 12: 14270, 4: 4871, 2: 728, 0: 47}, + ("Twos", 6, 8): {12: 20612, 6: 11432, 10: 37237, 8: 27864, 4: 2544, 2: 299, 0: 12}, + ("Twos", 7, 0): {0: 100000}, + ("Twos", 7, 1): {2: 39060, 0: 27683, 8: 1580, 4: 23574, 6: 7899, 10: 192, 12: 12}, + ("Twos", 7, 2): {2: 24031, 6: 23095, 4: 31764, 0: 7824, 8: 10154, 10: 2733, 12: 376, 14: 23}, + ("Twos", 7, 3): {2: 11019, 6: 29599, 10: 9338, 8: 21250, 0: 2148, 4: 24197, 12: 2233, 14: 216}, + ("Twos", 7, 4): {10: 18080, 6: 26395, 4: 14571, 8: 28409, 2: 4465, 12: 6519, 14: 997, 0: 564}, + ("Twos", 7, 5): {8: 29039, 2: 1738, 10: 26129, 6: 19287, 4: 7911, 14: 2798, 12: 12923, 0: 175}, + ("Twos", 7, 6): {8: 25752, 10: 30413, 6: 12897, 14: 5951, 12: 20324, 4: 3961, 0: 54, 2: 648}, + ("Twos", 7, 7): {12: 27347, 14: 10079, 10: 32054, 6: 8007, 8: 20334, 4: 1926, 2: 240, 0: 13}, + ("Twos", 7, 8): {8: 15233, 10: 30248, 14: 15699, 12: 33276, 6: 4602, 4: 861, 2: 76, 0: 5}, + ("Twos", 8, 0): {0: 100000}, + ("Twos", 8, 1): {0: 23378, 6: 10451, 2: 37157, 4: 26082, 8: 2497, 10: 391, 12: 44}, + ("Twos", 8, 2): {8: 14198, 4: 29216, 12: 1104, 6: 25677, 0: 5420, 2: 19164, 10: 5089, 14: 127, 16: 5}, + ("Twos", 8, 3): {4: 18793, 12: 5201, 6: 27054, 10: 14462, 8: 24712, 2: 7289, 14: 1109, 0: 1271, 16: 109}, + ("Twos", 8, 4): {8: 27389, 12: 12609, 10: 23232, 4: 9310, 6: 20242, 14: 3815, 16: 514, 2: 2604, 0: 285}, + ("Twos", 8, 5): {10: 27882, 12: 20768, 16: 1604, 6: 12669, 8: 23322, 14: 8692, 4: 4184, 0: 58, 2: 821}, + ("Twos", 8, 6): {8: 17148, 12: 27048, 10: 27398, 14: 15513, 6: 6992, 16: 3860, 2: 251, 4: 1774, 0: 16}, + ("Twos", 8, 7): {8: 11479, 10: 23675, 6: 3547, 14: 22454, 12: 30829, 16: 7275, 4: 667, 2: 71, 0: 3}, + ("Twos", 8, 8): {10: 18697, 14: 28983, 12: 31310, 16: 11977, 4: 286, 8: 6980, 6: 1746, 2: 21}, + ("Threes", 0, 0): {0: 100000}, + ("Threes", 0, 1): {0: 100000}, + ("Threes", 0, 2): {0: 100000}, + ("Threes", 0, 3): {0: 100000}, + ("Threes", 0, 4): {0: 100000}, + ("Threes", 0, 5): {0: 100000}, + ("Threes", 0, 6): {0: 100000}, + ("Threes", 0, 7): {0: 100000}, + ("Threes", 0, 8): {0: 100000}, + ("Threes", 1, 0): {0: 100000}, + ("Threes", 1, 1): {0: 83343, 3: 16657}, + ("Threes", 1, 2): {0: 69569, 3: 30431}, + ("Threes", 1, 3): {0: 57872, 3: 42128}, + ("Threes", 1, 4): {3: 51919, 0: 48081}, + ("Threes", 1, 5): {0: 40271, 3: 59729}, + ("Threes", 1, 6): {3: 66799, 0: 33201}, + ("Threes", 1, 7): {3: 72097, 0: 27903}, + ("Threes", 1, 8): {3: 76760, 0: 23240}, + ("Threes", 2, 0): {0: 100000}, + ("Threes", 2, 1): {0: 69419, 6: 2783, 3: 27798}, + ("Threes", 2, 2): {0: 48202, 3: 42590, 6: 9208}, + ("Threes", 2, 3): {6: 17775, 0: 33376, 3: 48849}, + ("Threes", 2, 4): {3: 49810, 6: 26914, 0: 23276}, + ("Threes", 2, 5): {6: 36190, 3: 47718, 0: 16092}, + ("Threes", 2, 6): {6: 44253, 3: 44515, 0: 11232}, + ("Threes", 2, 7): {6: 51952, 3: 40459, 0: 7589}, + ("Threes", 2, 8): {3: 35804, 6: 58749, 0: 5447}, + ("Threes", 3, 0): {0: 100000}, + ("Threes", 3, 1): {0: 57964, 6: 6868, 3: 34701, 9: 467}, + ("Threes", 3, 2): {3: 44263, 0: 33637, 6: 19213, 9: 2887}, + ("Threes", 3, 3): {3: 42382, 6: 30676, 0: 19520, 9: 7422}, + ("Threes", 3, 4): {3: 35772, 6: 39042, 0: 11265, 9: 13921}, + ("Threes", 3, 5): {3: 28916, 9: 21404, 6: 43261, 0: 6419}, + ("Threes", 3, 6): {3: 22496, 9: 29306, 6: 44388, 0: 3810}, + ("Threes", 3, 7): {6: 43720, 9: 37231, 3: 16875, 0: 2174}, + ("Threes", 3, 8): {9: 45070, 6: 41222, 3: 12471, 0: 1237}, + ("Threes", 4, 0): {0: 100000}, + ("Threes", 4, 1): {3: 38786, 0: 48121, 9: 1483, 6: 11540, 12: 70}, + ("Threes", 4, 2): {3: 40989, 0: 23296, 6: 26998, 9: 7851, 12: 866}, + ("Threes", 4, 3): {3: 32653, 12: 3183, 6: 35710, 9: 17221, 0: 11233}, + ("Threes", 4, 4): {9: 26734, 6: 37468, 3: 23270, 12: 7065, 0: 5463}, + ("Threes", 4, 5): {6: 34539, 9: 34635, 3: 15496, 12: 12639, 0: 2691}, + ("Threes", 4, 6): {12: 19732, 9: 39190, 6: 29811, 3: 10046, 0: 1221}, + ("Threes", 4, 7): {0: 599, 3: 6322, 6: 24420, 12: 27045, 9: 41614}, + ("Threes", 4, 8): {12: 34736, 9: 42236, 6: 18843, 3: 3876, 0: 309}, + ("Threes", 5, 0): {0: 100000}, + ("Threes", 5, 1): {0: 40183, 3: 40377, 6: 16039, 9: 3046, 12: 336, 15: 19}, + ("Threes", 5, 2): {3: 35494, 0: 16197, 6: 30937, 9: 13946, 12: 3139, 15: 287}, + ("Threes", 5, 3): {3: 23394, 6: 34432, 9: 25239, 15: 1325, 12: 9027, 0: 6583}, + ("Threes", 5, 4): {6: 30134, 9: 32371, 12: 17169, 0: 2636, 3: 14072, 15: 3618}, + ("Threes", 5, 5): {6: 23010, 3: 7804, 9: 34811, 12: 25702, 15: 7598, 0: 1075}, + ("Threes", 5, 6): {9: 32809, 12: 32892, 6: 16654, 3: 4234, 15: 12993, 0: 418}, + ("Threes", 5, 7): {6: 11416, 12: 37604, 15: 19543, 9: 29072, 3: 2203, 0: 162}, + ("Threes", 5, 8): {9: 24603, 15: 26464, 12: 40262, 6: 7425, 3: 1175, 0: 71}, + ("Threes", 6, 0): {0: 100000}, + ("Threes", 6, 1): {0: 33473, 6: 20151, 3: 40175, 9: 5369, 12: 775, 15: 55, 18: 2}, + ("Threes", 6, 2): {3: 29592, 9: 19287, 0: 11147, 6: 32630, 12: 6160, 15: 1102, 18: 82}, + ("Threes", 6, 3): {12: 15888, 9: 29006, 3: 16528, 0: 3628, 6: 29814, 15: 4565, 18: 571}, + ("Threes", 6, 4): {9: 30953, 15: 10810, 18: 1919, 6: 21987, 12: 24833, 3: 8236, 0: 1262}, + ("Threes", 6, 5): {6: 13949, 9: 27798, 15: 18256, 12: 31197, 3: 3820, 18: 4564, 0: 416}, + ("Threes", 6, 6): {9: 22175, 12: 32897, 15: 26264, 18: 8496, 6: 8372, 3: 1642, 0: 154}, + ("Threes", 6, 7): {12: 31385, 15: 32666, 18: 14084, 9: 16346, 6: 4728, 3: 740, 0: 51}, + ("Threes", 6, 8): {12: 28320, 15: 36982, 3: 297, 9: 11202, 18: 20528, 6: 2651, 0: 20}, + ("Threes", 7, 0): {0: 100000}, + ("Threes", 7, 1): {9: 7886, 3: 39105, 0: 27933, 6: 23338, 12: 1559, 15: 170, 21: 2, 18: 7}, + ("Threes", 7, 2): {9: 23110, 6: 31832, 3: 23896, 12: 10218, 0: 7794, 15: 2739, 18: 392, 21: 19}, + ("Threes", 7, 3): {3: 11098, 9: 29316, 6: 24140, 0: 2138, 12: 21386, 15: 9413, 18: 2263, 21: 246}, + ("Threes", 7, 4): {9: 26233, 12: 28244, 18: 6438, 15: 18118, 3: 4648, 6: 14737, 0: 590, 21: 992}, + ("Threes", 7, 5): {15: 26078, 9: 19439, 12: 28977, 18: 12957, 6: 7953, 21: 2655, 3: 1777, 0: 164}, + ("Threes", 7, 6): {15: 30535, 18: 20208, 12: 25793, 9: 13025, 6: 3938, 21: 5783, 3: 664, 0: 54}, + ("Threes", 7, 7): {15: 31859, 21: 10191, 9: 7941, 12: 20571, 18: 27374, 6: 1790, 3: 267, 0: 7}, + ("Threes", 7, 8): {15: 30313, 18: 33133, 21: 15727, 12: 15117, 9: 4747, 6: 854, 3: 104, 0: 5}, + ("Threes", 8, 0): {0: 100000}, + ("Threes", 8, 1): {3: 37232, 9: 10377, 0: 23337, 6: 25968, 12: 2630, 15: 423, 18: 31, 21: 2}, + ("Threes", 8, 2): {6: 29232, 3: 18930, 9: 26016, 12: 14399, 15: 4847, 0: 5310, 18: 1124, 21: 138, 24: 4}, + ("Threes", 8, 3): {12: 24703, 18: 5285, 9: 27141, 6: 18754, 15: 14251, 21: 1111, 0: 1328, 3: 7328, 24: 99}, + ("Threes", 8, 4): {15: 23402, 9: 20607, 12: 26898, 18: 12452, 21: 3839, 6: 9554, 3: 2428, 0: 291, 24: 529}, + ("Threes", 8, 5): {18: 20616, 15: 27931, 6: 4240, 21: 8743, 12: 23248, 3: 838, 9: 12608, 24: 1709, 0: 67}, + ("Threes", 8, 6): {18: 27276, 9: 6890, 12: 17302, 21: 15571, 24: 3812, 6: 1657, 15: 27235, 3: 243, 0: 14}, + ("Threes", 8, 7): {21: 22546, 15: 23682, 18: 30401, 12: 11580, 24: 7444, 9: 3547, 6: 718, 3: 76, 0: 6}, + ("Threes", 8, 8): {18: 30657, 15: 18980, 12: 7211, 9: 1748, 24: 12037, 21: 29074, 6: 273, 3: 19, 0: 1}, + ("Fours", 0, 0): {0: 100000}, + ("Fours", 0, 1): {0: 100000}, + ("Fours", 0, 2): {0: 100000}, + ("Fours", 0, 3): {0: 100000}, + ("Fours", 0, 4): {0: 100000}, + ("Fours", 0, 5): {0: 100000}, + ("Fours", 0, 6): {0: 100000}, + ("Fours", 0, 7): {0: 100000}, + ("Fours", 0, 8): {0: 100000}, + ("Fours", 1, 0): {0: 100000}, + ("Fours", 1, 1): {0: 83260, 4: 16740}, + ("Fours", 1, 2): {0: 69514, 4: 30486}, + ("Fours", 1, 3): {4: 41983, 0: 58017}, + ("Fours", 1, 4): {4: 51611, 0: 48389}, + ("Fours", 1, 5): {0: 40201, 4: 59799}, + ("Fours", 1, 6): {4: 66504, 0: 33496}, + ("Fours", 1, 7): {4: 71948, 0: 28052}, + ("Fours", 1, 8): {4: 76569, 0: 23431}, + ("Fours", 2, 0): {0: 100000}, + ("Fours", 2, 1): {0: 69379, 4: 27817, 8: 2804}, + ("Fours", 2, 2): {0: 48538, 4: 42240, 8: 9222}, + ("Fours", 2, 3): {4: 48555, 8: 17689, 0: 33756}, + ("Fours", 2, 4): {4: 49916, 8: 27014, 0: 23070}, + ("Fours", 2, 5): {8: 35769, 4: 48009, 0: 16222}, + ("Fours", 2, 6): {4: 44400, 8: 44475, 0: 11125}, + ("Fours", 2, 7): {8: 51865, 4: 40216, 0: 7919}, + ("Fours", 2, 8): {4: 35757, 8: 58895, 0: 5348}, + ("Fours", 3, 0): {0: 100000}, + ("Fours", 3, 1): {4: 34622, 0: 57914, 8: 7022, 12: 442}, + ("Fours", 3, 2): {4: 44110, 0: 33621, 8: 19466, 12: 2803}, + ("Fours", 3, 3): {8: 30898, 4: 42425, 0: 19153, 12: 7524}, + ("Fours", 3, 4): {12: 13840, 8: 39024, 4: 36011, 0: 11125}, + ("Fours", 3, 5): {12: 21325, 0: 6367, 8: 43192, 4: 29116}, + ("Fours", 3, 6): {4: 22457, 12: 29423, 8: 44477, 0: 3643}, + ("Fours", 3, 7): {8: 43275, 12: 37745, 4: 16802, 0: 2178}, + ("Fours", 3, 8): {8: 41132, 12: 45312, 4: 12301, 0: 1255}, + ("Fours", 4, 0): {0: 100000}, + ("Fours", 4, 1): {0: 48465, 4: 38398, 12: 1570, 8: 11492, 16: 75}, + ("Fours", 4, 2): {8: 27073, 4: 40911, 0: 23296, 12: 7871, 16: 849}, + ("Fours", 4, 3): {12: 17222, 8: 35337, 0: 11200, 4: 33191, 16: 3050}, + ("Fours", 4, 4): {8: 37441, 4: 23066, 12: 26861, 0: 5447, 16: 7185}, + ("Fours", 4, 5): {0: 2533, 8: 34781, 12: 34222, 4: 15668, 16: 12796}, + ("Fours", 4, 6): {0: 1314, 8: 29850, 12: 39425, 16: 19410, 4: 10001}, + ("Fours", 4, 7): {12: 41917, 4: 6231, 0: 592, 8: 24250, 16: 27010}, + ("Fours", 4, 8): {16: 34777, 8: 19168, 12: 41866, 4: 3887, 0: 302}, + ("Fours", 5, 0): {0: 100000}, + ("Fours", 5, 1): {4: 40127, 0: 40215, 8: 16028, 12: 3303, 16: 319, 20: 8}, + ("Fours", 5, 2): {8: 31158, 0: 15946, 12: 13998, 4: 35579, 16: 3049, 20: 270}, + ("Fours", 5, 3): {8: 34575, 20: 1347, 12: 24783, 4: 23705, 0: 6479, 16: 9111}, + ("Fours", 5, 4): {8: 30079, 12: 32428, 4: 13889, 20: 3706, 16: 17263, 0: 2635}, + ("Fours", 5, 5): {16: 25803, 8: 23332, 12: 34254, 4: 7756, 20: 7695, 0: 1160}, + ("Fours", 5, 6): {20: 13131, 12: 32910, 16: 32752, 8: 16525, 4: 4248, 0: 434}, + ("Fours", 5, 7): {12: 29123, 20: 19471, 16: 37701, 8: 11414, 4: 2122, 0: 169}, + ("Fours", 5, 8): {16: 40144, 8: 7340, 20: 26442, 12: 24807, 4: 1192, 0: 75}, + ("Fours", 6, 0): {0: 100000}, + ("Fours", 6, 1): {4: 39856, 8: 20225, 0: 33632, 12: 5348, 16: 865, 20: 72, 24: 2}, + ("Fours", 6, 2): {4: 29824, 16: 6225, 8: 32381, 0: 11175, 12: 19179, 24: 100, 20: 1116}, + ("Fours", 6, 3): {12: 29071, 4: 16329, 8: 29939, 16: 15808, 0: 3698, 20: 4594, 24: 561}, + ("Fours", 6, 4): {24: 1875, 12: 31107, 16: 25281, 8: 21748, 20: 10816, 4: 7889, 0: 1284}, + ("Fours", 6, 5): {12: 27817, 24: 4501, 16: 31233, 20: 18386, 4: 3792, 8: 13809, 0: 462}, + ("Fours", 6, 6): {24: 8835, 20: 26192, 16: 32690, 12: 22156, 8: 8344, 4: 1636, 0: 147}, + ("Fours", 6, 7): {24: 14130, 12: 16285, 20: 32639, 16: 31490, 8: 4689, 4: 733, 0: 34}, + ("Fours", 6, 8): {24: 20510, 12: 11388, 16: 27841, 20: 37380, 8: 2524, 4: 349, 0: 8}, + ("Fours", 7, 0): {0: 100000}, + ("Fours", 7, 1): {4: 39289, 0: 27821, 12: 7807, 8: 23327, 16: 1564, 20: 181, 24: 11}, + ("Fours", 7, 2): {16: 10162, 12: 23169, 4: 24026, 8: 31633, 0: 7950, 20: 2637, 24: 403, 28: 20}, + ("Fours", 7, 3): {8: 24107, 12: 29411, 20: 9251, 0: 2194, 16: 21390, 4: 11153, 24: 2231, 28: 263}, + ("Fours", 7, 4): {8: 14788, 16: 28118, 20: 18174, 12: 26330, 24: 6535, 4: 4503, 28: 992, 0: 560}, + ("Fours", 7, 5): {16: 29003, 20: 26113, 12: 19425, 24: 12972, 8: 7862, 28: 2767, 4: 1687, 0: 171}, + ("Fours", 7, 6): {12: 12863, 24: 20147, 20: 30724, 16: 25831, 28: 5860, 8: 3896, 4: 630, 0: 49}, + ("Fours", 7, 7): {28: 10189, 16: 20524, 12: 7978, 20: 31843, 24: 27368, 8: 1846, 4: 239, 0: 13}, + ("Fours", 7, 8): {28: 15645, 24: 33428, 16: 15198, 20: 30153, 12: 4712, 8: 776, 4: 88}, + ("Fours", 8, 0): {0: 100000}, + ("Fours", 8, 1): {0: 23275, 12: 10570, 4: 37161, 8: 25964, 20: 402, 16: 2594, 24: 33, 28: 1}, + ("Fours", 8, 2): {8: 29259, 0: 5421, 20: 4887, 12: 25812, 4: 19014, 16: 14387, 24: 1084, 28: 131, 32: 5}, + ("Fours", 8, 3): {24: 5162, 16: 25138, 8: 18330, 12: 27186, 4: 7349, 20: 14371, 0: 1277, 28: 1090, 32: 97}, + ("Fours", 8, 4): {16: 26960, 28: 3827, 12: 20282, 24: 12927, 20: 23292, 8: 9366, 4: 2563, 0: 289, 32: 494}, + ("Fours", 8, 5): {24: 20767, 20: 27754, 16: 23588, 12: 12492, 8: 4214, 28: 8693, 4: 776, 0: 59, 32: 1657}, + ("Fours", 8, 6): {28: 15457, 20: 27398, 24: 27074, 12: 6892, 16: 17296, 8: 1771, 32: 3843, 4: 248, 0: 21}, + ("Fours", 8, 7): {24: 30628, 28: 22590, 12: 3649, 20: 23737, 16: 11420, 32: 7231, 8: 648, 4: 95, 0: 2}, + ("Fours", 8, 8): {20: 18630, 24: 31109, 12: 1683, 28: 29548, 32: 11743, 16: 7021, 8: 249, 4: 16, 0: 1}, + ("Fives", 0, 0): {0: 100000}, + ("Fives", 0, 1): {0: 100000}, + ("Fives", 0, 2): {0: 100000}, + ("Fives", 0, 3): {0: 100000}, + ("Fives", 0, 4): {0: 100000}, + ("Fives", 0, 5): {0: 100000}, + ("Fives", 0, 6): {0: 100000}, + ("Fives", 0, 7): {0: 100000}, + ("Fives", 0, 8): {0: 100000}, + ("Fives", 1, 0): {0: 100000}, + ("Fives", 1, 1): {5: 16662, 0: 83338}, + ("Fives", 1, 2): {0: 69499, 5: 30501}, + ("Fives", 1, 3): {5: 42201, 0: 57799}, + ("Fives", 1, 4): {5: 51689, 0: 48311}, + ("Fives", 1, 5): {5: 59916, 0: 40084}, + ("Fives", 1, 6): {0: 33440, 5: 66560}, + ("Fives", 1, 7): {0: 27730, 5: 72270}, + ("Fives", 1, 8): {5: 76790, 0: 23210}, + ("Fives", 2, 0): {0: 100000}, + ("Fives", 2, 1): {5: 27864, 0: 69299, 10: 2837}, + ("Fives", 2, 2): {0: 48156, 5: 42526, 10: 9318}, + ("Fives", 2, 3): {0: 33225, 5: 49153, 10: 17622}, + ("Fives", 2, 4): {0: 23218, 5: 50075, 10: 26707}, + ("Fives", 2, 5): {5: 48313, 0: 15939, 10: 35748}, + ("Fives", 2, 6): {5: 44324, 10: 44336, 0: 11340}, + ("Fives", 2, 7): {10: 51790, 5: 40388, 0: 7822}, + ("Fives", 2, 8): {10: 58978, 5: 35636, 0: 5386}, + ("Fives", 3, 0): {0: 100000}, + ("Fives", 3, 1): {5: 34541, 0: 58034, 10: 6946, 15: 479}, + ("Fives", 3, 2): {10: 19403, 15: 2904, 0: 33466, 5: 44227}, + ("Fives", 3, 3): {0: 19231, 10: 30794, 5: 42483, 15: 7492}, + ("Fives", 3, 4): {5: 36192, 10: 38673, 15: 13939, 0: 11196}, + ("Fives", 3, 5): {5: 29163, 10: 43014, 15: 21262, 0: 6561}, + ("Fives", 3, 6): {15: 29489, 10: 44611, 5: 22181, 0: 3719}, + ("Fives", 3, 7): {15: 37618, 5: 16817, 10: 43466, 0: 2099}, + ("Fives", 3, 8): {15: 45310, 10: 40936, 5: 12473, 0: 1281}, + ("Fives", 4, 0): {0: 100000}, + ("Fives", 4, 1): {5: 38345, 0: 48377, 10: 11611, 15: 1587, 20: 80}, + ("Fives", 4, 2): {10: 27041, 5: 40940, 0: 23126, 15: 8003, 20: 890}, + ("Fives", 4, 3): {20: 3208, 5: 32597, 15: 17250, 10: 35753, 0: 11192}, + ("Fives", 4, 4): {10: 37379, 5: 23073, 15: 26968, 0: 5362, 20: 7218}, + ("Fives", 4, 5): {15: 34186, 10: 34602, 5: 15662, 20: 12895, 0: 2655}, + ("Fives", 4, 6): {15: 39417, 20: 19500, 5: 9959, 10: 29833, 0: 1291}, + ("Fives", 4, 7): {15: 41779, 20: 27007, 10: 24360, 5: 6231, 0: 623}, + ("Fives", 4, 8): {20: 34729, 15: 41957, 10: 19164, 5: 3837, 0: 313}, + ("Fives", 5, 0): {0: 100000}, + ("Fives", 5, 1): {5: 40561, 10: 16029, 0: 39911, 15: 3164, 20: 322, 25: 13}, + ("Fives", 5, 2): {10: 31246, 0: 16178, 5: 35517, 15: 13793, 20: 3019, 25: 247}, + ("Fives", 5, 3): {20: 8948, 5: 23716, 0: 6526, 10: 34430, 15: 25017, 25: 1363}, + ("Fives", 5, 4): {15: 32247, 10: 30133, 20: 17219, 5: 13975, 25: 3811, 0: 2615}, + ("Fives", 5, 5): {10: 23203, 15: 34489, 20: 25757, 5: 7876, 25: 7612, 0: 1063}, + ("Fives", 5, 6): {15: 32855, 20: 32891, 10: 16696, 25: 13038, 5: 4091, 0: 429}, + ("Fives", 5, 7): {15: 29416, 20: 37778, 10: 11298, 25: 19138, 5: 2211, 0: 159}, + ("Fives", 5, 8): {15: 24456, 10: 7453, 25: 26297, 20: 40615, 5: 1127, 0: 52}, + ("Fives", 6, 0): {0: 100000}, + ("Fives", 6, 1): {10: 20181, 0: 33476, 5: 40167, 15: 5317, 20: 780, 25: 76, 30: 3}, + ("Fives", 6, 2): {10: 32664, 20: 6194, 5: 29613, 25: 1125, 15: 19004, 0: 11322, 30: 78}, + ("Fives", 6, 3): {5: 16288, 10: 29770, 20: 15759, 0: 3765, 15: 29233, 25: 4563, 30: 622}, + ("Fives", 6, 4): {10: 21518, 5: 8226, 20: 25160, 15: 31229, 25: 10712, 0: 1201, 30: 1954}, + ("Fives", 6, 5): {20: 30800, 15: 27961, 10: 14005, 25: 18442, 5: 3874, 30: 4485, 0: 433}, + ("Fives", 6, 6): {10: 8354, 20: 32744, 15: 22226, 25: 26341, 5: 1686, 30: 8508, 0: 141}, + ("Fives", 6, 7): {20: 31363, 30: 14151, 25: 32784, 15: 16206, 10: 4724, 5: 730, 0: 42}, + ("Fives", 6, 8): {15: 11279, 20: 28004, 30: 20619, 25: 37178, 10: 2623, 5: 278, 0: 19}, + ("Fives", 7, 0): {0: 100000}, + ("Fives", 7, 1): {10: 23567, 0: 27826, 5: 39154, 20: 1543, 15: 7734, 25: 159, 30: 17}, + ("Fives", 7, 2): {0: 7609, 15: 23214, 5: 24193, 10: 31722, 20: 10140, 25: 2694, 30: 406, 35: 22}, + ("Fives", 7, 3): {15: 29307, 25: 9164, 10: 24443, 5: 11013, 20: 21387, 35: 218, 30: 2206, 0: 2262}, + ("Fives", 7, 4): {30: 6453, 25: 18050, 10: 14761, 20: 28335, 15: 26159, 5: 4583, 0: 618, 35: 1041}, + ("Fives", 7, 5): {30: 12883, 20: 28915, 25: 26000, 15: 19685, 10: 7909, 35: 2718, 5: 1707, 0: 183}, + ("Fives", 7, 6): {25: 30456, 20: 25572, 30: 20695, 15: 13042, 35: 5729, 10: 3836, 5: 618, 0: 52}, + ("Fives", 7, 7): {35: 10115, 30: 27333, 25: 31883, 10: 1852, 20: 20696, 15: 7866, 5: 246, 0: 9}, + ("Fives", 7, 8): {30: 33015, 25: 30298, 20: 15292, 35: 15768, 15: 4700, 5: 92, 10: 829, 0: 6}, + ("Fives", 8, 0): {0: 100000}, + ("Fives", 8, 1): {5: 37259, 0: 23333, 10: 25947, 20: 2598, 15: 10392, 25: 433, 30: 36, 35: 2}, + ("Fives", 8, 2): {10: 29380, 5: 18915, 15: 25994, 20: 14056, 25: 4971, 0: 5425, 30: 1131, 35: 122, 40: 6}, + ("Fives", 8, 3): {20: 24542, 10: 18783, 25: 14322, 15: 27375, 35: 1058, 30: 5252, 5: 7317, 0: 1258, 40: 93}, + ("Fives", 8, 4): {15: 20267, 20: 27158, 25: 23589, 30: 12529, 10: 9383, 5: 2481, 35: 3817, 40: 505, 0: 271}, + ("Fives", 8, 5): {20: 23115, 35: 8917, 25: 27968, 15: 12456, 30: 20704, 10: 4260, 5: 879, 40: 1637, 0: 64}, + ("Fives", 8, 6): {35: 15414, 20: 17201, 15: 6936, 30: 27178, 25: 27484, 40: 3817, 10: 1689, 0: 15, 5: 266}, + ("Fives", 8, 7): {30: 30426, 40: 7470, 35: 22677, 15: 3535, 20: 11429, 25: 23717, 10: 661, 5: 81, 0: 4}, + ("Fives", 8, 8): {35: 29126, 25: 18714, 30: 31084, 20: 7148, 40: 11888, 15: 1779, 5: 21, 10: 239, 0: 1}, + ("Sixes", 0, 0): {0: 100000}, + ("Sixes", 0, 1): {0: 100000}, + ("Sixes", 0, 2): {0: 100000}, + ("Sixes", 0, 3): {0: 100000}, + ("Sixes", 0, 4): {0: 100000}, + ("Sixes", 0, 5): {0: 100000}, + ("Sixes", 0, 6): {0: 100000}, + ("Sixes", 0, 7): {0: 100000}, + ("Sixes", 0, 8): {0: 100000}, + ("Sixes", 1, 0): {0: 100000}, + ("Sixes", 1, 1): {0: 83168, 6: 16832}, + ("Sixes", 1, 2): {0: 69548, 6: 30452}, + ("Sixes", 1, 3): {0: 57697, 6: 42303}, + ("Sixes", 1, 4): {6: 51957, 0: 48043}, + ("Sixes", 1, 5): {0: 39912, 6: 60088}, + ("Sixes", 1, 6): {6: 66501, 0: 33499}, + ("Sixes", 1, 7): {0: 28251, 6: 71749}, + ("Sixes", 1, 8): {6: 76794, 0: 23206}, + ("Sixes", 2, 0): {0: 100000}, + ("Sixes", 2, 1): {0: 69463, 6: 27651, 12: 2886}, + ("Sixes", 2, 2): {6: 42794, 12: 9310, 0: 47896}, + ("Sixes", 2, 3): {6: 48757, 0: 33394, 12: 17849}, + ("Sixes", 2, 4): {6: 49554, 12: 26894, 0: 23552}, + ("Sixes", 2, 5): {6: 48098, 12: 35812, 0: 16090}, + ("Sixes", 2, 6): {12: 44094, 6: 44833, 0: 11073}, + ("Sixes", 2, 7): {0: 7737, 6: 40480, 12: 51783}, + ("Sixes", 2, 8): {6: 35672, 12: 58949, 0: 5379}, + ("Sixes", 3, 0): {0: 100000}, + ("Sixes", 3, 1): {6: 34818, 12: 6994, 0: 57718, 18: 470}, + ("Sixes", 3, 2): {6: 44328, 12: 19159, 0: 33610, 18: 2903}, + ("Sixes", 3, 3): {6: 42246, 18: 7436, 0: 19366, 12: 30952}, + ("Sixes", 3, 4): {6: 36281, 0: 11144, 12: 38817, 18: 13758}, + ("Sixes", 3, 5): {12: 43114, 18: 21581, 0: 6414, 6: 28891}, + ("Sixes", 3, 6): {12: 44318, 6: 22394, 18: 29418, 0: 3870}, + ("Sixes", 3, 7): {18: 37522, 12: 43487, 6: 16803, 0: 2188}, + ("Sixes", 3, 8): {18: 45208, 6: 12421, 12: 41082, 0: 1289}, + ("Sixes", 4, 0): {0: 100000}, + ("Sixes", 4, 1): {0: 48197, 6: 38521, 12: 11677, 18: 1516, 24: 89}, + ("Sixes", 4, 2): {6: 41179, 0: 23155, 12: 26935, 18: 7839, 24: 892}, + ("Sixes", 4, 3): {6: 32609, 18: 17390, 0: 11256, 12: 35588, 24: 3157}, + ("Sixes", 4, 4): {12: 37209, 0: 5324, 6: 23265, 18: 26929, 24: 7273}, + ("Sixes", 4, 5): {18: 34476, 6: 15488, 12: 34685, 24: 12693, 0: 2658}, + ("Sixes", 4, 6): {18: 39379, 6: 9997, 12: 29855, 24: 19487, 0: 1282}, + ("Sixes", 4, 7): {18: 41935, 24: 26879, 12: 24396, 6: 6202, 0: 588}, + ("Sixes", 4, 8): {6: 3863, 18: 42180, 12: 19042, 24: 34598, 0: 317}, + ("Sixes", 5, 0): {0: 100000}, + ("Sixes", 5, 1): {0: 40393, 6: 39904, 12: 16206, 18: 3173, 24: 311, 30: 13}, + ("Sixes", 5, 2): {0: 16202, 12: 31241, 6: 35664, 18: 13612, 24: 3017, 30: 264}, + ("Sixes", 5, 3): {18: 25020, 12: 34585, 6: 23539, 0: 6456, 30: 1318, 24: 9082}, + ("Sixes", 5, 4): {12: 30355, 24: 17115, 6: 13980, 18: 32198, 30: 3771, 0: 2581}, + ("Sixes", 5, 5): {18: 34716, 30: 7759, 24: 25568, 6: 7775, 12: 23063, 0: 1119}, + ("Sixes", 5, 6): {24: 32829, 12: 16724, 30: 13092, 18: 32792, 6: 4171, 0: 392}, + ("Sixes", 5, 7): {24: 37560, 18: 29190, 30: 19426, 12: 11509, 6: 2118, 0: 197}, + ("Sixes", 5, 8): {30: 26656, 24: 40134, 12: 7404, 18: 24560, 6: 1176, 0: 70}, + ("Sixes", 6, 0): {0: 100000}, + ("Sixes", 6, 1): {12: 20198, 0: 33316, 6: 40218, 18: 5373, 24: 839, 30: 54, 36: 2}, + ("Sixes", 6, 2): {18: 19196, 6: 29444, 12: 32590, 0: 11256, 24: 6278, 36: 84, 30: 1152}, + ("Sixes", 6, 3): {18: 29107, 12: 29873, 36: 579, 24: 15863, 6: 16266, 0: 3787, 30: 4525}, + ("Sixes", 6, 4): {0: 1286, 12: 21653, 18: 31264, 6: 8066, 24: 25039, 36: 1913, 30: 10779}, + ("Sixes", 6, 5): {24: 30919, 18: 27705, 12: 13962, 30: 18670, 36: 4554, 6: 3777, 0: 413}, + ("Sixes", 6, 6): {24: 32923, 30: 26086, 6: 1658, 18: 22320, 36: 8485, 12: 8382, 0: 146}, + ("Sixes", 6, 7): {18: 16286, 30: 32487, 36: 14138, 24: 31577, 12: 4698, 6: 763, 0: 51}, + ("Sixes", 6, 8): {36: 20392, 24: 28064, 30: 37212, 18: 11446, 12: 2558, 6: 306, 0: 22}, + ("Sixes", 7, 0): {0: 100000}, + ("Sixes", 7, 1): {24: 1548, 12: 23499, 6: 38984, 0: 27852, 18: 7935, 30: 171, 36: 11}, + ("Sixes", 7, 2): {12: 31558, 6: 23846, 0: 7883, 18: 23295, 24: 10316, 30: 2667, 36: 405, 42: 30}, + ("Sixes", 7, 3): {6: 10928, 12: 24321, 30: 9209, 36: 2296, 18: 29650, 24: 21177, 0: 2186, 42: 233}, + ("Sixes", 7, 4): {18: 26303, 24: 28335, 30: 18228, 12: 14673, 42: 933, 6: 4459, 36: 6466, 0: 603}, + ("Sixes", 7, 5): {24: 29254, 18: 19381, 36: 12992, 30: 25790, 12: 7879, 6: 1775, 42: 2757, 0: 172}, + ("Sixes", 7, 6): {30: 30698, 18: 13039, 36: 20143, 12: 3864, 24: 25760, 42: 5792, 6: 652, 0: 52}, + ("Sixes", 7, 7): {36: 27546, 24: 20557, 30: 31709, 42: 10074, 18: 8033, 12: 1824, 6: 246, 0: 11}, + ("Sixes", 7, 8): {30: 30259, 36: 33183, 42: 15609, 12: 799, 24: 15419, 18: 4658, 6: 72, 0: 1}, + ("Sixes", 8, 0): {0: 100000}, + ("Sixes", 8, 1): {0: 23220, 12: 25961, 6: 37213, 18: 10483, 24: 2622, 30: 441, 36: 56, 42: 4}, + ("Sixes", 8, 2): {24: 14170, 18: 25777, 12: 29664, 6: 18943, 30: 4965, 0: 5280, 36: 1059, 42: 134, 48: 8}, + ("Sixes", 8, 3): {18: 27277, 30: 14351, 24: 24802, 12: 18757, 6: 7112, 36: 5260, 42: 1085, 0: 1246, 48: 110}, + ("Sixes", 8, 4): {30: 23403, 24: 27146, 36: 12524, 6: 2460, 18: 20247, 12: 9584, 42: 3889, 0: 301, 48: 446}, + ("Sixes", 8, 5): {24: 23471, 30: 27655, 36: 20803, 42: 8841, 18: 12477, 12: 4241, 6: 774, 48: 1653, 0: 85}, + ("Sixes", 8, 6): {24: 17373, 36: 27024, 30: 27347, 12: 1790, 18: 6866, 42: 15394, 48: 3929, 6: 255, 0: 22}, + ("Sixes", 8, 7): {42: 22654, 48: 7273, 30: 23581, 24: 11451, 36: 30772, 18: 3503, 12: 689, 6: 75, 0: 2}, + ("Sixes", 8, 8): {30: 18755, 24: 7116, 36: 31116, 42: 28870, 48: 12131, 18: 1750, 12: 241, 6: 21}, + ("Choice", 0, 0): {0: 100000}, + ("Choice", 0, 1): {0: 100000}, + ("Choice", 0, 2): {0: 100000}, + ("Choice", 0, 3): {0: 100000}, + ("Choice", 0, 4): {0: 100000}, + ("Choice", 0, 5): {0: 100000}, + ("Choice", 0, 6): {0: 100000}, + ("Choice", 0, 7): {0: 100000}, + ("Choice", 0, 8): {0: 100000}, + ("Choice", 1, 0): {0: 100000}, + ("Choice", 1, 1): {1: 16642, 5: 16618, 2: 16673, 6: 16639, 3: 16828, 4: 16600}, + ("Choice", 1, 2): {5: 27898, 4: 11333, 6: 27788, 1: 10921, 2: 11161, 3: 10899}, + ("Choice", 1, 3): {6: 39927, 5: 22740, 3: 9263, 1: 9416, 4: 9338, 2: 9316}, + ("Choice", 1, 4): {6: 49709, 5: 19312, 2: 7715, 1: 7775, 4: 7791, 3: 7698}, + ("Choice", 1, 5): {6: 58421, 2: 6427, 5: 16005, 1: 6390, 3: 6241, 4: 6516}, + ("Choice", 1, 6): {6: 65344, 1: 5313, 3: 5363, 5: 13424, 2: 5200, 4: 5356}, + ("Choice", 1, 7): {6: 71171, 5: 11028, 3: 4321, 4: 4587, 1: 4428, 2: 4465}, + ("Choice", 1, 8): {6: 76004, 1: 3644, 5: 9298, 2: 3648, 4: 3633, 3: 3773}, + ("Choice", 2, 0): {0: 100000}, + ("Choice", 2, 1): { + 7: 16670, + 8: 13823, + 6: 13681, + 9: 11170, + 10: 8384, + 5: 11014, + 4: 8292, + 3: 5647, + 11: 5596, + 12: 2866, + 2: 2857, + }, + ("Choice", 2, 2): { + 8: 13639, + 9: 12220, + 10: 13755, + 5: 4889, + 6: 9840, + 7: 14772, + 12: 7780, + 11: 15622, + 2: 1269, + 3: 2445, + 4: 3769, + }, + ("Choice", 2, 3): { + 12: 16019, + 11: 18510, + 7: 13487, + 10: 12684, + 2: 840, + 8: 12296, + 9: 11489, + 4: 2567, + 3: 1706, + 5: 3532, + 6: 6870, + }, + ("Choice", 2, 4): { + 9: 10694, + 8: 11395, + 11: 19145, + 7: 11794, + 12: 24860, + 10: 11421, + 5: 2349, + 6: 4766, + 3: 1203, + 2: 580, + 4: 1793, + }, + ("Choice", 2, 5): { + 11: 18504, + 9: 9457, + 12: 33919, + 10: 10101, + 7: 10459, + 5: 1683, + 6: 3327, + 8: 9985, + 4: 1282, + 3: 820, + 2: 463, + }, + ("Choice", 2, 6): { + 10: 8640, + 6: 2289, + 8: 8711, + 11: 17310, + 12: 42514, + 7: 9329, + 9: 8343, + 5: 1127, + 4: 897, + 2: 278, + 3: 562, + }, + ("Choice", 2, 7): { + 9: 7474, + 12: 50376, + 8: 7580, + 11: 15801, + 6: 1586, + 7: 7617, + 5: 804, + 10: 7514, + 3: 412, + 4: 631, + 2: 205, + }, + ("Choice", 2, 8): { + 12: 57425, + 7: 6849, + 8: 6457, + 10: 6546, + 5: 551, + 11: 14067, + 6: 1114, + 9: 6208, + 4: 385, + 2: 136, + 3: 262, + }, + ("Choice", 3, 0): {0: 100000}, + ("Choice", 3, 1): { + 14: 6922, + 12: 11648, + 18: 460, + 10: 12552, + 6: 4574, + 15: 4476, + 7: 6986, + 9: 11635, + 13: 9762, + 5: 2727, + 8: 9834, + 11: 12455, + 16: 2778, + 4: 1375, + 17: 1329, + 3: 487, + }, + ("Choice", 3, 2): { + 13: 13398, + 15: 9806, + 17: 6384, + 14: 11409, + 8: 4722, + 12: 13008, + 9: 6436, + 5: 883, + 7: 2555, + 11: 10449, + 16: 8963, + 10: 7981, + 6: 1345, + 3: 113, + 18: 2164, + 4: 384, + }, + ("Choice", 3, 3): { + 8: 3168, + 7: 1551, + 16: 10859, + 12: 10775, + 9: 4651, + 18: 6287, + 15: 10908, + 13: 13633, + 14: 12157, + 6: 816, + 17: 10915, + 11: 7570, + 10: 5921, + 3: 85, + 4: 226, + 5: 478, + }, + ("Choice", 3, 4): { + 9: 3219, + 17: 14452, + 14: 11945, + 11: 5627, + 18: 12299, + 6: 466, + 5: 288, + 13: 13346, + 16: 11330, + 15: 10762, + 12: 8677, + 7: 929, + 10: 4350, + 4: 138, + 8: 2116, + 3: 56, + }, + ("Choice", 3, 5): { + 13: 12249, + 17: 16329, + 16: 11082, + 15: 10586, + 12: 6699, + 10: 3230, + 18: 19447, + 14: 11562, + 9: 2335, + 5: 158, + 8: 1365, + 11: 4057, + 7: 533, + 6: 259, + 4: 90, + 3: 19, + }, + ("Choice", 3, 6): { + 17: 17096, + 14: 10603, + 15: 9701, + 18: 27775, + 13: 11050, + 8: 1005, + 16: 10252, + 11: 2960, + 9: 1634, + 12: 5006, + 7: 306, + 10: 2306, + 6: 147, + 5: 100, + 4: 45, + 3: 14, + }, + ("Choice", 3, 7): { + 13: 9808, + 15: 9022, + 18: 35842, + 14: 9250, + 17: 17010, + 16: 9459, + 9: 1136, + 12: 3692, + 10: 1679, + 11: 2084, + 8: 675, + 6: 82, + 7: 176, + 5: 45, + 4: 30, + 3: 10, + }, + ("Choice", 3, 8): { + 13: 8621, + 18: 43506, + 15: 8108, + 17: 16142, + 11: 1492, + 16: 8392, + 9: 824, + 14: 8389, + 8: 454, + 12: 2698, + 10: 1179, + 5: 32, + 7: 98, + 6: 41, + 3: 5, + 4: 19, + }, + ("Choice", 4, 0): {0: 100000}, + ("Choice", 4, 1): { + 19: 4323, + 14: 11229, + 15: 10673, + 11: 8105, + 10: 6187, + 22: 736, + 9: 4374, + 7: 1574, + 8: 2687, + 20: 2726, + 16: 9725, + 13: 10880, + 12: 9516, + 17: 8088, + 18: 6186, + 24: 68, + 21: 1512, + 6: 723, + 23: 286, + 5: 318, + 4: 84, + }, + ("Choice", 4, 2): { + 21: 6005, + 15: 9539, + 22: 4467, + 18: 11247, + 10: 2080, + 16: 10496, + 11: 3014, + 12: 4393, + 19: 9825, + 20: 7880, + 17: 11349, + 14: 8110, + 9: 1277, + 13: 6253, + 7: 285, + 24: 600, + 23: 2326, + 8: 609, + 5: 56, + 6: 172, + 4: 17, + }, + ("Choice", 4, 3): { + 21: 8490, + 20: 9895, + 23: 5811, + 18: 11621, + 15: 7482, + 22: 7386, + 14: 5818, + 12: 2634, + 19: 11785, + 16: 8383, + 17: 9883, + 13: 4063, + 9: 675, + 10: 1179, + 24: 2507, + 11: 1850, + 8: 309, + 7: 128, + 6: 65, + 5: 28, + 4: 8, + }, + ("Choice", 4, 4): { + 21: 9541, + 16: 6768, + 17: 8169, + 20: 11157, + 18: 10557, + 13: 2517, + 23: 9579, + 19: 12760, + 22: 9333, + 7: 71, + 14: 4089, + 15: 5448, + 24: 6200, + 12: 1624, + 10: 658, + 9: 312, + 11: 1021, + 8: 132, + 5: 19, + 6: 41, + 4: 4, + }, + ("Choice", 4, 5): { + 17: 6331, + 18: 9020, + 20: 11414, + 22: 10446, + 23: 12551, + 9: 180, + 16: 5012, + 21: 10261, + 24: 11379, + 15: 3993, + 12: 924, + 19: 12893, + 14: 2916, + 13: 1575, + 8: 60, + 10: 389, + 11: 599, + 7: 32, + 6: 14, + 5: 10, + 4: 1, + }, + ("Choice", 4, 6): { + 20: 11246, + 21: 10350, + 24: 18222, + 19: 12054, + 23: 14883, + 11: 348, + 17: 4745, + 12: 512, + 18: 7311, + 15: 2911, + 14: 1923, + 16: 3870, + 22: 10306, + 10: 189, + 13: 962, + 9: 104, + 8: 34, + 7: 23, + 4: 1, + 5: 5, + 6: 1, + }, + ("Choice", 4, 7): { + 18: 5654, + 22: 10265, + 23: 15911, + 20: 10646, + 17: 3629, + 15: 2120, + 24: 25318, + 21: 9719, + 16: 2832, + 19: 11206, + 9: 50, + 11: 230, + 12: 333, + 14: 1379, + 8: 18, + 13: 540, + 10: 136, + 7: 10, + 5: 2, + 6: 2, + }, + ("Choice", 4, 8): { + 24: 33185, + 23: 16241, + 20: 9548, + 19: 10211, + 22: 9596, + 21: 9030, + 12: 172, + 18: 4294, + 16: 1967, + 17: 2697, + 15: 1524, + 13: 359, + 10: 73, + 14: 948, + 11: 111, + 9: 32, + 8: 7, + 7: 2, + 5: 2, + 6: 1, + }, + ("Choice", 5, 0): {0: 100000}, + ("Choice", 5, 1): { + 21: 7039, + 16: 9529, + 18: 9956, + 14: 6758, + 13: 5372, + 17: 10211, + 15: 8305, + 12: 3976, + 24: 2664, + 20: 8205, + 23: 3986, + 19: 9571, + 25: 1646, + 22: 5328, + 11: 2671, + 27: 430, + 10: 1646, + 9: 866, + 26: 872, + 6: 74, + 28: 189, + 7: 195, + 8: 435, + 29: 57, + 30: 14, + 5: 5, + }, + ("Choice", 5, 2): { + 16: 4608, + 24: 8226, + 21: 9902, + 27: 3308, + 19: 8702, + 20: 9600, + 17: 5788, + 26: 4778, + 18: 7330, + 28: 1996, + 12: 891, + 25: 6329, + 22: 10013, + 13: 1430, + 23: 9510, + 15: 3317, + 14: 2286, + 29: 837, + 11: 486, + 9: 138, + 10: 271, + 7: 22, + 30: 172, + 8: 53, + 5: 1, + 6: 6, + }, + ("Choice", 5, 3): { + 22: 9536, + 27: 5769, + 16: 2672, + 23: 10122, + 24: 10309, + 25: 9165, + 21: 8990, + 19: 6481, + 28: 4603, + 15: 1876, + 20: 8079, + 13: 672, + 29: 2846, + 26: 7319, + 18: 4821, + 14: 1120, + 17: 3768, + 30: 1011, + 12: 402, + 9: 63, + 11: 218, + 10: 118, + 8: 24, + 6: 7, + 7: 9, + }, + ("Choice", 5, 4): { + 27: 7903, + 21: 7298, + 26: 9341, + 16: 1649, + 18: 3083, + 23: 9471, + 24: 10886, + 20: 6124, + 22: 8263, + 30: 3111, + 28: 7076, + 25: 11012, + 19: 4294, + 15: 1052, + 29: 5839, + 17: 2215, + 10: 57, + 13: 387, + 14: 595, + 12: 189, + 11: 115, + 9: 21, + 7: 7, + 8: 10, + 6: 1, + 5: 1, + }, + ("Choice", 5, 5): { + 25: 12129, + 23: 7952, + 20: 4533, + 29: 9384, + 17: 1431, + 15: 556, + 28: 8745, + 21: 5662, + 27: 9106, + 26: 10402, + 24: 10206, + 18: 1938, + 22: 6727, + 19: 2991, + 30: 6731, + 16: 897, + 13: 170, + 14: 262, + 12: 96, + 11: 43, + 8: 3, + 9: 9, + 10: 22, + 7: 4, + 6: 1, + }, + ("Choice", 5, 6): { + 29: 11896, + 30: 11798, + 25: 12335, + 28: 9678, + 27: 9839, + 24: 9077, + 26: 11056, + 23: 6481, + 20: 3055, + 21: 4282, + 15: 298, + 22: 5378, + 19: 1921, + 16: 542, + 14: 166, + 18: 1217, + 13: 81, + 17: 810, + 12: 45, + 10: 13, + 11: 24, + 9: 5, + 7: 1, + 8: 2, + }, + ("Choice", 5, 7): { + 29: 14323, + 24: 7418, + 25: 11791, + 27: 9773, + 28: 10189, + 20: 2297, + 30: 18039, + 26: 10837, + 16: 301, + 18: 676, + 23: 5083, + 17: 498, + 22: 4016, + 21: 3251, + 19: 1172, + 15: 180, + 14: 74, + 11: 5, + 12: 26, + 13: 43, + 10: 4, + 8: 2, + 9: 2, + }, + ("Choice", 5, 8): { + 17: 299, + 28: 9897, + 22: 2979, + 24: 5927, + 30: 25220, + 23: 3761, + 26: 10403, + 29: 15421, + 25: 11074, + 27: 9715, + 21: 2281, + 20: 1533, + 18: 431, + 13: 22, + 15: 86, + 16: 167, + 19: 736, + 14: 35, + 12: 4, + 11: 6, + 10: 2, + 9: 1, + }, + ("Choice", 6, 0): {0: 100000}, + ("Choice", 6, 1): { + 26: 4860, + 17: 6178, + 19: 8212, + 32: 256, + 22: 9220, + 25: 6226, + 14: 2489, + 24: 7379, + 13: 1658, + 27: 3548, + 23: 8405, + 18: 7257, + 31: 508, + 20: 8945, + 29: 1608, + 16: 4809, + 11: 532, + 21: 9367, + 15: 3502, + 28: 2495, + 30: 938, + 10: 282, + 12: 962, + 34: 53, + 33: 121, + 8: 49, + 9: 114, + 7: 15, + 35: 9, + 36: 2, + 6: 1, + }, + ("Choice", 6, 2): { + 22: 6866, + 25: 9290, + 18: 2440, + 24: 8800, + 28: 7991, + 30: 5310, + 27: 8618, + 23: 7807, + 20: 4423, + 26: 9222, + 32: 2553, + 29: 6823, + 21: 5609, + 34: 767, + 19: 3344, + 17: 1733, + 31: 3853, + 16: 1159, + 13: 227, + 15: 686, + 9: 12, + 12: 113, + 33: 1577, + 14: 387, + 36: 47, + 10: 21, + 35: 264, + 11: 52, + 8: 6, + }, + ("Choice", 6, 3): { + 30: 8077, + 16: 498, + 25: 7982, + 32: 5102, + 19: 1728, + 26: 8870, + 23: 5606, + 28: 9118, + 22: 4620, + 29: 9042, + 24: 6840, + 20: 2544, + 31: 6647, + 33: 3768, + 35: 1364, + 27: 9225, + 34: 2548, + 21: 3452, + 17: 833, + 18: 1190, + 15: 259, + 36: 381, + 14: 172, + 13: 66, + 12: 36, + 11: 16, + 9: 2, + 10: 9, + 6: 1, + 8: 3, + 7: 1, + }, + ("Choice", 6, 4): { + 25: 6167, + 30: 9858, + 29: 9441, + 32: 7395, + 35: 3606, + 28: 8910, + 31: 9026, + 27: 8452, + 36: 1528, + 22: 2782, + 26: 7683, + 33: 5996, + 20: 1380, + 24: 4848, + 34: 4876, + 21: 2028, + 19: 913, + 23: 3755, + 16: 190, + 18: 570, + 9: 3, + 13: 42, + 15: 114, + 17: 345, + 14: 65, + 11: 7, + 12: 16, + 10: 4, + }, + ("Choice", 6, 5): { + 35: 6320, + 25: 4419, + 27: 6891, + 30: 10288, + 29: 8850, + 31: 11006, + 32: 9067, + 23: 2479, + 33: 7800, + 24: 3379, + 21: 1169, + 34: 7012, + 28: 7872, + 26: 5900, + 22: 1736, + 36: 4024, + 19: 463, + 17: 158, + 20: 719, + 18: 283, + 10: 1, + 13: 10, + 16: 84, + 14: 19, + 12: 5, + 15: 44, + 11: 2, + }, + ("Choice", 6, 6): { + 30: 9632, + 35: 9505, + 34: 8614, + 29: 7718, + 33: 9115, + 36: 7767, + 31: 11682, + 28: 6555, + 26: 4339, + 27: 5474, + 32: 10420, + 21: 670, + 15: 26, + 25: 3023, + 24: 2068, + 18: 125, + 23: 1491, + 17: 76, + 22: 1051, + 16: 38, + 20: 384, + 19: 214, + 14: 10, + 13: 3, + }, + ("Choice", 6, 7): { + 36: 12922, + 30: 8579, + 26: 3251, + 33: 9746, + 32: 10723, + 34: 9580, + 27: 4378, + 31: 11844, + 35: 12063, + 25: 1996, + 23: 890, + 29: 6253, + 28: 5095, + 24: 1320, + 21: 333, + 19: 111, + 22: 593, + 20: 190, + 15: 6, + 18: 68, + 17: 29, + 13: 6, + 14: 2, + 16: 21, + 12: 1, + }, + ("Choice", 6, 8): { + 32: 10601, + 27: 3220, + 36: 18975, + 29: 4925, + 31: 11529, + 28: 4004, + 33: 9674, + 35: 14109, + 30: 7305, + 34: 9888, + 26: 2320, + 23: 583, + 22: 366, + 24: 803, + 25: 1291, + 20: 84, + 21: 197, + 17: 12, + 19: 69, + 14: 2, + 15: 4, + 16: 5, + 18: 31, + 13: 2, + 12: 1, + }, + ("Choice", 7, 0): {0: 100000}, + ("Choice", 7, 1): { + 25: 8584, + 29: 5372, + 31: 3311, + 22: 7434, + 30: 4364, + 32: 2300, + 26: 8246, + 35: 620, + 20: 5480, + 27: 7412, + 28: 6528, + 17: 2350, + 15: 1013, + 23: 8119, + 21: 6693, + 18: 3206, + 19: 4340, + 16: 1531, + 24: 8658, + 14: 645, + 36: 331, + 13: 303, + 33: 1609, + 37: 144, + 34: 1003, + 38: 75, + 12: 182, + 40: 7, + 11: 68, + 10: 31, + 9: 5, + 39: 31, + 41: 2, + 8: 2, + 7: 1, + }, + ("Choice", 7, 2): { + 24: 4282, + 27: 7379, + 32: 7574, + 23: 3300, + 31: 8185, + 28: 8075, + 33: 6776, + 34: 5580, + 25: 5385, + 40: 295, + 22: 2549, + 19: 869, + 30: 8645, + 36: 3021, + 20: 1291, + 26: 6611, + 29: 8544, + 39: 723, + 35: 4362, + 17: 312, + 38: 1338, + 37: 2072, + 21: 1820, + 16: 162, + 18: 535, + 15: 117, + 13: 23, + 41: 96, + 14: 48, + 12: 13, + 11: 3, + 10: 4, + 42: 11, + }, + ("Choice", 7, 3): { + 20: 512, + 32: 8692, + 38: 3242, + 26: 4072, + 35: 7062, + 27: 5195, + 29: 7128, + 31: 8536, + 33: 8367, + 25: 3166, + 34: 7897, + 40: 1429, + 37: 4709, + 28: 6052, + 23: 1757, + 39: 2296, + 30: 7918, + 36: 6068, + 24: 2399, + 18: 216, + 22: 1180, + 41: 650, + 21: 772, + 19: 332, + 42: 142, + 16: 74, + 17: 84, + 15: 22, + 14: 17, + 13: 10, + 11: 2, + 10: 1, + 12: 1, + }, + ("Choice", 7, 4): { + 37: 7340, + 32: 8315, + 40: 3283, + 34: 8797, + 27: 3286, + 39: 4403, + 36: 8345, + 35: 8640, + 33: 8544, + 41: 2041, + 29: 5212, + 30: 6351, + 28: 4189, + 24: 1174, + 26: 2450, + 38: 5585, + 31: 7270, + 25: 1741, + 22: 552, + 23: 853, + 42: 774, + 21: 364, + 20: 213, + 18: 63, + 19: 137, + 15: 12, + 16: 24, + 17: 37, + 14: 4, + 13: 1, + }, + ("Choice", 7, 5): { + 34: 8605, + 35: 9013, + 42: 2216, + 40: 5376, + 38: 7940, + 32: 6951, + 36: 9807, + 37: 9314, + 41: 4370, + 30: 4537, + 33: 7741, + 29: 3538, + 26: 1374, + 39: 6342, + 31: 5755, + 27: 1997, + 25: 911, + 28: 2619, + 21: 149, + 23: 426, + 22: 233, + 24: 591, + 19: 51, + 20: 86, + 17: 19, + 15: 5, + 18: 25, + 12: 1, + 16: 6, + 14: 1, + 13: 1, + }, + ("Choice", 7, 6): { + 36: 9866, + 40: 7308, + 34: 7593, + 39: 7997, + 41: 7152, + 32: 5519, + 35: 8456, + 31: 4130, + 42: 4911, + 30: 3023, + 33: 6703, + 37: 10964, + 29: 2381, + 19: 21, + 38: 9214, + 27: 1160, + 28: 1666, + 24: 330, + 25: 496, + 26: 717, + 23: 188, + 21: 63, + 20: 27, + 22: 99, + 18: 6, + 17: 5, + 16: 3, + 14: 1, + 15: 1, + }, + ("Choice", 7, 7): { + 36: 9373, + 41: 10070, + 39: 9031, + 31: 2880, + 35: 7249, + 32: 4085, + 40: 8781, + 33: 5339, + 42: 9078, + 30: 1983, + 37: 11510, + 34: 6308, + 38: 10233, + 28: 1034, + 26: 398, + 29: 1440, + 27: 609, + 20: 21, + 25: 258, + 24: 162, + 23: 84, + 22: 43, + 17: 2, + 18: 1, + 21: 17, + 19: 10, + 16: 1, + }, + ("Choice", 7, 8): { + 36: 8240, + 38: 10538, + 35: 5945, + 40: 9402, + 42: 14556, + 39: 9681, + 37: 11908, + 41: 12225, + 30: 1277, + 33: 3997, + 34: 4959, + 32: 3072, + 29: 962, + 31: 1838, + 20: 7, + 28: 595, + 25: 116, + 21: 12, + 26: 189, + 27: 351, + 24: 67, + 23: 42, + 22: 17, + 14: 1, + 19: 2, + 17: 1, + }, + ("Choice", 8, 0): {0: 100000}, + ("Choice", 8, 1): { + 37: 1519, + 30: 7423, + 36: 2152, + 24: 5910, + 32: 5875, + 29: 7997, + 28: 8093, + 23: 4938, + 25: 6829, + 33: 4822, + 22: 3783, + 21: 3014, + 34: 3978, + 20: 2288, + 18: 961, + 27: 7879, + 38: 1040, + 26: 7482, + 31: 6835, + 19: 1530, + 39: 601, + 42: 99, + 17: 592, + 15: 215, + 41: 205, + 35: 2971, + 16: 353, + 13: 52, + 40: 344, + 14: 99, + 43: 54, + 12: 22, + 45: 10, + 44: 23, + 11: 8, + 10: 3, + 46: 1, + }, + ("Choice", 8, 2): { + 36: 7415, + 29: 5278, + 32: 7556, + 35: 7836, + 40: 3569, + 41: 2514, + 25: 1878, + 30: 6157, + 39: 4551, + 38: 5614, + 34: 7996, + 33: 8107, + 31: 6977, + 26: 2602, + 43: 1084, + 28: 4293, + 37: 6440, + 24: 1433, + 27: 3436, + 23: 997, + 20: 248, + 42: 1681, + 19: 136, + 44: 579, + 45: 279, + 46: 97, + 21: 412, + 16: 29, + 18: 82, + 22: 614, + 47: 33, + 17: 44, + 48: 6, + 14: 6, + 11: 1, + 15: 14, + 13: 5, + 12: 1, + }, + ("Choice", 8, 3): { + 36: 8217, + 25: 833, + 33: 6427, + 32: 5591, + 34: 7101, + 23: 354, + 37: 8047, + 42: 4148, + 41: 5414, + 38: 7791, + 35: 7685, + 46: 720, + 39: 7085, + 28: 2231, + 43: 2992, + 40: 6337, + 31: 4589, + 30: 3867, + 44: 2012, + 29: 3038, + 27: 1654, + 26: 1176, + 24: 575, + 45: 1291, + 22: 203, + 20: 77, + 47: 289, + 18: 22, + 21: 112, + 48: 57, + 12: 1, + 17: 13, + 16: 8, + 19: 40, + 15: 1, + 14: 1, + 13: 1, + }, + ("Choice", 8, 4): { + 35: 6237, + 34: 5503, + 33: 4479, + 39: 8280, + 41: 7615, + 37: 7892, + 45: 3075, + 44: 4161, + 26: 495, + 32: 3646, + 40: 7908, + 29: 1554, + 47: 1209, + 31: 2802, + 27: 803, + 38: 8522, + 30: 2128, + 42: 6672, + 36: 7186, + 43: 5546, + 46: 2005, + 24: 223, + 48: 376, + 28: 1074, + 23: 122, + 25: 316, + 22: 78, + 20: 24, + 19: 14, + 21: 43, + 17: 4, + 18: 6, + 16: 2, + }, + ("Choice", 8, 5): { + 44: 6279, + 48: 1363, + 43: 7642, + 47: 2872, + 42: 8489, + 38: 7810, + 34: 3845, + 29: 785, + 37: 6718, + 46: 4022, + 45: 4966, + 40: 8603, + 39: 8295, + 41: 8710, + 31: 1635, + 36: 5564, + 33: 2972, + 35: 4650, + 27: 352, + 32: 2214, + 28: 492, + 25: 137, + 26: 197, + 30: 1214, + 22: 28, + 24: 70, + 23: 46, + 21: 13, + 19: 5, + 20: 8, + 17: 2, + 18: 1, + 16: 1, + }, + ("Choice", 8, 6): { + 37: 5165, + 45: 6764, + 41: 8845, + 36: 4138, + 44: 8244, + 39: 7403, + 34: 2514, + 40: 8083, + 38: 6531, + 43: 9707, + 46: 6010, + 48: 3190, + 47: 5381, + 42: 9405, + 31: 877, + 35: 3155, + 33: 1755, + 29: 354, + 28: 244, + 32: 1318, + 30: 573, + 20: 4, + 26: 88, + 27: 147, + 25: 44, + 24: 35, + 22: 9, + 23: 12, + 21: 2, + 18: 1, + 16: 1, + 19: 1, + }, + ("Choice", 8, 7): { + 45: 8216, + 47: 8070, + 42: 9590, + 40: 6939, + 46: 7645, + 41: 8066, + 43: 11127, + 44: 9360, + 34: 1492, + 38: 5107, + 48: 6428, + 39: 6267, + 37: 3824, + 36: 2861, + 35: 2132, + 33: 1061, + 32: 685, + 30: 243, + 31: 442, + 25: 22, + 27: 66, + 24: 11, + 29: 201, + 28: 105, + 26: 33, + 23: 4, + 22: 1, + 20: 1, + 21: 1, + }, + ("Choice", 8, 8): { + 46: 8827, + 37: 2642, + 40: 5881, + 44: 10176, + 43: 11631, + 48: 10818, + 42: 8984, + 45: 9102, + 47: 10686, + 41: 7044, + 39: 4860, + 34: 909, + 38: 3885, + 36: 1776, + 33: 601, + 35: 1256, + 32: 341, + 30: 141, + 31: 232, + 27: 37, + 29: 90, + 28: 45, + 26: 21, + 25: 9, + 24: 3, + 23: 2, + 20: 1, + }, + ("Pair", 0, 0): {0: 100000}, + ("Pair", 0, 1): {0: 100000}, + ("Pair", 0, 2): {0: 100000}, + ("Pair", 0, 3): {0: 100000}, + ("Pair", 0, 4): {0: 100000}, + ("Pair", 0, 5): {0: 100000}, + ("Pair", 0, 6): {0: 100000}, + ("Pair", 0, 7): {0: 100000}, + ("Pair", 0, 8): {0: 100000}, + ("Pair", 1, 0): {0: 100000}, + ("Pair", 1, 1): {0: 100000}, + ("Pair", 1, 2): {0: 100000}, + ("Pair", 1, 3): {0: 100000}, + ("Pair", 1, 4): {0: 100000}, + ("Pair", 1, 5): {0: 100000}, + ("Pair", 1, 6): {0: 100000}, + ("Pair", 1, 7): {0: 100000}, + ("Pair", 1, 8): {0: 100000}, + ("Pair", 2, 0): {0: 100000}, + ("Pair", 2, 1): {0: 83388, 10: 16612}, + ("Pair", 2, 2): {0: 69422, 10: 30578}, + ("Pair", 2, 3): {0: 57830, 10: 42170}, + ("Pair", 2, 4): {0: 48195, 10: 51805}, + ("Pair", 2, 5): {10: 59883, 0: 40117}, + ("Pair", 2, 6): {10: 66714, 0: 33286}, + ("Pair", 2, 7): {10: 72083, 0: 27917}, + ("Pair", 2, 8): {10: 76646, 0: 23354}, + ("Pair", 3, 0): {0: 100000}, + ("Pair", 3, 1): {0: 55518, 10: 44482}, + ("Pair", 3, 2): {10: 69096, 0: 30904}, + ("Pair", 3, 3): {10: 82758, 0: 17242}, + ("Pair", 3, 4): {10: 90514, 0: 9486}, + ("Pair", 3, 5): {10: 94638, 0: 5362}, + ("Pair", 3, 6): {10: 97091, 0: 2909}, + ("Pair", 3, 7): {10: 98426, 0: 1574}, + ("Pair", 3, 8): {10: 99098, 0: 902}, + ("Pair", 4, 0): {0: 100000}, + ("Pair", 4, 1): {10: 72211, 0: 27789}, + ("Pair", 4, 2): {10: 92201, 0: 7799}, + ("Pair", 4, 3): {10: 97887, 0: 2113}, + ("Pair", 4, 4): {10: 99399, 0: 601}, + ("Pair", 4, 5): {10: 99845, 0: 155}, + ("Pair", 4, 6): {10: 99957, 0: 43}, + ("Pair", 4, 7): {10: 99990, 0: 10}, + ("Pair", 4, 8): {10: 99997, 0: 3}, + ("Pair", 5, 0): {0: 100000}, + ("Pair", 5, 1): {10: 90702, 0: 9298}, + ("Pair", 5, 2): {10: 99137, 0: 863}, + ("Pair", 5, 3): {10: 99921, 0: 79}, + ("Pair", 5, 4): {10: 99998, 0: 2}, + ("Pair", 5, 5): {10: 99998, 0: 2}, + ("Pair", 5, 6): {10: 100000}, + ("Pair", 5, 7): {10: 100000}, + ("Pair", 5, 8): {10: 100000}, + ("Pair", 6, 0): {0: 100000}, + ("Pair", 6, 1): {10: 98459, 0: 1541}, + ("Pair", 6, 2): {10: 99977, 0: 23}, + ("Pair", 6, 3): {10: 100000}, + ("Pair", 6, 4): {10: 100000}, + ("Pair", 6, 5): {10: 100000}, + ("Pair", 6, 6): {10: 100000}, + ("Pair", 6, 7): {10: 100000}, + ("Pair", 6, 8): {10: 100000}, + ("Pair", 7, 0): {0: 100000}, + ("Pair", 7, 1): {10: 100000}, + ("Pair", 7, 2): {10: 100000}, + ("Pair", 7, 3): {10: 100000}, + ("Pair", 7, 4): {10: 100000}, + ("Pair", 7, 5): {10: 100000}, + ("Pair", 7, 6): {10: 100000}, + ("Pair", 7, 7): {10: 100000}, + ("Pair", 7, 8): {10: 100000}, + ("Pair", 8, 0): {0: 100000}, + ("Pair", 8, 1): {10: 100000}, + ("Pair", 8, 2): {10: 100000}, + ("Pair", 8, 3): {10: 100000}, + ("Pair", 8, 4): {10: 100000}, + ("Pair", 8, 5): {10: 100000}, + ("Pair", 8, 6): {10: 100000}, + ("Pair", 8, 7): {10: 100000}, + ("Pair", 8, 8): {10: 100000}, + ("ThreeOfAKind", 0, 0): {0: 100000}, + ("ThreeOfAKind", 0, 1): {0: 100000}, + ("ThreeOfAKind", 0, 2): {0: 100000}, + ("ThreeOfAKind", 0, 3): {0: 100000}, + ("ThreeOfAKind", 0, 4): {0: 100000}, + ("ThreeOfAKind", 0, 5): {0: 100000}, + ("ThreeOfAKind", 0, 6): {0: 100000}, + ("ThreeOfAKind", 0, 7): {0: 100000}, + ("ThreeOfAKind", 0, 8): {0: 100000}, + ("ThreeOfAKind", 1, 0): {0: 100000}, + ("ThreeOfAKind", 1, 1): {0: 100000}, + ("ThreeOfAKind", 1, 2): {0: 100000}, + ("ThreeOfAKind", 1, 3): {0: 100000}, + ("ThreeOfAKind", 1, 4): {0: 100000}, + ("ThreeOfAKind", 1, 5): {0: 100000}, + ("ThreeOfAKind", 1, 6): {0: 100000}, + ("ThreeOfAKind", 1, 7): {0: 100000}, + ("ThreeOfAKind", 1, 8): {0: 100000}, + ("ThreeOfAKind", 2, 0): {0: 100000}, + ("ThreeOfAKind", 2, 1): {0: 100000}, + ("ThreeOfAKind", 2, 2): {0: 100000}, + ("ThreeOfAKind", 2, 3): {0: 100000}, + ("ThreeOfAKind", 2, 4): {0: 100000}, + ("ThreeOfAKind", 2, 5): {0: 100000}, + ("ThreeOfAKind", 2, 6): {0: 100000}, + ("ThreeOfAKind", 2, 7): {0: 100000}, + ("ThreeOfAKind", 2, 8): {0: 100000}, + ("ThreeOfAKind", 3, 0): {0: 100000}, + ("ThreeOfAKind", 3, 1): {0: 97222, 20: 2778}, + ("ThreeOfAKind", 3, 2): {0: 88880, 20: 11120}, + ("ThreeOfAKind", 3, 3): {0: 78187, 20: 21813}, + ("ThreeOfAKind", 3, 4): {0: 67476, 20: 32524}, + ("ThreeOfAKind", 3, 5): {20: 42524, 0: 57476}, + ("ThreeOfAKind", 3, 6): {20: 51490, 0: 48510}, + ("ThreeOfAKind", 3, 7): {20: 59079, 0: 40921}, + ("ThreeOfAKind", 3, 8): {20: 65467, 0: 34533}, + ("ThreeOfAKind", 4, 0): {0: 100000}, + ("ThreeOfAKind", 4, 1): {0: 90316, 20: 9684}, + ("ThreeOfAKind", 4, 2): {20: 31599, 0: 68401}, + ("ThreeOfAKind", 4, 3): {20: 50617, 0: 49383}, + ("ThreeOfAKind", 4, 4): {20: 65601, 0: 34399}, + ("ThreeOfAKind", 4, 5): {20: 75846, 0: 24154}, + ("ThreeOfAKind", 4, 6): {20: 83198, 0: 16802}, + ("ThreeOfAKind", 4, 7): {20: 88377, 0: 11623}, + ("ThreeOfAKind", 4, 8): {20: 91895, 0: 8105}, + ("ThreeOfAKind", 5, 0): {0: 100000}, + ("ThreeOfAKind", 5, 1): {0: 78629, 20: 21371}, + ("ThreeOfAKind", 5, 2): {0: 46013, 20: 53987}, + ("ThreeOfAKind", 5, 3): {20: 74302, 0: 25698}, + ("ThreeOfAKind", 5, 4): {20: 85795, 0: 14205}, + ("ThreeOfAKind", 5, 5): {20: 92068, 0: 7932}, + ("ThreeOfAKind", 5, 6): {20: 95643, 0: 4357}, + ("ThreeOfAKind", 5, 7): {20: 97568, 0: 2432}, + ("ThreeOfAKind", 5, 8): {20: 98622, 0: 1378}, + ("ThreeOfAKind", 6, 0): {0: 100000}, + ("ThreeOfAKind", 6, 1): {0: 63231, 20: 36769}, + ("ThreeOfAKind", 6, 2): {20: 73182, 0: 26818}, + ("ThreeOfAKind", 6, 3): {20: 88925, 0: 11075}, + ("ThreeOfAKind", 6, 4): {20: 95251, 0: 4749}, + ("ThreeOfAKind", 6, 5): {20: 98018, 0: 1982}, + ("ThreeOfAKind", 6, 6): {20: 99173, 0: 827}, + ("ThreeOfAKind", 6, 7): {20: 99642, 0: 358}, + ("ThreeOfAKind", 6, 8): {20: 99854, 0: 146}, + ("ThreeOfAKind", 7, 0): {0: 100000}, + ("ThreeOfAKind", 7, 1): {0: 45975, 20: 54025}, + ("ThreeOfAKind", 7, 2): {20: 86793, 0: 13207}, + ("ThreeOfAKind", 7, 3): {20: 96273, 0: 3727}, + ("ThreeOfAKind", 7, 4): {20: 98903, 0: 1097}, + ("ThreeOfAKind", 7, 5): {20: 99687, 0: 313}, + ("ThreeOfAKind", 7, 6): {20: 99904, 0: 96}, + ("ThreeOfAKind", 7, 7): {20: 99978, 0: 22}, + ("ThreeOfAKind", 7, 8): {20: 99992, 0: 8}, + ("ThreeOfAKind", 8, 0): {0: 100000}, + ("ThreeOfAKind", 8, 1): {20: 70684, 0: 29316}, + ("ThreeOfAKind", 8, 2): {20: 94973, 0: 5027}, + ("ThreeOfAKind", 8, 3): {20: 99143, 0: 857}, + ("ThreeOfAKind", 8, 4): {20: 99838, 0: 162}, + ("ThreeOfAKind", 8, 5): {20: 99975, 0: 25}, + ("ThreeOfAKind", 8, 6): {20: 99996, 0: 4}, + ("ThreeOfAKind", 8, 7): {20: 99999, 0: 1}, + ("ThreeOfAKind", 8, 8): {20: 100000}, + ("FourOfAKind", 0, 0): {0: 100000}, + ("FourOfAKind", 0, 1): {0: 100000}, + ("FourOfAKind", 0, 2): {0: 100000}, + ("FourOfAKind", 0, 3): {0: 100000}, + ("FourOfAKind", 0, 4): {0: 100000}, + ("FourOfAKind", 0, 5): {0: 100000}, + ("FourOfAKind", 0, 6): {0: 100000}, + ("FourOfAKind", 0, 7): {0: 100000}, + ("FourOfAKind", 0, 8): {0: 100000}, + ("FourOfAKind", 1, 0): {0: 100000}, + ("FourOfAKind", 1, 1): {0: 100000}, + ("FourOfAKind", 1, 2): {0: 100000}, + ("FourOfAKind", 1, 3): {0: 100000}, + ("FourOfAKind", 1, 4): {0: 100000}, + ("FourOfAKind", 1, 5): {0: 100000}, + ("FourOfAKind", 1, 6): {0: 100000}, + ("FourOfAKind", 1, 7): {0: 100000}, + ("FourOfAKind", 1, 8): {0: 100000}, + ("FourOfAKind", 2, 0): {0: 100000}, + ("FourOfAKind", 2, 1): {0: 100000}, + ("FourOfAKind", 2, 2): {0: 100000}, + ("FourOfAKind", 2, 3): {0: 100000}, + ("FourOfAKind", 2, 4): {0: 100000}, + ("FourOfAKind", 2, 5): {0: 100000}, + ("FourOfAKind", 2, 6): {0: 100000}, + ("FourOfAKind", 2, 7): {0: 100000}, + ("FourOfAKind", 2, 8): {0: 100000}, + ("FourOfAKind", 3, 0): {0: 100000}, + ("FourOfAKind", 3, 1): {0: 100000}, + ("FourOfAKind", 3, 2): {0: 100000}, + ("FourOfAKind", 3, 3): {0: 100000}, + ("FourOfAKind", 3, 4): {0: 100000}, + ("FourOfAKind", 3, 5): {0: 100000}, + ("FourOfAKind", 3, 6): {0: 100000}, + ("FourOfAKind", 3, 7): {0: 100000}, + ("FourOfAKind", 3, 8): {0: 100000}, + ("FourOfAKind", 4, 0): {0: 100000}, + ("FourOfAKind", 4, 1): {0: 99516, 30: 484}, + ("FourOfAKind", 4, 2): {0: 96122, 30: 3878}, + ("FourOfAKind", 4, 3): {0: 89867, 30: 10133}, + ("FourOfAKind", 4, 4): {0: 81771, 30: 18229}, + ("FourOfAKind", 4, 5): {0: 72893, 30: 27107}, + ("FourOfAKind", 4, 6): {0: 64000, 30: 36000}, + ("FourOfAKind", 4, 7): {0: 55921, 30: 44079}, + ("FourOfAKind", 4, 8): {0: 48175, 30: 51825}, + ("FourOfAKind", 5, 0): {0: 100000}, + ("FourOfAKind", 5, 1): {0: 97938, 30: 2062}, + ("FourOfAKind", 5, 2): {0: 86751, 30: 13249}, + ("FourOfAKind", 5, 3): {30: 29114, 0: 70886}, + ("FourOfAKind", 5, 4): {0: 54807, 30: 45193}, + ("FourOfAKind", 5, 5): {30: 58271, 0: 41729}, + ("FourOfAKind", 5, 6): {30: 69040, 0: 30960}, + ("FourOfAKind", 5, 7): {0: 22207, 30: 77793}, + ("FourOfAKind", 5, 8): {30: 83973, 0: 16027}, + ("FourOfAKind", 6, 0): {0: 100000}, + ("FourOfAKind", 6, 1): {0: 94810, 30: 5190}, + ("FourOfAKind", 6, 2): {0: 73147, 30: 26853}, + ("FourOfAKind", 6, 3): {30: 50127, 0: 49873}, + ("FourOfAKind", 6, 4): {0: 31913, 30: 68087}, + ("FourOfAKind", 6, 5): {30: 80123, 0: 19877}, + ("FourOfAKind", 6, 6): {30: 88027, 0: 11973}, + ("FourOfAKind", 6, 7): {30: 92676, 0: 7324}, + ("FourOfAKind", 6, 8): {30: 95779, 0: 4221}, + ("FourOfAKind", 7, 0): {0: 100000}, + ("FourOfAKind", 7, 1): {0: 89422, 30: 10578}, + ("FourOfAKind", 7, 2): {30: 42951, 0: 57049}, + ("FourOfAKind", 7, 3): {30: 69097, 0: 30903}, + ("FourOfAKind", 7, 4): {30: 84038, 0: 15962}, + ("FourOfAKind", 7, 5): {30: 91852, 0: 8148}, + ("FourOfAKind", 7, 6): {30: 96057, 0: 3943}, + ("FourOfAKind", 7, 7): {30: 98067, 0: 1933}, + ("FourOfAKind", 7, 8): {30: 99088, 0: 912}, + ("FourOfAKind", 8, 0): {0: 100000}, + ("FourOfAKind", 8, 1): {0: 81614, 30: 18386}, + ("FourOfAKind", 8, 2): {30: 59476, 0: 40524}, + ("FourOfAKind", 8, 3): {30: 82574, 0: 17426}, + ("FourOfAKind", 8, 4): {30: 93042, 0: 6958}, + ("FourOfAKind", 8, 5): {30: 97138, 0: 2862}, + ("FourOfAKind", 8, 6): {30: 98951, 0: 1049}, + ("FourOfAKind", 8, 7): {30: 99599, 0: 401}, + ("FourOfAKind", 8, 8): {30: 99844, 0: 156}, + ("TinyStraight", 0, 0): {0: 100000}, + ("TinyStraight", 0, 1): {0: 100000}, + ("TinyStraight", 0, 2): {0: 100000}, + ("TinyStraight", 0, 3): {0: 100000}, + ("TinyStraight", 0, 4): {0: 100000}, + ("TinyStraight", 0, 5): {0: 100000}, + ("TinyStraight", 0, 6): {0: 100000}, + ("TinyStraight", 0, 7): {0: 100000}, + ("TinyStraight", 0, 8): {0: 100000}, + ("TinyStraight", 1, 0): {0: 100000}, + ("TinyStraight", 1, 1): {0: 100000}, + ("TinyStraight", 1, 2): {0: 100000}, + ("TinyStraight", 1, 3): {0: 100000}, + ("TinyStraight", 1, 4): {0: 100000}, + ("TinyStraight", 1, 5): {0: 100000}, + ("TinyStraight", 1, 6): {0: 100000}, + ("TinyStraight", 1, 7): {0: 100000}, + ("TinyStraight", 1, 8): {0: 100000}, + ("TinyStraight", 2, 0): {0: 100000}, + ("TinyStraight", 2, 1): {0: 100000}, + ("TinyStraight", 2, 2): {0: 100000}, + ("TinyStraight", 2, 3): {0: 100000}, + ("TinyStraight", 2, 4): {0: 100000}, + ("TinyStraight", 2, 5): {0: 100000}, + ("TinyStraight", 2, 6): {0: 100000}, + ("TinyStraight", 2, 7): {0: 100000}, + ("TinyStraight", 2, 8): {0: 100000}, + ("TinyStraight", 3, 0): {0: 100000}, + ("TinyStraight", 3, 1): {0: 91672, 20: 8328}, + ("TinyStraight", 3, 2): {0: 79082, 20: 20918}, + ("TinyStraight", 3, 3): {0: 66490, 20: 33510}, + ("TinyStraight", 3, 4): {0: 55797, 20: 44203}, + ("TinyStraight", 3, 5): {0: 46967, 20: 53033}, + ("TinyStraight", 3, 6): {20: 60405, 0: 39595}, + ("TinyStraight", 3, 7): {20: 66616, 0: 33384}, + ("TinyStraight", 3, 8): {20: 71253, 0: 28747}, + ("TinyStraight", 4, 0): {0: 100000}, + ("TinyStraight", 4, 1): {0: 78812, 20: 21188}, + ("TinyStraight", 4, 2): {0: 55525, 20: 44475}, + ("TinyStraight", 4, 3): {0: 38148, 20: 61852}, + ("TinyStraight", 4, 4): {20: 73568, 0: 26432}, + ("TinyStraight", 4, 5): {20: 81775, 0: 18225}, + ("TinyStraight", 4, 6): {20: 87242, 0: 12758}, + ("TinyStraight", 4, 7): {20: 91009, 0: 8991}, + ("TinyStraight", 4, 8): {20: 93675, 0: 6325}, + ("TinyStraight", 5, 0): {0: 100000}, + ("TinyStraight", 5, 1): {20: 35021, 0: 64979}, + ("TinyStraight", 5, 2): {0: 36509, 20: 63491}, + ("TinyStraight", 5, 3): {20: 79424, 0: 20576}, + ("TinyStraight", 5, 4): {20: 88415, 0: 11585}, + ("TinyStraight", 5, 5): {20: 93126, 0: 6874}, + ("TinyStraight", 5, 6): {20: 96202, 0: 3798}, + ("TinyStraight", 5, 7): {20: 97786, 0: 2214}, + ("TinyStraight", 5, 8): {20: 98728, 0: 1272}, + ("TinyStraight", 6, 0): {0: 100000}, + ("TinyStraight", 6, 1): {0: 52157, 20: 47843}, + ("TinyStraight", 6, 2): {20: 76359, 0: 23641}, + ("TinyStraight", 6, 3): {20: 89117, 0: 10883}, + ("TinyStraight", 6, 4): {20: 94873, 0: 5127}, + ("TinyStraight", 6, 5): {20: 97558, 0: 2442}, + ("TinyStraight", 6, 6): {20: 98842, 0: 1158}, + ("TinyStraight", 6, 7): {20: 99458, 0: 542}, + ("TinyStraight", 6, 8): {20: 99748, 0: 252}, + ("TinyStraight", 7, 0): {0: 100000}, + ("TinyStraight", 7, 1): {20: 58508, 0: 41492}, + ("TinyStraight", 7, 2): {0: 15072, 20: 84928}, + ("TinyStraight", 7, 3): {20: 94095, 0: 5905}, + ("TinyStraight", 7, 4): {20: 97754, 0: 2246}, + ("TinyStraight", 7, 5): {20: 99058, 0: 942}, + ("TinyStraight", 7, 6): {20: 99663, 0: 337}, + ("TinyStraight", 7, 7): {20: 99845, 0: 155}, + ("TinyStraight", 7, 8): {20: 99939, 0: 61}, + ("TinyStraight", 8, 0): {0: 100000}, + ("TinyStraight", 8, 1): {0: 32993, 20: 67007}, + ("TinyStraight", 8, 2): {20: 89926, 0: 10074}, + ("TinyStraight", 8, 3): {20: 96842, 0: 3158}, + ("TinyStraight", 8, 4): {20: 98940, 0: 1060}, + ("TinyStraight", 8, 5): {20: 99644, 0: 356}, + ("TinyStraight", 8, 6): {20: 99883, 0: 117}, + ("TinyStraight", 8, 7): {20: 99968, 0: 32}, + ("TinyStraight", 8, 8): {20: 99990, 0: 10}, + ("SmallStraight", 0, 0): {0: 100000}, + ("SmallStraight", 0, 1): {0: 100000}, + ("SmallStraight", 0, 2): {0: 100000}, + ("SmallStraight", 0, 3): {0: 100000}, + ("SmallStraight", 0, 4): {0: 100000}, + ("SmallStraight", 0, 5): {0: 100000}, + ("SmallStraight", 0, 6): {0: 100000}, + ("SmallStraight", 0, 7): {0: 100000}, + ("SmallStraight", 0, 8): {0: 100000}, + ("SmallStraight", 1, 0): {0: 100000}, + ("SmallStraight", 1, 1): {0: 100000}, + ("SmallStraight", 1, 2): {0: 100000}, + ("SmallStraight", 1, 3): {0: 100000}, + ("SmallStraight", 1, 4): {0: 100000}, + ("SmallStraight", 1, 5): {0: 100000}, + ("SmallStraight", 1, 6): {0: 100000}, + ("SmallStraight", 1, 7): {0: 100000}, + ("SmallStraight", 1, 8): {0: 100000}, + ("SmallStraight", 2, 0): {0: 100000}, + ("SmallStraight", 2, 1): {0: 100000}, + ("SmallStraight", 2, 2): {0: 100000}, + ("SmallStraight", 2, 3): {0: 100000}, + ("SmallStraight", 2, 4): {0: 100000}, + ("SmallStraight", 2, 5): {0: 100000}, + ("SmallStraight", 2, 6): {0: 100000}, + ("SmallStraight", 2, 7): {0: 100000}, + ("SmallStraight", 2, 8): {0: 100000}, + ("SmallStraight", 3, 0): {0: 100000}, + ("SmallStraight", 3, 1): {0: 100000}, + ("SmallStraight", 3, 2): {0: 100000}, + ("SmallStraight", 3, 3): {0: 100000}, + ("SmallStraight", 3, 4): {0: 100000}, + ("SmallStraight", 3, 5): {0: 100000}, + ("SmallStraight", 3, 6): {0: 100000}, + ("SmallStraight", 3, 7): {0: 100000}, + ("SmallStraight", 3, 8): {0: 100000}, + ("SmallStraight", 4, 0): {0: 100000}, + ("SmallStraight", 4, 1): {0: 94516, 30: 5484}, + ("SmallStraight", 4, 2): {0: 82700, 30: 17300}, + ("SmallStraight", 4, 3): {0: 67926, 30: 32074}, + ("SmallStraight", 4, 4): {30: 45735, 0: 54265}, + ("SmallStraight", 4, 5): {0: 42130, 30: 57870}, + ("SmallStraight", 4, 6): {0: 32536, 30: 67464}, + ("SmallStraight", 4, 7): {0: 25008, 30: 74992}, + ("SmallStraight", 4, 8): {30: 80405, 0: 19595}, + ("SmallStraight", 5, 0): {0: 100000}, + ("SmallStraight", 5, 1): {0: 84528, 30: 15472}, + ("SmallStraight", 5, 2): {0: 60775, 30: 39225}, + ("SmallStraight", 5, 3): {0: 39543, 30: 60457}, + ("SmallStraight", 5, 4): {30: 75240, 0: 24760}, + ("SmallStraight", 5, 5): {30: 84287, 0: 15713}, + ("SmallStraight", 5, 6): {30: 89801, 0: 10199}, + ("SmallStraight", 5, 7): {30: 93382, 0: 6618}, + ("SmallStraight", 5, 8): {30: 95795, 0: 4205}, + ("SmallStraight", 6, 0): {0: 100000}, + ("SmallStraight", 6, 1): {0: 73121, 30: 26879}, + ("SmallStraight", 6, 2): {30: 58168, 0: 41832}, + ("SmallStraight", 6, 3): {30: 78051, 0: 21949}, + ("SmallStraight", 6, 4): {30: 88696, 0: 11304}, + ("SmallStraight", 6, 5): {30: 93937, 0: 6063}, + ("SmallStraight", 6, 6): {30: 96638, 0: 3362}, + ("SmallStraight", 6, 7): {30: 98201, 0: 1799}, + ("SmallStraight", 6, 8): {30: 98931, 0: 1069}, + ("SmallStraight", 7, 0): {0: 100000}, + ("SmallStraight", 7, 1): {0: 61837, 30: 38163}, + ("SmallStraight", 7, 2): {30: 71798, 0: 28202}, + ("SmallStraight", 7, 3): {30: 87813, 0: 12187}, + ("SmallStraight", 7, 4): {30: 94573, 0: 5427}, + ("SmallStraight", 7, 5): {30: 97556, 0: 2444}, + ("SmallStraight", 7, 6): {30: 98856, 0: 1144}, + ("SmallStraight", 7, 7): {30: 99412, 0: 588}, + ("SmallStraight", 7, 8): {30: 99742, 0: 258}, + ("SmallStraight", 8, 0): {0: 100000}, + ("SmallStraight", 8, 1): {30: 48606, 0: 51394}, + ("SmallStraight", 8, 2): {30: 80910, 0: 19090}, + ("SmallStraight", 8, 3): {0: 7104, 30: 92896}, + ("SmallStraight", 8, 4): {30: 97355, 0: 2645}, + ("SmallStraight", 8, 5): {30: 98990, 0: 1010}, + ("SmallStraight", 8, 6): {30: 99592, 0: 408}, + ("SmallStraight", 8, 7): {30: 99847, 0: 153}, + ("SmallStraight", 8, 8): {30: 99922, 0: 78}, + ("LargeStraight", 0, 0): {0: 100000}, + ("LargeStraight", 0, 1): {0: 100000}, + ("LargeStraight", 0, 2): {0: 100000}, + ("LargeStraight", 0, 3): {0: 100000}, + ("LargeStraight", 0, 4): {0: 100000}, + ("LargeStraight", 0, 5): {0: 100000}, + ("LargeStraight", 0, 6): {0: 100000}, + ("LargeStraight", 0, 7): {0: 100000}, + ("LargeStraight", 0, 8): {0: 100000}, + ("LargeStraight", 1, 0): {0: 100000}, + ("LargeStraight", 1, 1): {0: 100000}, + ("LargeStraight", 1, 2): {0: 100000}, + ("LargeStraight", 1, 3): {0: 100000}, + ("LargeStraight", 1, 4): {0: 100000}, + ("LargeStraight", 1, 5): {0: 100000}, + ("LargeStraight", 1, 6): {0: 100000}, + ("LargeStraight", 1, 7): {0: 100000}, + ("LargeStraight", 1, 8): {0: 100000}, + ("LargeStraight", 2, 0): {0: 100000}, + ("LargeStraight", 2, 1): {0: 100000}, + ("LargeStraight", 2, 2): {0: 100000}, + ("LargeStraight", 2, 3): {0: 100000}, + ("LargeStraight", 2, 4): {0: 100000}, + ("LargeStraight", 2, 5): {0: 100000}, + ("LargeStraight", 2, 6): {0: 100000}, + ("LargeStraight", 2, 7): {0: 100000}, + ("LargeStraight", 2, 8): {0: 100000}, + ("LargeStraight", 3, 0): {0: 100000}, + ("LargeStraight", 3, 1): {0: 100000}, + ("LargeStraight", 3, 2): {0: 100000}, + ("LargeStraight", 3, 3): {0: 100000}, + ("LargeStraight", 3, 4): {0: 100000}, + ("LargeStraight", 3, 5): {0: 100000}, + ("LargeStraight", 3, 6): {0: 100000}, + ("LargeStraight", 3, 7): {0: 100000}, + ("LargeStraight", 3, 8): {0: 100000}, + ("LargeStraight", 4, 0): {0: 100000}, + ("LargeStraight", 4, 1): {0: 100000}, + ("LargeStraight", 4, 2): {0: 100000}, + ("LargeStraight", 4, 3): {0: 100000}, + ("LargeStraight", 4, 4): {0: 100000}, + ("LargeStraight", 4, 5): {0: 100000}, + ("LargeStraight", 4, 6): {0: 100000}, + ("LargeStraight", 4, 7): {0: 100000}, + ("LargeStraight", 4, 8): {0: 100000}, + ("LargeStraight", 5, 0): {0: 100000}, + ("LargeStraight", 5, 1): {0: 96929, 40: 3071}, + ("LargeStraight", 5, 2): {0: 87056, 40: 12944}, + ("LargeStraight", 5, 3): {0: 75101, 40: 24899}, + ("LargeStraight", 5, 4): {0: 63617, 40: 36383}, + ("LargeStraight", 5, 5): {0: 53149, 40: 46851}, + ("LargeStraight", 5, 6): {0: 44321, 40: 55679}, + ("LargeStraight", 5, 7): {40: 63052, 0: 36948}, + ("LargeStraight", 5, 8): {0: 30661, 40: 69339}, + ("LargeStraight", 6, 0): {0: 100000}, + ("LargeStraight", 6, 1): {0: 90756, 40: 9244}, + ("LargeStraight", 6, 2): {0: 69805, 40: 30195}, + ("LargeStraight", 6, 3): {0: 49814, 40: 50186}, + ("LargeStraight", 6, 4): {40: 64898, 0: 35102}, + ("LargeStraight", 6, 5): {40: 75615, 0: 24385}, + ("LargeStraight", 6, 6): {40: 82982, 0: 17018}, + ("LargeStraight", 6, 7): {40: 88261, 0: 11739}, + ("LargeStraight", 6, 8): {40: 92028, 0: 7972}, + ("LargeStraight", 7, 0): {0: 100000}, + ("LargeStraight", 7, 1): {0: 82840, 40: 17160}, + ("LargeStraight", 7, 2): {0: 52821, 40: 47179}, + ("LargeStraight", 7, 3): {40: 68652, 0: 31348}, + ("LargeStraight", 7, 4): {40: 81834, 0: 18166}, + ("LargeStraight", 7, 5): {40: 89310, 0: 10690}, + ("LargeStraight", 7, 6): {40: 93949, 0: 6051}, + ("LargeStraight", 7, 7): {40: 96383, 0: 3617}, + ("LargeStraight", 7, 8): {40: 98059, 0: 1941}, + ("LargeStraight", 8, 0): {0: 100000}, + ("LargeStraight", 8, 1): {40: 26480, 0: 73520}, + ("LargeStraight", 8, 2): {40: 60969, 0: 39031}, + ("LargeStraight", 8, 3): {40: 80844, 0: 19156}, + ("LargeStraight", 8, 4): {40: 90696, 0: 9304}, + ("LargeStraight", 8, 5): {40: 95580, 0: 4420}, + ("LargeStraight", 8, 6): {40: 97859, 0: 2141}, + ("LargeStraight", 8, 7): {40: 98963, 0: 1037}, + ("LargeStraight", 8, 8): {40: 99489, 0: 511}, + ("FullHouse", 0, 0): {0: 100000}, + ("FullHouse", 0, 1): {0: 100000}, + ("FullHouse", 0, 2): {0: 100000}, + ("FullHouse", 0, 3): {0: 100000}, + ("FullHouse", 0, 4): {0: 100000}, + ("FullHouse", 0, 5): {0: 100000}, + ("FullHouse", 0, 6): {0: 100000}, + ("FullHouse", 0, 7): {0: 100000}, + ("FullHouse", 0, 8): {0: 100000}, + ("FullHouse", 1, 0): {0: 100000}, + ("FullHouse", 1, 1): {0: 100000}, + ("FullHouse", 1, 2): {0: 100000}, + ("FullHouse", 1, 3): {0: 100000}, + ("FullHouse", 1, 4): {0: 100000}, + ("FullHouse", 1, 5): {0: 100000}, + ("FullHouse", 1, 6): {0: 100000}, + ("FullHouse", 1, 7): {0: 100000}, + ("FullHouse", 1, 8): {0: 100000}, + ("FullHouse", 2, 0): {0: 100000}, + ("FullHouse", 2, 1): {0: 100000}, + ("FullHouse", 2, 2): {0: 100000}, + ("FullHouse", 2, 3): {0: 100000}, + ("FullHouse", 2, 4): {0: 100000}, + ("FullHouse", 2, 5): {0: 100000}, + ("FullHouse", 2, 6): {0: 100000}, + ("FullHouse", 2, 7): {0: 100000}, + ("FullHouse", 2, 8): {0: 100000}, + ("FullHouse", 3, 0): {0: 100000}, + ("FullHouse", 3, 1): {0: 100000}, + ("FullHouse", 3, 2): {0: 100000}, + ("FullHouse", 3, 3): {0: 100000}, + ("FullHouse", 3, 4): {0: 100000}, + ("FullHouse", 3, 5): {0: 100000}, + ("FullHouse", 3, 6): {0: 100000}, + ("FullHouse", 3, 7): {0: 100000}, + ("FullHouse", 3, 8): {0: 100000}, + ("FullHouse", 4, 0): {0: 100000}, + ("FullHouse", 4, 1): {0: 100000}, + ("FullHouse", 4, 2): {0: 100000}, + ("FullHouse", 4, 3): {0: 100000}, + ("FullHouse", 4, 4): {0: 100000}, + ("FullHouse", 4, 5): {0: 100000}, + ("FullHouse", 4, 6): {0: 100000}, + ("FullHouse", 4, 7): {0: 100000}, + ("FullHouse", 4, 8): {0: 100000}, + ("FullHouse", 5, 0): {0: 100000}, + ("FullHouse", 5, 1): {0: 96155, 25: 3845}, + ("FullHouse", 5, 2): {0: 81391, 25: 18609}, + ("FullHouse", 5, 3): {25: 35700, 0: 64300}, + ("FullHouse", 5, 4): {25: 50331, 0: 49669}, + ("FullHouse", 5, 5): {25: 61981, 0: 38019}, + ("FullHouse", 5, 6): {25: 70249, 0: 29751}, + ("FullHouse", 5, 7): {25: 77040, 0: 22960}, + ("FullHouse", 5, 8): {25: 81350, 0: 18650}, + ("FullHouse", 6, 0): {0: 100000}, + ("FullHouse", 6, 1): {25: 17011, 0: 82989}, + ("FullHouse", 6, 2): {0: 47153, 25: 52847}, + ("FullHouse", 6, 3): {25: 75849, 0: 24151}, + ("FullHouse", 6, 4): {0: 12519, 25: 87481}, + ("FullHouse", 6, 5): {25: 93476, 0: 6524}, + ("FullHouse", 6, 6): {0: 3606, 25: 96394}, + ("FullHouse", 6, 7): {25: 98041, 0: 1959}, + ("FullHouse", 6, 8): {25: 98974, 0: 1026}, + ("FullHouse", 7, 0): {0: 100000}, + ("FullHouse", 7, 1): {0: 60232, 25: 39768}, + ("FullHouse", 7, 2): {25: 81106, 0: 18894}, + ("FullHouse", 7, 3): {25: 94318, 0: 5682}, + ("FullHouse", 7, 4): {25: 98294, 0: 1706}, + ("FullHouse", 7, 5): {25: 99478, 0: 522}, + ("FullHouse", 7, 6): {25: 99854, 0: 146}, + ("FullHouse", 7, 7): {25: 99946, 0: 54}, + ("FullHouse", 7, 8): {25: 99982, 0: 18}, + ("FullHouse", 8, 0): {0: 100000}, + ("FullHouse", 8, 1): {0: 35909, 25: 64091}, + ("FullHouse", 8, 2): {25: 94288, 0: 5712}, + ("FullHouse", 8, 3): {25: 99070, 0: 930}, + ("FullHouse", 8, 4): {25: 99835, 0: 165}, + ("FullHouse", 8, 5): {25: 99981, 0: 19}, + ("FullHouse", 8, 6): {25: 99994, 0: 6}, + ("FullHouse", 8, 7): {25: 100000}, + ("FullHouse", 8, 8): {25: 100000}, + ("Yacht", 0, 0): {0: 100000}, + ("Yacht", 0, 1): {0: 100000}, + ("Yacht", 0, 2): {0: 100000}, + ("Yacht", 0, 3): {0: 100000}, + ("Yacht", 0, 4): {0: 100000}, + ("Yacht", 0, 5): {0: 100000}, + ("Yacht", 0, 6): {0: 100000}, + ("Yacht", 0, 7): {0: 100000}, + ("Yacht", 0, 8): {0: 100000}, + ("Yacht", 1, 0): {0: 100000}, + ("Yacht", 1, 1): {0: 100000}, + ("Yacht", 1, 2): {0: 100000}, + ("Yacht", 1, 3): {0: 100000}, + ("Yacht", 1, 4): {0: 100000}, + ("Yacht", 1, 5): {0: 100000}, + ("Yacht", 1, 6): {0: 100000}, + ("Yacht", 1, 7): {0: 100000}, + ("Yacht", 1, 8): {0: 100000}, + ("Yacht", 2, 0): {0: 100000}, + ("Yacht", 2, 1): {0: 100000}, + ("Yacht", 2, 2): {0: 100000}, + ("Yacht", 2, 3): {0: 100000}, + ("Yacht", 2, 4): {0: 100000}, + ("Yacht", 2, 5): {0: 100000}, + ("Yacht", 2, 6): {0: 100000}, + ("Yacht", 2, 7): {0: 100000}, + ("Yacht", 2, 8): {0: 100000}, + ("Yacht", 3, 0): {0: 100000}, + ("Yacht", 3, 1): {0: 100000}, + ("Yacht", 3, 2): {0: 100000}, + ("Yacht", 3, 3): {0: 100000}, + ("Yacht", 3, 4): {0: 100000}, + ("Yacht", 3, 5): {0: 100000}, + ("Yacht", 3, 6): {0: 100000}, + ("Yacht", 3, 7): {0: 100000}, + ("Yacht", 3, 8): {0: 100000}, + ("Yacht", 4, 0): {0: 100000}, + ("Yacht", 4, 1): {0: 100000}, + ("Yacht", 4, 2): {0: 100000}, + ("Yacht", 4, 3): {0: 100000}, + ("Yacht", 4, 4): {0: 100000}, + ("Yacht", 4, 5): {0: 100000}, + ("Yacht", 4, 6): {0: 100000}, + ("Yacht", 4, 7): {0: 100000}, + ("Yacht", 4, 8): {0: 100000}, + ("Yacht", 5, 0): {0: 100000}, + ("Yacht", 5, 1): {0: 99919, 50: 81}, + ("Yacht", 5, 2): {0: 98727, 50: 1273}, + ("Yacht", 5, 3): {50: 4653, 0: 95347}, + ("Yacht", 5, 4): {0: 89969, 50: 10031}, + ("Yacht", 5, 5): {0: 83124, 50: 16876}, + ("Yacht", 5, 6): {0: 75023, 50: 24977}, + ("Yacht", 5, 7): {0: 67007, 50: 32993}, + ("Yacht", 5, 8): {0: 58618, 50: 41382}, + ("Yacht", 6, 0): {0: 100000}, + ("Yacht", 6, 1): {0: 99571, 50: 429}, + ("Yacht", 6, 2): {0: 94726, 50: 5274}, + ("Yacht", 6, 3): {0: 84366, 50: 15634}, + ("Yacht", 6, 4): {50: 29218, 0: 70782}, + ("Yacht", 6, 5): {0: 56573, 50: 43427}, + ("Yacht", 6, 6): {50: 55794, 0: 44206}, + ("Yacht", 6, 7): {50: 66422, 0: 33578}, + ("Yacht", 6, 8): {0: 25079, 50: 74921}, + ("Yacht", 7, 0): {0: 100000}, + ("Yacht", 7, 1): {0: 98833, 50: 1167}, + ("Yacht", 7, 2): {0: 87511, 50: 12489}, + ("Yacht", 7, 3): {0: 68252, 50: 31748}, + ("Yacht", 7, 4): {0: 49065, 50: 50935}, + ("Yacht", 7, 5): {0: 33364, 50: 66636}, + ("Yacht", 7, 6): {50: 78517, 0: 21483}, + ("Yacht", 7, 7): {50: 86403, 0: 13597}, + ("Yacht", 7, 8): {50: 91517, 0: 8483}, + ("Yacht", 8, 0): {0: 100000}, + ("Yacht", 8, 1): {0: 97212, 50: 2788}, + ("Yacht", 8, 2): {50: 23038, 0: 76962}, + ("Yacht", 8, 3): {0: 50533, 50: 49467}, + ("Yacht", 8, 4): {50: 70019, 0: 29981}, + ("Yacht", 8, 5): {50: 83224, 0: 16776}, + ("Yacht", 8, 6): {50: 90921, 0: 9079}, + ("Yacht", 8, 7): {50: 95295, 0: 4705}, + ("Yacht", 8, 8): {50: 97637, 0: 2363}, + ("Distincts", 1, 1): {1: 100000}, + ("Distincts", 1, 2): {1: 100000}, + ("Distincts", 1, 3): {1: 100000}, + ("Distincts", 1, 4): {1: 100000}, + ("Distincts", 1, 5): {1: 100000}, + ("Distincts", 1, 6): {1: 100000}, + ("Distincts", 1, 7): {1: 100000}, + ("Distincts", 1, 8): {1: 100000}, + ("Distincts", 2, 1): {2: 83196, 1: 16804}, + ("Distincts", 2, 2): {2: 97314, 1: 2686}, + ("Distincts", 2, 3): {2: 99537, 1: 463}, + ("Distincts", 2, 4): {2: 99934, 1: 66}, + ("Distincts", 2, 5): {2: 99989, 1: 11}, + ("Distincts", 2, 6): {2: 99999, 1: 1}, + ("Distincts", 2, 7): {2: 100000}, + ("Distincts", 2, 8): {2: 100000}, + ("Distincts", 3, 1): {2: 41714, 3: 55526, 1: 2760}, + ("Distincts", 3, 2): {2: 14936, 3: 84986, 1: 78}, + ("Distincts", 3, 3): {3: 95134, 2: 4865, 1: 1}, + ("Distincts", 3, 4): {3: 98341, 2: 1659}, + ("Distincts", 3, 5): {3: 99425, 2: 575}, + ("Distincts", 3, 6): {3: 99800, 2: 200}, + ("Distincts", 3, 7): {3: 99931, 2: 69}, + ("Distincts", 3, 8): {3: 99978, 2: 22}, + ("Distincts", 4, 1): {3: 55471, 2: 16140, 4: 27895, 1: 494}, + ("Distincts", 4, 2): {3: 36922, 4: 61185, 2: 1891, 1: 2}, + ("Distincts", 4, 3): {4: 80139, 3: 19631, 2: 230}, + ("Distincts", 4, 4): {4: 90121, 3: 9858, 2: 21}, + ("Distincts", 4, 5): {4: 95094, 3: 4904, 2: 2}, + ("Distincts", 4, 6): {4: 97506, 3: 2494}, + ("Distincts", 4, 7): {4: 98703, 3: 1297}, + ("Distincts", 4, 8): {4: 99389, 3: 611}, + ("Distincts", 5, 1): {4: 46379, 5: 9285, 3: 38538, 2: 5717, 1: 81}, + ("Distincts", 5, 2): {4: 56472, 5: 31685, 3: 11647, 2: 196}, + ("Distincts", 5, 3): {4: 44724, 5: 52254, 3: 3016, 2: 6}, + ("Distincts", 5, 4): {4: 31632, 5: 67646, 3: 722}, + ("Distincts", 5, 5): {5: 78394, 4: 21391, 3: 215}, + ("Distincts", 5, 6): {5: 85475, 4: 14470, 3: 55}, + ("Distincts", 5, 7): {5: 90340, 4: 9645, 3: 15}, + ("Distincts", 5, 8): {5: 93537, 4: 6461, 3: 2}, + ("Distincts", 6, 1): {3: 22985, 5: 23032, 4: 50464, 2: 2019, 6: 1492, 1: 8}, + ("Distincts", 6, 2): {5: 52573, 4: 35174, 6: 8954, 3: 3273, 2: 26}, + ("Distincts", 6, 3): {4: 17376, 5: 62578, 6: 19629, 3: 417}, + ("Distincts", 6, 4): {5: 61029, 6: 31140, 4: 7787, 3: 44}, + ("Distincts", 6, 5): {6: 41304, 5: 54997, 4: 3690, 3: 9}, + ("Distincts", 6, 6): {5: 47225, 6: 51218, 4: 1557}, + ("Distincts", 6, 7): {6: 58807, 5: 40465, 4: 728}, + ("Distincts", 6, 8): {6: 65828, 5: 33851, 4: 321}, + ("Distincts", 7, 1): {4: 44964, 5: 36020, 3: 13006, 6: 5345, 2: 661, 1: 4}, + ("Distincts", 7, 2): {5: 56731, 6: 23583, 4: 18847, 3: 838, 2: 1}, + ("Distincts", 7, 3): {5: 50312, 6: 43637, 4: 5983, 3: 68}, + ("Distincts", 7, 4): {6: 59811, 5: 38393, 4: 1792, 3: 4}, + ("Distincts", 7, 5): {5: 27728, 6: 71743, 4: 529}, + ("Distincts", 7, 6): {6: 80419, 5: 19417, 4: 164}, + ("Distincts", 7, 7): {6: 86382, 5: 13565, 4: 53}, + ("Distincts", 7, 8): {6: 90455, 5: 9531, 4: 14}, + ("Distincts", 8, 1): {5: 44977, 4: 36582, 6: 11304, 3: 6939, 2: 197, 1: 1}, + ("Distincts", 8, 2): {6: 39803, 5: 50783, 4: 9181, 3: 231, 2: 2}, + ("Distincts", 8, 3): {6: 63276, 5: 34748, 4: 1967, 3: 9}, + ("Distincts", 8, 4): {6: 78603, 5: 21008, 4: 389}, + ("Distincts", 8, 5): {6: 87408, 5: 12514, 4: 78}, + ("Distincts", 8, 6): {6: 92823, 5: 7159, 4: 18}, + ("Distincts", 8, 7): {6: 95821, 5: 4175, 4: 4}, + ("Distincts", 8, 8): {6: 97560, 5: 2440}, + ("TwosAndThrees", 1, 1): {0: 66466, 2: 16929, 3: 16605}, + ("TwosAndThrees", 1, 2): {0: 55640, 2: 13812, 3: 30548}, + ("TwosAndThrees", 1, 3): {3: 42178, 0: 46223, 2: 11599}, + ("TwosAndThrees", 1, 4): {3: 51830, 0: 38552, 2: 9618}, + ("TwosAndThrees", 1, 5): {0: 32320, 3: 59706, 2: 7974}, + ("TwosAndThrees", 1, 6): {0: 26733, 3: 66583, 2: 6684}, + ("TwosAndThrees", 1, 7): {3: 72148, 0: 22289, 2: 5563}, + ("TwosAndThrees", 1, 8): {3: 76636, 0: 18676, 2: 4688}, + ("TwosAndThrees", 2, 1): {3: 22335, 2: 21965, 0: 44565, 4: 2837, 5: 5615, 6: 2683}, + ("TwosAndThrees", 2, 2): {3: 33956, 0: 30855, 6: 9438, 2: 15480, 5: 8278, 4: 1993}, + ("TwosAndThrees", 2, 3): {0: 21509, 3: 38995, 6: 17586, 2: 10838, 5: 9727, 4: 1345}, + ("TwosAndThrees", 2, 4): {6: 26659, 3: 40188, 5: 9825, 2: 7489, 0: 14935, 4: 904}, + ("TwosAndThrees", 2, 5): {3: 38402, 6: 35581, 2: 5169, 5: 9671, 0: 10492, 4: 685}, + ("TwosAndThrees", 2, 6): {3: 35460, 6: 44295, 5: 8994, 0: 7185, 2: 3590, 4: 476}, + ("TwosAndThrees", 2, 7): {6: 52017, 3: 32147, 0: 4880, 5: 8139, 2: 2495, 4: 322}, + ("TwosAndThrees", 2, 8): {3: 28213, 5: 7294, 6: 59058, 0: 3464, 4: 223, 2: 1748}, + ("TwosAndThrees", 3, 1): {3: 22284, 0: 29892, 6: 6003, 4: 5497, 5: 11005, 2: 22136, 8: 1368, 7: 1366, 9: 449}, + ("TwosAndThrees", 3, 2): {5: 14092, 2: 12757, 3: 28287, 6: 15822, 0: 17285, 7: 1730, 4: 3213, 9: 2873, 8: 3941}, + ("TwosAndThrees", 3, 3): {6: 24863, 3: 27111, 9: 7340, 5: 13522, 8: 6154, 0: 9889, 4: 1847, 2: 7547, 7: 1727}, + ("TwosAndThrees", 3, 4): {9: 13765, 6: 31427, 5: 11617, 3: 23072, 8: 7719, 0: 5717, 4: 1000, 2: 4245, 7: 1438}, + ("TwosAndThrees", 3, 5): {5: 9296, 6: 34570, 0: 3347, 3: 18506, 4: 617, 9: 21395, 2: 2448, 8: 8683, 7: 1138}, + ("TwosAndThrees", 3, 6): {8: 8820, 3: 14399, 6: 35444, 5: 7148, 9: 29632, 0: 1821, 2: 1452, 7: 943, 4: 341}, + ("TwosAndThrees", 3, 7): {9: 37501, 3: 10672, 8: 8739, 6: 34879, 5: 5345, 7: 725, 2: 835, 4: 222, 0: 1082}, + ("TwosAndThrees", 3, 8): {6: 33047, 9: 45099, 3: 8099, 8: 8018, 5: 4003, 0: 667, 2: 457, 7: 490, 4: 120}, + ("TwosAndThrees", 4, 1): { + 3: 19811, + 9: 1565, + 2: 19764, + 0: 19619, + 6: 8721, + 5: 14893, + 4: 7306, + 8: 3801, + 11: 319, + 7: 3672, + 12: 60, + 10: 469, + }, + ("TwosAndThrees", 4, 2): { + 2: 9519, + 9: 6678, + 5: 15873, + 6: 18083, + 7: 3876, + 8: 8667, + 3: 20826, + 0: 9395, + 4: 3581, + 12: 830, + 10: 1077, + 11: 1595, + }, + ("TwosAndThrees", 4, 3): { + 12: 3245, + 3: 16598, + 8: 11445, + 5: 12541, + 2: 4676, + 6: 23294, + 0: 4538, + 11: 3442, + 4: 1694, + 10: 1454, + 9: 14017, + 7: 3056, + }, + ("TwosAndThrees", 4, 4): { + 8: 11841, + 12: 7183, + 6: 24218, + 3: 11827, + 9: 21496, + 11: 5412, + 10: 1447, + 4: 827, + 7: 2251, + 5: 9096, + 0: 2183, + 2: 2219, + }, + ("TwosAndThrees", 4, 5): { + 5: 6024, + 9: 27693, + 8: 11169, + 12: 12776, + 3: 7946, + 10: 1428, + 6: 22064, + 2: 1078, + 11: 6926, + 0: 987, + 4: 381, + 7: 1528, + }, + ("TwosAndThrees", 4, 6): { + 9: 31606, + 5: 3815, + 8: 9649, + 11: 7894, + 3: 5070, + 12: 19495, + 6: 19042, + 10: 1243, + 2: 514, + 7: 971, + 0: 530, + 4: 171, + }, + ("TwosAndThrees", 4, 7): { + 6: 15556, + 3: 3337, + 9: 33379, + 12: 26771, + 5: 2427, + 11: 8601, + 2: 239, + 8: 7881, + 10: 918, + 0: 224, + 7: 584, + 4: 83, + }, + ("TwosAndThrees", 4, 8): { + 11: 8379, + 6: 12179, + 8: 6079, + 9: 33703, + 2: 130, + 12: 34875, + 3: 1931, + 5: 1468, + 10: 738, + 7: 353, + 0: 123, + 4: 42, + }, + ("TwosAndThrees", 5, 1): { + 8: 6572, + 5: 16396, + 6: 10247, + 4: 8172, + 3: 16607, + 2: 16414, + 7: 6170, + 0: 13070, + 9: 3061, + 10: 1591, + 11: 1136, + 12: 374, + 13: 124, + 14: 55, + 15: 11, + }, + ("TwosAndThrees", 5, 2): { + 6: 16838, + 8: 12090, + 5: 14763, + 7: 5565, + 2: 6515, + 3: 14466, + 10: 3040, + 0: 5213, + 9: 9616, + 12: 2659, + 4: 3294, + 11: 4470, + 14: 636, + 13: 578, + 15: 257, + }, + ("TwosAndThrees", 5, 3): { + 5: 9700, + 3: 9638, + 6: 17947, + 11: 8066, + 9: 16835, + 8: 13214, + 13: 1039, + 7: 3741, + 0: 2126, + 12: 7402, + 4: 1321, + 2: 2581, + 15: 1332, + 14: 1842, + 10: 3216, + }, + ("TwosAndThrees", 5, 4): { + 6: 15410, + 9: 20661, + 15: 3811, + 5: 5781, + 14: 3435, + 10: 3042, + 11: 10468, + 8: 11579, + 7: 2157, + 3: 5807, + 12: 14158, + 0: 848, + 13: 1264, + 2: 1086, + 4: 493, + }, + ("TwosAndThrees", 5, 5): { + 12: 20783, + 14: 5166, + 6: 12042, + 9: 22225, + 8: 8829, + 11: 11126, + 3: 3222, + 7: 1226, + 10: 2220, + 15: 7632, + 5: 3184, + 13: 1346, + 2: 401, + 0: 380, + 4: 218, + }, + ("TwosAndThrees", 5, 6): { + 15: 13013, + 14: 6551, + 12: 26214, + 9: 21305, + 11: 10593, + 10: 1597, + 8: 6610, + 6: 8412, + 5: 1670, + 13: 1307, + 3: 1698, + 7: 653, + 0: 123, + 2: 172, + 4: 82, + }, + ("TwosAndThrees", 5, 7): { + 14: 7512, + 11: 9332, + 9: 18653, + 6: 5940, + 8: 4428, + 15: 19396, + 12: 30190, + 13: 1142, + 10: 1106, + 3: 896, + 7: 332, + 5: 908, + 4: 41, + 0: 59, + 2: 65, + }, + ("TwosAndThrees", 5, 8): { + 6: 3768, + 9: 15520, + 14: 7963, + 15: 26880, + 12: 32501, + 11: 7771, + 8: 2819, + 10: 666, + 13: 973, + 5: 459, + 2: 30, + 3: 470, + 7: 153, + 0: 13, + 4: 14, + }, + ("TwosAndThrees", 6, 1): { + 3: 13212, + 2: 13135, + 10: 3108, + 0: 8955, + 4: 8191, + 8: 8621, + 5: 16659, + 6: 10713, + 9: 4879, + 7: 8276, + 13: 496, + 11: 2290, + 14: 282, + 17: 18, + 12: 1026, + 15: 100, + 16: 37, + 18: 2, + }, + ("TwosAndThrees", 6, 2): { + 13: 1940, + 9: 11416, + 2: 4382, + 11: 7676, + 10: 5032, + 6: 14157, + 5: 11978, + 8: 13344, + 12: 4905, + 3: 9661, + 14: 2123, + 15: 1026, + 7: 6021, + 0: 2944, + 4: 2851, + 16: 247, + 17: 202, + 18: 95, + }, + ("TwosAndThrees", 6, 3): { + 9: 15493, + 11: 11208, + 2: 1507, + 13: 2828, + 15: 3924, + 10: 4567, + 6: 12595, + 14: 5229, + 5: 6758, + 8: 12211, + 12: 10862, + 3: 5429, + 7: 3404, + 17: 912, + 4: 933, + 18: 529, + 0: 977, + 16: 634, + }, + ("TwosAndThrees", 6, 4): { + 8: 9036, + 15: 8762, + 11: 12021, + 10: 3287, + 12: 16325, + 9: 16299, + 14: 8216, + 18: 1928, + 17: 2081, + 6: 9147, + 7: 1667, + 4: 294, + 2: 545, + 16: 1007, + 5: 3351, + 3: 2723, + 13: 2991, + 0: 320, + }, + ("TwosAndThrees", 6, 5): { + 15: 15030, + 9: 14359, + 13: 2648, + 10: 2136, + 12: 20394, + 8: 5744, + 6: 5681, + 14: 10049, + 11: 10563, + 18: 4564, + 17: 3669, + 5: 1525, + 3: 1189, + 16: 1251, + 2: 184, + 7: 777, + 4: 123, + 0: 114, + }, + ("TwosAndThrees", 6, 6): { + 11: 8492, + 15: 21066, + 12: 21369, + 17: 5246, + 6: 3342, + 16: 1335, + 14: 10649, + 8: 3453, + 18: 8568, + 10: 1300, + 9: 11370, + 3: 543, + 13: 2098, + 5: 696, + 7: 350, + 2: 64, + 4: 25, + 0: 34, + }, + ("TwosAndThrees", 6, 7): { + 18: 14118, + 14: 10107, + 17: 6654, + 15: 26139, + 12: 20371, + 9: 8281, + 13: 1535, + 16: 1221, + 3: 221, + 11: 6214, + 6: 1923, + 8: 1973, + 10: 715, + 5: 334, + 7: 158, + 0: 14, + 4: 5, + 2: 17, + }, + ("TwosAndThrees", 6, 8): { + 15: 29815, + 18: 20433, + 5: 123, + 11: 4522, + 12: 17854, + 14: 8991, + 17: 7602, + 3: 107, + 9: 5741, + 8: 1043, + 10: 416, + 13: 1062, + 16: 1197, + 6: 1007, + 7: 69, + 0: 7, + 2: 9, + 4: 2, + }, + ("TwosAndThrees", 7, 1): { + 8: 10304, + 0: 5802, + 2: 10380, + 11: 3830, + 7: 9559, + 10: 5017, + 5: 15384, + 4: 7689, + 3: 10100, + 9: 6289, + 13: 1211, + 6: 11027, + 12: 2088, + 14: 735, + 15: 309, + 16: 177, + 17: 59, + 19: 11, + 18: 27, + 20: 2, + }, + ("TwosAndThrees", 7, 2): { + 10: 6466, + 0: 1605, + 8: 13172, + 7: 5824, + 11: 9919, + 13: 3610, + 9: 11600, + 14: 4206, + 2: 2810, + 6: 11269, + 5: 9442, + 12: 6844, + 15: 2299, + 3: 6242, + 17: 923, + 16: 966, + 4: 2215, + 18: 376, + 19: 114, + 20: 76, + 21: 22, + }, + ("TwosAndThrees", 7, 3): { + 6: 8288, + 7: 2641, + 3: 2956, + 9: 13017, + 8: 10013, + 14: 8279, + 16: 2082, + 12: 12302, + 11: 12133, + 13: 4465, + 18: 1968, + 15: 6674, + 10: 5028, + 17: 3001, + 5: 4265, + 2: 792, + 20: 437, + 21: 258, + 4: 558, + 0: 471, + 19: 372, + }, + ("TwosAndThrees", 7, 4): { + 15: 12396, + 9: 10994, + 18: 5400, + 21: 1006, + 5: 1774, + 17: 5917, + 14: 10700, + 12: 15357, + 11: 11007, + 20: 1270, + 10: 3007, + 8: 6030, + 7: 1160, + 6: 4949, + 3: 1218, + 13: 3950, + 16: 2660, + 2: 211, + 19: 710, + 4: 157, + 0: 127, + }, + ("TwosAndThrees", 7, 5): { + 17: 8259, + 20: 2565, + 15: 17220, + 9: 8155, + 5: 671, + 18: 10513, + 21: 2728, + 6: 2533, + 11: 8026, + 12: 15164, + 16: 2851, + 8: 3249, + 14: 11317, + 13: 3008, + 19: 1041, + 4: 47, + 7: 426, + 10: 1653, + 3: 478, + 2: 56, + 0: 40, + }, + ("TwosAndThrees", 7, 6): { + 12: 13233, + 14: 10114, + 18: 16405, + 15: 19936, + 16: 2451, + 21: 5650, + 6: 1331, + 20: 4044, + 17: 9948, + 11: 5449, + 10: 827, + 9: 5335, + 19: 1171, + 13: 1883, + 8: 1584, + 7: 180, + 5: 249, + 3: 166, + 2: 18, + 0: 9, + 4: 17, + }, + ("TwosAndThrees", 7, 7): { + 17: 10123, + 20: 5583, + 18: 22122, + 15: 20423, + 14: 7969, + 21: 10113, + 12: 10638, + 11: 3321, + 9: 3282, + 16: 1910, + 13: 1273, + 19: 1293, + 6: 591, + 8: 779, + 7: 55, + 5: 86, + 3: 59, + 10: 368, + 2: 4, + 0: 6, + 4: 2, + }, + ("TwosAndThrees", 7, 8): { + 17: 9621, + 21: 15780, + 20: 6667, + 12: 7854, + 18: 26592, + 14: 5885, + 15: 19476, + 5: 36, + 8: 318, + 19: 1247, + 16: 1458, + 9: 1983, + 11: 1880, + 13: 707, + 6: 249, + 10: 197, + 7: 19, + 3: 27, + 2: 2, + 0: 2, + }, + ("TwosAndThrees", 8, 1): { + 12: 3210, + 0: 3799, + 7: 10309, + 5: 13610, + 10: 6648, + 6: 10144, + 3: 7840, + 2: 7917, + 9: 7504, + 8: 11477, + 4: 6794, + 13: 2299, + 11: 5342, + 14: 1498, + 16: 444, + 15: 738, + 17: 245, + 19: 51, + 18: 105, + 20: 20, + 21: 4, + 22: 1, + 23: 1, + }, + ("TwosAndThrees", 8, 2): { + 11: 11041, + 12: 8197, + 5: 6900, + 18: 1088, + 9: 10605, + 14: 6195, + 8: 11961, + 16: 2205, + 10: 7327, + 13: 5337, + 6: 8536, + 0: 902, + 4: 1547, + 15: 3891, + 3: 4041, + 7: 5214, + 20: 384, + 2: 1872, + 17: 2062, + 21: 155, + 22: 37, + 19: 479, + 23: 17, + 24: 7, + }, + ("TwosAndThrees", 8, 3): { + 11: 11338, + 12: 11675, + 13: 5514, + 15: 8898, + 6: 5105, + 17: 5667, + 9: 9728, + 8: 7389, + 18: 3828, + 22: 206, + 19: 1391, + 14: 10523, + 16: 3854, + 10: 4686, + 7: 1931, + 23: 227, + 21: 1014, + 20: 1681, + 3: 1598, + 4: 392, + 5: 2625, + 2: 422, + 0: 201, + 24: 107, + }, + ("TwosAndThrees", 8, 4): { + 17: 9133, + 12: 11960, + 15: 13098, + 16: 4254, + 11: 8286, + 9: 6908, + 20: 3995, + 21: 3323, + 14: 11359, + 10: 2363, + 18: 8743, + 13: 4118, + 19: 2217, + 8: 3661, + 24: 520, + 7: 648, + 6: 2558, + 23: 768, + 22: 471, + 3: 518, + 2: 97, + 5: 884, + 4: 75, + 0: 43, + }, + ("TwosAndThrees", 8, 5): { + 21: 7245, + 13: 2524, + 16: 3469, + 12: 9934, + 11: 5061, + 17: 10743, + 15: 14970, + 18: 14072, + 24: 1671, + 14: 9578, + 10: 1007, + 20: 6621, + 6: 1110, + 9: 4201, + 19: 2728, + 23: 1727, + 8: 1714, + 22: 848, + 5: 316, + 3: 188, + 7: 211, + 0: 16, + 2: 16, + 4: 30, + }, + ("TwosAndThrees", 8, 6): { + 20: 8749, + 15: 14205, + 8: 683, + 14: 7037, + 18: 17783, + 17: 10618, + 23: 3141, + 9: 2273, + 24: 3858, + 5: 96, + 12: 7143, + 21: 12731, + 13: 1405, + 11: 2957, + 22: 1109, + 19: 2548, + 6: 474, + 16: 2612, + 10: 436, + 3: 57, + 7: 68, + 2: 8, + 4: 6, + 0: 3, + }, + ("TwosAndThrees", 8, 7): { + 21: 18331, + 18: 19896, + 20: 9757, + 16: 1804, + 23: 4503, + 19: 2324, + 24: 7305, + 17: 8935, + 12: 4725, + 15: 12345, + 22: 1237, + 13: 775, + 9: 1167, + 14: 4727, + 11: 1485, + 6: 176, + 8: 251, + 10: 195, + 3: 16, + 7: 19, + 5: 24, + 0: 1, + 4: 1, + 2: 1, + }, + ("TwosAndThrees", 8, 8): { + 21: 23586, + 20: 10020, + 15: 9640, + 18: 19736, + 24: 12112, + 17: 7289, + 23: 5802, + 22: 1233, + 14: 2918, + 19: 1781, + 12: 2912, + 9: 557, + 16: 1068, + 13: 390, + 11: 718, + 8: 90, + 6: 66, + 7: 7, + 10: 61, + 5: 7, + 3: 7, + }, + ("SumOfOdds", 1, 1): {0: 50084, 3: 16584, 1: 16488, 5: 16844}, + ("SumOfOdds", 1, 2): {0: 33472, 3: 27886, 1: 11017, 5: 27625}, + ("SumOfOdds", 1, 3): {0: 27892, 5: 39809, 1: 9293, 3: 23006}, + ("SumOfOdds", 1, 4): {3: 19299, 5: 49784, 0: 23060, 1: 7857}, + ("SumOfOdds", 1, 5): {5: 58167, 3: 15941, 1: 6559, 0: 19333}, + ("SumOfOdds", 1, 6): {5: 65098, 0: 16250, 1: 5428, 3: 13224}, + ("SumOfOdds", 1, 7): {5: 70969, 3: 11191, 0: 13420, 1: 4420}, + ("SumOfOdds", 1, 8): {5: 75949, 0: 11042, 3: 9361, 1: 3648}, + ("SumOfOdds", 2, 1): {5: 16856, 8: 5540, 6: 8312, 4: 5580, 0: 24611, 1: 16800, 3: 16654, 2: 2815, 10: 2832}, + ("SumOfOdds", 2, 2): {8: 15414, 3: 18386, 6: 13858, 0: 11216, 4: 6190, 5: 18558, 10: 7773, 1: 7355, 2: 1250}, + ("SumOfOdds", 2, 3): {1: 5252, 6: 12709, 3: 12782, 8: 18363, 5: 22224, 10: 15919, 0: 7666, 4: 4273, 2: 812}, + ("SumOfOdds", 2, 4): {3: 8914, 6: 11358, 5: 23132, 4: 2928, 10: 24940, 0: 5392, 1: 3585, 8: 19129, 2: 622}, + ("SumOfOdds", 2, 5): {5: 22529, 0: 3735, 3: 6203, 4: 2093, 10: 33791, 8: 18712, 2: 415, 6: 10020, 1: 2502}, + ("SumOfOdds", 2, 6): {0: 2606, 8: 17272, 6: 8852, 10: 42502, 3: 4279, 5: 20970, 1: 1769, 4: 1468, 2: 282}, + ("SumOfOdds", 2, 7): {5: 19160, 8: 15860, 6: 7664, 10: 50054, 1: 1225, 3: 2939, 4: 1039, 0: 1872, 2: 187}, + ("SumOfOdds", 2, 8): {5: 16853, 8: 14179, 10: 57618, 3: 2121, 6: 6400, 1: 781, 0: 1230, 4: 671, 2: 147}, + ("SumOfOdds", 3, 1): { + 4: 8109, + 5: 13902, + 2: 4149, + 8: 8321, + 6: 12607, + 1: 12587, + 7: 2743, + 3: 12861, + 0: 12467, + 9: 3339, + 10: 4223, + 11: 2801, + 15: 479, + 13: 1412, + }, + ("SumOfOdds", 3, 2): { + 8: 15592, + 1: 3633, + 5: 10240, + 13: 6362, + 3: 9469, + 10: 7709, + 15: 2120, + 6: 13852, + 11: 9070, + 9: 7284, + 4: 6110, + 7: 3557, + 0: 3750, + 2: 1252, + }, + ("SumOfOdds", 3, 3): { + 6: 10744, + 10: 13273, + 7: 2564, + 8: 15277, + 3: 5427, + 13: 11044, + 11: 10759, + 5: 9729, + 15: 6204, + 1: 2180, + 9: 6354, + 4: 3603, + 0: 2140, + 2: 702, + }, + ("SumOfOdds", 3, 4): { + 8: 13319, + 6: 7837, + 11: 11288, + 9: 5211, + 13: 14216, + 15: 12408, + 4: 2122, + 3: 3247, + 10: 17343, + 7: 1738, + 5: 8380, + 1: 1212, + 0: 1265, + 2: 414, + }, + ("SumOfOdds", 3, 5): { + 11: 10985, + 10: 19378, + 13: 16370, + 5: 6682, + 6: 5931, + 8: 10857, + 9: 4058, + 15: 19804, + 7: 1250, + 1: 660, + 3: 1831, + 2: 246, + 4: 1236, + 0: 712, + }, + ("SumOfOdds", 3, 6): { + 15: 27548, + 5: 5144, + 13: 17133, + 10: 20496, + 8: 8411, + 11: 10472, + 6: 4205, + 9: 2961, + 1: 398, + 2: 146, + 3: 1070, + 4: 746, + 7: 864, + 0: 406, + }, + ("SumOfOdds", 3, 7): { + 8: 6397, + 15: 35967, + 10: 20125, + 9: 2262, + 5: 3882, + 0: 233, + 4: 399, + 11: 9495, + 13: 16763, + 6: 3021, + 7: 607, + 1: 235, + 3: 539, + 2: 75, + }, + ("SumOfOdds", 3, 8): { + 15: 43436, + 6: 2174, + 10: 19242, + 13: 16221, + 11: 8430, + 8: 4737, + 9: 1594, + 5: 2863, + 3: 352, + 7: 406, + 1: 130, + 0: 146, + 4: 214, + 2: 55, + }, + ("SumOfOdds", 4, 1): { + 11: 5334, + 12: 1465, + 5: 11215, + 14: 1216, + 3: 9225, + 6: 12932, + 1: 8440, + 7: 5618, + 4: 8433, + 10: 5290, + 0: 6192, + 8: 9117, + 16: 760, + 9: 6474, + 2: 4238, + 13: 2744, + 15: 930, + 18: 299, + 20: 78, + }, + ("SumOfOdds", 4, 2): { + 7: 4928, + 20: 589, + 9: 9721, + 14: 5301, + 18: 2447, + 13: 8342, + 10: 7201, + 4: 4099, + 8: 11060, + 15: 2925, + 6: 9467, + 3: 4253, + 11: 11978, + 12: 3975, + 1: 1599, + 16: 4530, + 5: 5463, + 0: 1267, + 2: 855, + }, + ("SumOfOdds", 4, 3): { + 15: 7108, + 8: 9018, + 10: 8843, + 20: 2524, + 18: 5690, + 16: 7373, + 9: 7238, + 11: 11998, + 12: 3466, + 13: 12173, + 14: 5857, + 4: 2033, + 6: 5991, + 1: 817, + 2: 382, + 3: 2070, + 5: 4051, + 0: 579, + 7: 2789, + }, + ("SumOfOdds", 4, 4): { + 5: 2645, + 14: 5928, + 8: 6372, + 11: 10474, + 13: 13555, + 12: 2765, + 16: 9426, + 15: 11453, + 18: 9512, + 10: 8758, + 6: 3695, + 20: 6196, + 4: 912, + 2: 187, + 9: 4810, + 3: 1009, + 0: 295, + 7: 1637, + 1: 371, + }, + ("SumOfOdds", 4, 5): { + 20: 11573, + 11: 8461, + 15: 15171, + 8: 4270, + 16: 10401, + 13: 12479, + 18: 12704, + 14: 5099, + 10: 8159, + 6: 2313, + 9: 3010, + 5: 1893, + 12: 2054, + 4: 520, + 7: 932, + 1: 194, + 3: 528, + 0: 136, + 2: 103, + }, + ("SumOfOdds", 4, 6): { + 14: 4251, + 10: 7130, + 15: 17784, + 11: 6594, + 20: 17780, + 18: 14865, + 13: 11039, + 16: 10571, + 8: 2849, + 9: 1928, + 6: 1369, + 12: 1509, + 7: 583, + 5: 1123, + 0: 75, + 3: 225, + 4: 198, + 1: 84, + 2: 43, + }, + ("SumOfOdds", 4, 7): { + 11: 5056, + 15: 19254, + 20: 25294, + 18: 15947, + 12: 1124, + 16: 10290, + 13: 9005, + 8: 1697, + 9: 1202, + 14: 3338, + 5: 703, + 3: 129, + 10: 5644, + 7: 317, + 6: 798, + 4: 112, + 2: 19, + 1: 38, + 0: 33, + }, + ("SumOfOdds", 4, 8): { + 15: 19503, + 18: 16250, + 10: 4365, + 20: 33016, + 13: 7294, + 16: 9512, + 11: 3635, + 14: 2618, + 6: 480, + 12: 747, + 9: 760, + 0: 15, + 8: 1001, + 4: 64, + 5: 448, + 1: 22, + 2: 17, + 7: 203, + 3: 50, + }, + ("SumOfOdds", 5, 1): { + 5: 8737, + 8: 8879, + 11: 7319, + 7: 7013, + 16: 1886, + 6: 11185, + 9: 8310, + 10: 6485, + 14: 3092, + 4: 7062, + 0: 3061, + 13: 4040, + 3: 6431, + 1: 5196, + 17: 609, + 12: 3785, + 15: 1883, + 19: 406, + 2: 3389, + 18: 788, + 21: 205, + 20: 172, + 23: 48, + 25: 19, + }, + ("SumOfOdds", 5, 2): { + 4: 2325, + 12: 6880, + 21: 1941, + 5: 2829, + 17: 3048, + 18: 4003, + 11: 10285, + 16: 7538, + 14: 8806, + 9: 8227, + 8: 6951, + 3: 1889, + 7: 4166, + 13: 8344, + 10: 6439, + 1: 723, + 6: 5351, + 19: 2919, + 15: 4531, + 0: 421, + 23: 787, + 20: 977, + 2: 455, + 25: 165, + }, + ("SumOfOdds", 5, 3): { + 13: 9355, + 7: 1955, + 15: 6633, + 23: 2922, + 10: 5293, + 9: 5007, + 8: 4456, + 11: 8533, + 5: 1584, + 16: 10471, + 14: 8325, + 18: 8174, + 6: 2861, + 21: 4463, + 12: 4910, + 3: 715, + 19: 4741, + 25: 1017, + 20: 3505, + 17: 3498, + 4: 938, + 1: 292, + 2: 179, + 0: 173, + }, + ("SumOfOdds", 5, 4): { + 15: 8218, + 10: 4157, + 11: 6088, + 21: 7049, + 6: 1464, + 18: 10977, + 9: 2814, + 12: 3036, + 17: 3222, + 23: 5968, + 16: 10748, + 13: 8276, + 19: 5463, + 20: 7264, + 14: 6799, + 3: 322, + 8: 2685, + 7: 929, + 25: 3023, + 5: 899, + 4: 353, + 0: 60, + 2: 65, + 1: 121, + }, + ("SumOfOdds", 5, 5): { + 23: 9242, + 21: 8982, + 18: 12099, + 16: 9890, + 13: 6376, + 14: 5000, + 7: 416, + 15: 8283, + 25: 6730, + 10: 2969, + 20: 11138, + 19: 5449, + 11: 4198, + 17: 2686, + 8: 1446, + 6: 749, + 9: 1508, + 12: 1961, + 5: 490, + 4: 169, + 3: 124, + 2: 23, + 1: 40, + 0: 32, + }, + ("SumOfOdds", 5, 6): { + 16: 8471, + 14: 3473, + 15: 7862, + 20: 14372, + 18: 11813, + 23: 11945, + 13: 4540, + 25: 11854, + 17: 2176, + 21: 9884, + 19: 5053, + 7: 214, + 11: 2724, + 10: 2039, + 12: 1252, + 5: 265, + 8: 764, + 9: 796, + 6: 351, + 3: 52, + 0: 14, + 4: 51, + 2: 10, + 1: 25, + }, + ("SumOfOdds", 5, 7): { + 21: 10043, + 15: 6797, + 18: 10646, + 20: 17146, + 16: 6743, + 23: 14100, + 25: 18070, + 14: 2413, + 13: 3129, + 17: 1582, + 11: 1707, + 19: 4232, + 10: 1317, + 12: 758, + 8: 419, + 9: 393, + 7: 117, + 6: 212, + 0: 4, + 5: 121, + 3: 14, + 4: 29, + 1: 5, + 2: 3, + }, + ("SumOfOdds", 5, 8): { + 19: 3530, + 25: 25173, + 16: 5196, + 14: 1481, + 23: 15254, + 20: 18491, + 21: 9907, + 18: 8924, + 15: 5707, + 11: 1045, + 17: 1194, + 13: 2121, + 9: 226, + 12: 432, + 10: 885, + 8: 209, + 6: 87, + 5: 73, + 3: 11, + 7: 43, + 2: 2, + 4: 7, + 0: 2, + }, + ("SumOfOdds", 6, 1): { + 3: 4224, + 8: 8145, + 5: 6613, + 7: 7139, + 11: 8130, + 4: 5575, + 1: 3156, + 12: 5541, + 14: 4722, + 18: 1450, + 15: 3188, + 6: 9118, + 9: 8689, + 10: 7075, + 16: 3201, + 19: 1145, + 13: 5215, + 2: 2581, + 0: 1673, + 17: 1683, + 21: 583, + 20: 581, + 22: 197, + 24: 99, + 23: 176, + 25: 45, + 26: 37, + 28: 18, + 30: 1, + }, + ("SumOfOdds", 6, 2): { + 21: 3933, + 14: 9068, + 15: 6211, + 16: 8370, + 17: 6093, + 23: 1654, + 6: 2896, + 20: 2831, + 18: 5227, + 19: 5836, + 13: 7405, + 10: 4912, + 12: 6840, + 9: 5601, + 3: 789, + 7: 2738, + 11: 7613, + 8: 4025, + 4: 1143, + 24: 1487, + 26: 784, + 5: 1464, + 2: 207, + 22: 1829, + 25: 309, + 28: 284, + 0: 153, + 30: 44, + 1: 254, + }, + ("SumOfOdds", 6, 3): { + 14: 7165, + 16: 8872, + 12: 4062, + 19: 7784, + 9: 2863, + 18: 7891, + 17: 5775, + 10: 3056, + 26: 2610, + 20: 4889, + 21: 7711, + 15: 6056, + 11: 4913, + 28: 1319, + 13: 6032, + 22: 2922, + 23: 4730, + 8: 2096, + 6: 1241, + 25: 1697, + 5: 678, + 24: 3166, + 7: 1136, + 4: 431, + 2: 81, + 3: 276, + 30: 408, + 0: 52, + 1: 88, + }, + ("SumOfOdds", 6, 4): { + 20: 6653, + 15: 5033, + 26: 4922, + 28: 3412, + 18: 8483, + 13: 4254, + 23: 8187, + 16: 7827, + 12: 2170, + 21: 9709, + 19: 7579, + 14: 4910, + 7: 425, + 17: 4469, + 9: 1345, + 24: 4611, + 25: 4315, + 22: 3138, + 11: 2995, + 10: 1844, + 8: 1069, + 30: 1562, + 6: 531, + 4: 139, + 3: 73, + 5: 291, + 1: 25, + 0: 14, + 2: 15, + }, + ("SumOfOdds", 6, 5): { + 11: 1732, + 24: 5058, + 10: 938, + 19: 6276, + 14: 2902, + 23: 10694, + 30: 3884, + 28: 6388, + 26: 7087, + 25: 7754, + 8: 448, + 22: 2967, + 16: 5943, + 15: 4038, + 21: 10212, + 20: 7845, + 18: 7634, + 17: 3138, + 12: 1215, + 13: 2669, + 4: 46, + 9: 598, + 5: 100, + 6: 204, + 3: 28, + 7: 171, + 0: 13, + 2: 9, + 1: 9, + }, + ("SumOfOdds", 6, 6): { + 18: 6055, + 28: 9447, + 25: 11411, + 16: 4061, + 14: 1658, + 30: 7796, + 23: 11565, + 21: 9505, + 4: 19, + 19: 4880, + 24: 5317, + 26: 8543, + 20: 7981, + 15: 2949, + 17: 1975, + 13: 1594, + 11: 893, + 22: 2547, + 9: 239, + 12: 598, + 10: 551, + 5: 59, + 8: 174, + 6: 80, + 7: 90, + 3: 8, + 2: 3, + 0: 1, + 1: 1, + }, + ("SumOfOdds", 6, 7): { + 28: 12043, + 23: 11329, + 18: 4376, + 20: 7612, + 25: 14467, + 26: 9526, + 30: 12675, + 11: 449, + 13: 945, + 19: 3515, + 21: 8189, + 15: 2047, + 22: 2096, + 16: 2827, + 24: 4812, + 14: 872, + 17: 1300, + 10: 331, + 7: 22, + 9: 105, + 12: 297, + 8: 92, + 4: 6, + 3: 3, + 6: 41, + 5: 19, + 2: 2, + 0: 1, + 1: 1, + }, + ("SumOfOdds", 6, 8): { + 30: 19239, + 24: 4175, + 25: 16723, + 28: 13964, + 20: 6522, + 21: 6637, + 26: 10048, + 23: 10221, + 19: 2288, + 17: 774, + 18: 3153, + 15: 1389, + 11: 234, + 16: 1736, + 22: 1566, + 14: 492, + 13: 439, + 12: 124, + 10: 167, + 6: 19, + 8: 30, + 9: 41, + 4: 2, + 5: 6, + 7: 8, + 2: 1, + 3: 1, + 0: 1, + }, + ("SumOfOdds", 7, 1): { + 9: 8090, + 4: 3909, + 8: 7190, + 14: 6179, + 12: 6713, + 5: 4975, + 11: 8138, + 21: 1127, + 6: 6784, + 10: 7566, + 17: 3068, + 1: 1789, + 15: 4550, + 24: 380, + 13: 6122, + 3: 2703, + 19: 2017, + 16: 4253, + 7: 6543, + 22: 680, + 18: 2417, + 2: 1824, + 23: 463, + 20: 1268, + 0: 802, + 26: 155, + 25: 164, + 27: 56, + 31: 7, + 28: 44, + 29: 18, + 30: 5, + 33: 1, + }, + ("SumOfOdds", 7, 2): { + 19: 7499, + 10: 3348, + 7: 1563, + 16: 7542, + 17: 7455, + 22: 4462, + 23: 2985, + 20: 5062, + 4: 563, + 27: 990, + 18: 6139, + 11: 5041, + 13: 5634, + 15: 6277, + 12: 5532, + 24: 3432, + 6: 1341, + 26: 1867, + 29: 691, + 21: 5434, + 14: 7465, + 8: 2287, + 9: 3363, + 25: 1595, + 31: 298, + 3: 298, + 5: 723, + 0: 40, + 33: 99, + 30: 113, + 28: 649, + 1: 111, + 2: 91, + 35: 11, + }, + ("SumOfOdds", 7, 3): { + 21: 7920, + 11: 2734, + 13: 3610, + 20: 5725, + 17: 5660, + 10: 1718, + 29: 2008, + 23: 5788, + 26: 5052, + 14: 4810, + 19: 7837, + 16: 6596, + 18: 6591, + 24: 6130, + 15: 4550, + 12: 2708, + 25: 3421, + 22: 5553, + 27: 2110, + 8: 962, + 28: 2665, + 6: 488, + 5: 250, + 4: 154, + 31: 1350, + 30: 762, + 9: 1363, + 7: 523, + 33: 629, + 35: 161, + 1: 33, + 0: 17, + 2: 19, + 3: 103, + }, + ("SumOfOdds", 7, 4): { + 18: 5325, + 20: 5489, + 14: 2709, + 25: 5310, + 28: 5802, + 24: 7375, + 29: 3397, + 16: 4487, + 17: 3663, + 15: 2790, + 11: 1257, + 23: 7672, + 26: 8008, + 19: 6437, + 22: 5187, + 9: 587, + 27: 2827, + 12: 1233, + 21: 8147, + 13: 2066, + 31: 3220, + 10: 716, + 30: 2521, + 8: 409, + 33: 2088, + 35: 770, + 6: 165, + 5: 81, + 7: 180, + 4: 41, + 3: 25, + 1: 8, + 2: 6, + 0: 2, + }, + ("SumOfOdds", 7, 5): { + 24: 7133, + 25: 7033, + 33: 4414, + 16: 2849, + 28: 8687, + 35: 2197, + 13: 980, + 31: 5303, + 27: 3002, + 21: 7246, + 20: 4800, + 15: 1670, + 19: 4345, + 23: 7919, + 29: 4449, + 26: 9503, + 22: 3977, + 18: 3857, + 11: 599, + 17: 2168, + 30: 5183, + 10: 346, + 14: 1322, + 8: 145, + 12: 495, + 6: 54, + 9: 201, + 7: 68, + 5: 37, + 4: 8, + 3: 5, + 0: 1, + 2: 2, + 1: 2, + }, + ("SumOfOdds", 7, 6): { + 31: 7294, + 28: 10769, + 29: 5124, + 25: 7570, + 26: 9650, + 20: 3690, + 30: 8537, + 24: 5818, + 19: 2712, + 21: 5469, + 23: 7084, + 33: 7232, + 18: 2465, + 35: 4969, + 27: 2863, + 17: 1177, + 14: 665, + 13: 480, + 22: 2955, + 15: 993, + 11: 287, + 16: 1639, + 10: 148, + 12: 238, + 5: 12, + 8: 40, + 9: 79, + 6: 19, + 7: 17, + 4: 3, + 2: 1, + 3: 1, + }, + ("SumOfOdds", 7, 7): { + 19: 1630, + 26: 9063, + 30: 11962, + 20: 2708, + 35: 9107, + 16: 885, + 31: 8823, + 28: 11070, + 33: 10174, + 23: 5761, + 24: 4413, + 17: 619, + 29: 4944, + 22: 1979, + 25: 7651, + 13: 225, + 27: 2410, + 21: 3931, + 15: 520, + 18: 1499, + 11: 123, + 12: 88, + 14: 292, + 9: 24, + 10: 62, + 8: 14, + 6: 9, + 7: 7, + 4: 3, + 5: 4, + }, + ("SumOfOdds", 7, 8): { + 33: 12445, + 35: 14140, + 30: 14871, + 29: 4570, + 23: 4230, + 31: 9462, + 26: 7674, + 15: 303, + 19: 911, + 25: 7288, + 18: 919, + 21: 2592, + 28: 11038, + 16: 456, + 20: 1916, + 27: 1973, + 24: 3297, + 22: 1227, + 17: 322, + 14: 120, + 11: 48, + 13: 98, + 9: 8, + 10: 39, + 8: 9, + 12: 41, + 0: 1, + 6: 2, + }, + ("SumOfOdds", 8, 1): { + 1: 1044, + 17: 4595, + 16: 5205, + 9: 7107, + 14: 6878, + 13: 6521, + 5: 3542, + 11: 7580, + 18: 3437, + 2: 1248, + 7: 5127, + 19: 3115, + 15: 5596, + 12: 7278, + 20: 2333, + 10: 6937, + 21: 1887, + 6: 5091, + 3: 1858, + 4: 2641, + 8: 6002, + 0: 378, + 24: 829, + 22: 1354, + 29: 103, + 26: 395, + 25: 463, + 23: 962, + 27: 236, + 28: 128, + 31: 46, + 30: 49, + 33: 9, + 32: 18, + 35: 1, + 36: 3, + 34: 3, + 38: 1, + }, + ("SumOfOdds", 8, 2): { + 17: 6885, + 14: 5466, + 23: 4676, + 16: 6218, + 8: 1212, + 13: 4133, + 27: 2787, + 18: 6191, + 21: 6155, + 9: 1946, + 26: 3036, + 25: 3414, + 19: 7293, + 11: 2990, + 12: 3804, + 7: 900, + 15: 5383, + 22: 6139, + 20: 6332, + 32: 520, + 24: 5102, + 10: 2215, + 29: 1691, + 2: 45, + 28: 1650, + 6: 675, + 30: 864, + 5: 337, + 35: 32, + 33: 257, + 3: 128, + 31: 801, + 34: 301, + 36: 100, + 0: 23, + 4: 215, + 1: 49, + 38: 29, + 40: 6, + }, + ("SumOfOdds", 8, 3): { + 21: 6969, + 33: 1451, + 26: 6224, + 20: 5410, + 22: 6440, + 18: 4806, + 19: 6137, + 25: 5103, + 9: 652, + 31: 3023, + 23: 6079, + 14: 2793, + 17: 4333, + 15: 2967, + 12: 1570, + 10: 812, + 8: 427, + 29: 4385, + 5: 96, + 38: 289, + 34: 1120, + 32: 1454, + 13: 2026, + 27: 4784, + 30: 2256, + 24: 7157, + 36: 707, + 35: 375, + 16: 4132, + 11: 1306, + 28: 4085, + 6: 195, + 7: 258, + 40: 58, + 4: 59, + 2: 11, + 1: 11, + 3: 37, + 0: 3, + }, + ("SumOfOdds", 8, 4): { + 21: 5745, + 19: 4245, + 15: 1461, + 20: 3884, + 33: 3862, + 36: 2079, + 22: 4858, + 29: 6408, + 18: 3110, + 32: 2327, + 24: 6969, + 26: 7943, + 27: 5213, + 25: 5462, + 17: 2281, + 23: 5931, + 30: 3992, + 13: 828, + 31: 6210, + 38: 1180, + 34: 2510, + 35: 1308, + 16: 2324, + 28: 6390, + 11: 509, + 12: 601, + 9: 192, + 14: 1230, + 10: 298, + 40: 337, + 5: 20, + 8: 128, + 7: 80, + 6: 61, + 3: 11, + 1: 3, + 4: 9, + 2: 1, + }, + ("SumOfOdds", 8, 5): { + 30: 5913, + 25: 5122, + 36: 3948, + 34: 3853, + 29: 6868, + 16: 1156, + 33: 6688, + 28: 7567, + 38: 2940, + 31: 8385, + 35: 3514, + 22: 3204, + 27: 4802, + 26: 7734, + 18: 1663, + 15: 753, + 24: 5327, + 19: 2326, + 21: 3892, + 23: 4850, + 17: 1077, + 20: 2586, + 11: 205, + 40: 1312, + 32: 2956, + 14: 495, + 13: 371, + 12: 208, + 10: 110, + 9: 62, + 4: 6, + 7: 20, + 3: 4, + 5: 15, + 6: 17, + 8: 48, + 1: 3, + }, + ("SumOfOdds", 8, 6): { + 33: 9446, + 35: 6507, + 29: 6546, + 34: 4622, + 32: 2924, + 27: 3588, + 38: 5286, + 31: 9459, + 22: 1931, + 26: 6417, + 36: 5901, + 28: 7465, + 23: 3410, + 25: 4312, + 19: 1215, + 30: 7060, + 21: 2361, + 24: 3816, + 40: 3186, + 14: 226, + 20: 1581, + 18: 966, + 17: 543, + 15: 328, + 16: 546, + 10: 30, + 13: 153, + 12: 62, + 11: 57, + 7: 3, + 8: 20, + 6: 8, + 9: 22, + 5: 2, + 4: 1, + }, + ("SumOfOdds", 8, 7): { + 23: 2239, + 35: 9851, + 31: 9499, + 33: 10568, + 28: 6608, + 30: 7550, + 36: 7726, + 26: 4869, + 38: 8073, + 40: 6294, + 34: 5082, + 27: 2522, + 18: 452, + 29: 5348, + 20: 945, + 22: 1065, + 32: 2682, + 15: 157, + 24: 2332, + 25: 3456, + 21: 1439, + 13: 69, + 19: 568, + 16: 238, + 17: 211, + 12: 16, + 8: 2, + 9: 9, + 14: 86, + 10: 14, + 11: 27, + 6: 2, + 7: 1, + }, + ("SumOfOdds", 8, 8): { + 35: 12876, + 38: 10622, + 33: 11230, + 40: 11063, + 36: 8889, + 29: 3977, + 34: 4830, + 31: 8466, + 30: 7469, + 28: 5138, + 23: 1371, + 16: 110, + 24: 1483, + 22: 581, + 21: 792, + 25: 2461, + 20: 523, + 27: 1712, + 32: 2248, + 14: 30, + 26: 3464, + 17: 87, + 19: 278, + 18: 198, + 9: 4, + 15: 54, + 12: 11, + 13: 20, + 4: 1, + 8: 2, + 11: 9, + 10: 1, + }, + ("SumOfEvens", 1, 1): {4: 16854, 0: 49585, 6: 16828, 2: 16733}, + ("SumOfEvens", 1, 2): {0: 33244, 6: 27644, 4: 28025, 2: 11087}, + ("SumOfEvens", 1, 3): {6: 35384, 4: 35040, 0: 22259, 2: 7317}, + ("SumOfEvens", 1, 4): {6: 45838, 4: 29418, 0: 18511, 2: 6233}, + ("SumOfEvens", 1, 5): {4: 24510, 6: 54916, 2: 5146, 0: 15428}, + ("SumOfEvens", 1, 6): {6: 62703, 4: 20115, 2: 4255, 0: 12927}, + ("SumOfEvens", 1, 7): {0: 10650, 6: 68761, 4: 17087, 2: 3502}, + ("SumOfEvens", 1, 8): {0: 8911, 6: 73853, 4: 14227, 2: 3009}, + ("SumOfEvens", 2, 1): {4: 19538, 0: 25229, 10: 5607, 2: 16545, 6: 21987, 8: 8263, 12: 2831}, + ("SumOfEvens", 2, 2): {6: 24451, 10: 15400, 4: 19661, 8: 13966, 12: 7840, 0: 11179, 2: 7503}, + ("SumOfEvens", 2, 3): {10: 24736, 8: 17887, 12: 12277, 6: 20647, 4: 16354, 0: 4850, 2: 3249}, + ("SumOfEvens", 2, 4): {10: 26976, 6: 20711, 4: 11219, 12: 21117, 0: 3419, 8: 14290, 2: 2268}, + ("SumOfEvens", 2, 5): {8: 11641, 6: 19247, 4: 7910, 12: 30369, 10: 26842, 0: 2376, 2: 1615}, + ("SumOfEvens", 2, 6): {6: 17810, 12: 39086, 8: 9468, 10: 25582, 4: 5313, 0: 1649, 2: 1092}, + ("SumOfEvens", 2, 7): {12: 47388, 10: 23307, 6: 15965, 8: 7645, 4: 3790, 0: 1122, 2: 783}, + ("SumOfEvens", 2, 8): {12: 54703, 10: 20879, 8: 6462, 6: 14006, 4: 2618, 2: 538, 0: 794}, + ("SumOfEvens", 3, 1): { + 2: 12516, + 0: 12538, + 4: 16530, + 8: 13745, + 10: 11209, + 6: 21270, + 14: 2828, + 16: 1389, + 12: 7524, + 18: 451, + }, + ("SumOfEvens", 3, 2): { + 10: 18955, + 12: 15021, + 4: 10459, + 16: 6476, + 14: 8937, + 8: 15032, + 2: 3738, + 6: 15644, + 0: 3666, + 18: 2072, + }, + ("SumOfEvens", 3, 3): { + 8: 12295, + 6: 8576, + 4: 5572, + 10: 20247, + 18: 4316, + 14: 15953, + 12: 18001, + 16: 12864, + 2: 1093, + 0: 1083, + }, + ("SumOfEvens", 3, 4): { + 12: 18975, + 4: 3238, + 8: 8218, + 10: 17232, + 0: 642, + 14: 15832, + 16: 18749, + 18: 9594, + 6: 6844, + 2: 676, + }, + ("SumOfEvens", 3, 5): { + 16: 21954, + 12: 19533, + 14: 14402, + 10: 13927, + 18: 16784, + 8: 5720, + 6: 5105, + 4: 1825, + 2: 377, + 0: 373, + }, + ("SumOfEvens", 3, 6): { + 16: 23882, + 14: 12940, + 18: 24491, + 12: 19070, + 10: 10614, + 8: 3796, + 6: 3732, + 4: 1064, + 0: 195, + 2: 216, + }, + ("SumOfEvens", 3, 7): { + 18: 32287, + 16: 24254, + 12: 18146, + 10: 8145, + 8: 2534, + 6: 2787, + 14: 10985, + 4: 613, + 0: 126, + 2: 123, + }, + ("SumOfEvens", 3, 8): {12: 16926, 10: 5777, 18: 40557, 14: 9402, 16: 23114, 8: 1718, 6: 2012, 0: 68, 4: 356, 2: 70}, + ("SumOfEvens", 4, 1): { + 8: 15427, + 4: 12405, + 14: 6828, + 0: 6214, + 10: 14158, + 12: 11354, + 16: 4295, + 6: 17434, + 2: 8516, + 18: 2141, + 20: 798, + 22: 338, + 24: 92, + }, + ("SumOfEvens", 4, 2): { + 12: 15715, + 14: 14104, + 10: 15154, + 18: 8084, + 8: 10702, + 16: 12485, + 2: 1632, + 0: 1236, + 22: 2382, + 20: 4536, + 4: 4894, + 6: 8468, + 24: 608, + }, + ("SumOfEvens", 4, 3): { + 14: 16224, + 16: 17484, + 20: 10518, + 22: 6099, + 18: 13847, + 8: 5715, + 2: 312, + 10: 10269, + 4: 1646, + 24: 1611, + 12: 12879, + 6: 3135, + 0: 261, + }, + ("SumOfEvens", 4, 4): { + 14: 12763, + 16: 17947, + 20: 13338, + 4: 842, + 22: 11215, + 18: 16566, + 12: 10298, + 8: 3179, + 10: 7096, + 24: 4534, + 6: 1945, + 2: 159, + 0: 118, + }, + ("SumOfEvens", 4, 5): { + 24: 9273, + 16: 16546, + 10: 4716, + 22: 16111, + 20: 14172, + 18: 18045, + 14: 9638, + 12: 8022, + 6: 1181, + 4: 395, + 8: 1765, + 0: 56, + 2: 80, + }, + ("SumOfEvens", 4, 6): { + 6: 734, + 22: 20013, + 18: 18805, + 14: 7068, + 20: 13848, + 24: 15118, + 16: 14021, + 12: 6097, + 10: 3003, + 8: 1036, + 4: 192, + 0: 31, + 2: 34, + }, + ("SumOfEvens", 4, 7): { + 22: 21947, + 16: 11590, + 20: 12601, + 24: 22395, + 18: 18952, + 12: 4654, + 6: 400, + 14: 4930, + 10: 1826, + 8: 583, + 2: 26, + 4: 80, + 0: 16, + }, + ("SumOfEvens", 4, 8): { + 22: 23056, + 18: 18203, + 14: 3386, + 20: 11505, + 24: 29714, + 16: 8943, + 12: 3395, + 10: 1156, + 8: 314, + 6: 243, + 4: 63, + 2: 15, + 0: 7, + }, + ("SumOfEvens", 5, 1): { + 16: 7574, + 10: 14656, + 4: 8648, + 12: 13468, + 2: 5181, + 18: 4873, + 14: 10245, + 0: 3192, + 24: 605, + 6: 13373, + 20: 2581, + 8: 13964, + 26: 198, + 28: 69, + 22: 1363, + 30: 10, + }, + ("SumOfEvens", 5, 2): { + 16: 14674, + 20: 9742, + 12: 12184, + 14: 13824, + 18: 12124, + 10: 9910, + 6: 4054, + 24: 4025, + 22: 6877, + 26: 2056, + 8: 6336, + 0: 405, + 28: 808, + 4: 2149, + 2: 663, + 30: 169, + }, + ("SumOfEvens", 5, 3): { + 20: 15282, + 10: 4446, + 24: 9361, + 16: 13128, + 26: 5826, + 12: 6558, + 14: 10339, + 8: 2217, + 18: 14686, + 22: 13294, + 30: 532, + 6: 1037, + 28: 2644, + 4: 501, + 2: 88, + 0: 61, + }, + ("SumOfEvens", 5, 4): { + 24: 12896, + 28: 6646, + 18: 12724, + 20: 14710, + 16: 10437, + 22: 16005, + 26: 9761, + 12: 4093, + 14: 6555, + 10: 2340, + 4: 222, + 30: 2105, + 0: 18, + 6: 471, + 8: 992, + 2: 25, + }, + ("SumOfEvens", 5, 5): { + 24: 15490, + 18: 10297, + 16: 7635, + 22: 16826, + 28: 11323, + 20: 12344, + 26: 12235, + 14: 4006, + 30: 5102, + 8: 464, + 6: 259, + 10: 1369, + 12: 2559, + 2: 12, + 0: 7, + 4: 72, + }, + ("SumOfEvens", 5, 6): { + 24: 17286, + 28: 15274, + 16: 5274, + 30: 9604, + 18: 8224, + 26: 13565, + 22: 16041, + 14: 2381, + 20: 9688, + 10: 671, + 12: 1618, + 8: 212, + 6: 124, + 4: 29, + 2: 5, + 0: 4, + }, + ("SumOfEvens", 5, 7): { + 26: 13349, + 20: 7478, + 22: 13863, + 16: 3465, + 30: 15365, + 24: 18114, + 28: 19048, + 18: 6367, + 14: 1478, + 6: 52, + 12: 973, + 8: 102, + 10: 330, + 4: 12, + 0: 3, + 2: 1, + }, + ("SumOfEvens", 5, 8): { + 28: 21211, + 30: 22142, + 26: 12500, + 24: 18376, + 22: 11699, + 20: 5406, + 18: 4912, + 14: 771, + 16: 2197, + 12: 537, + 10: 172, + 6: 22, + 8: 45, + 4: 9, + 0: 1, + }, + ("SumOfEvens", 6, 1): { + 12: 13855, + 8: 11527, + 6: 9535, + 14: 12217, + 10: 13220, + 18: 7641, + 20: 5155, + 4: 5715, + 16: 10036, + 2: 3110, + 22: 3134, + 24: 1769, + 0: 1657, + 26: 882, + 28: 364, + 32: 46, + 30: 125, + 34: 9, + 36: 3, + }, + ("SumOfEvens", 6, 2): { + 16: 12112, + 14: 10495, + 18: 12962, + 20: 12458, + 22: 10842, + 4: 936, + 30: 1777, + 12: 8107, + 10: 5781, + 24: 8362, + 28: 3560, + 26: 5714, + 8: 3286, + 34: 279, + 6: 1999, + 0: 149, + 32: 841, + 2: 295, + 36: 45, + }, + ("SumOfEvens", 6, 3): { + 34: 1114, + 26: 11930, + 28: 8967, + 16: 7714, + 18: 10098, + 22: 13809, + 24: 13594, + 20: 12628, + 10: 1732, + 12: 3009, + 30: 5778, + 32: 3126, + 14: 5066, + 8: 774, + 6: 309, + 36: 205, + 4: 127, + 2: 12, + 0: 8, + }, + ("SumOfEvens", 6, 4): { + 16: 4678, + 26: 13991, + 20: 9551, + 24: 13471, + 18: 6764, + 32: 6534, + 4: 36, + 34: 3599, + 28: 12906, + 22: 12530, + 30: 9662, + 10: 774, + 14: 2613, + 12: 1479, + 36: 987, + 2: 13, + 8: 287, + 6: 122, + 0: 3, + }, + ("SumOfEvens", 6, 5): { + 32: 9788, + 24: 11810, + 34: 7399, + 30: 12927, + 26: 13874, + 28: 15232, + 16: 2702, + 18: 4392, + 20: 6604, + 22: 9916, + 36: 2699, + 14: 1416, + 12: 740, + 10: 322, + 6: 51, + 8: 108, + 4: 15, + 0: 2, + 2: 3, + }, + ("SumOfEvens", 6, 6): { + 26: 11838, + 22: 7418, + 30: 15534, + 34: 11679, + 36: 5973, + 24: 9870, + 28: 15982, + 20: 4214, + 32: 12014, + 18: 2686, + 12: 322, + 10: 156, + 8: 52, + 14: 664, + 16: 1568, + 6: 26, + 4: 2, + 2: 1, + 0: 1, + }, + ("SumOfEvens", 6, 7): { + 30: 17083, + 28: 15301, + 22: 5154, + 26: 9426, + 32: 13001, + 20: 2576, + 34: 15604, + 24: 8221, + 36: 10524, + 18: 1673, + 16: 848, + 14: 336, + 12: 179, + 10: 53, + 6: 9, + 8: 11, + 4: 1, + }, + ("SumOfEvens", 6, 8): { + 22: 3449, + 36: 16329, + 26: 7209, + 32: 12842, + 30: 18101, + 34: 18840, + 28: 13662, + 20: 1500, + 24: 6361, + 18: 984, + 16: 453, + 14: 154, + 12: 87, + 10: 22, + 8: 4, + 4: 1, + 6: 2, + }, + ("SumOfEvens", 7, 1): { + 8: 8939, + 24: 3564, + 16: 11578, + 12: 12690, + 10: 11183, + 18: 9725, + 4: 3653, + 6: 6451, + 20: 7614, + 14: 12463, + 30: 591, + 22: 5306, + 28: 1178, + 26: 2087, + 32: 276, + 0: 780, + 2: 1804, + 34: 79, + 38: 9, + 36: 28, + 42: 1, + 40: 1, + }, + ("SumOfEvens", 7, 2): { + 20: 11747, + 22: 12101, + 18: 10694, + 30: 4969, + 34: 1637, + 12: 4933, + 28: 7140, + 10: 3020, + 16: 9103, + 14: 7121, + 26: 9407, + 40: 95, + 32: 2990, + 24: 10947, + 8: 1631, + 6: 866, + 36: 742, + 38: 279, + 4: 405, + 2: 118, + 0: 44, + 42: 11, + }, + ("SumOfEvens", 7, 3): { + 28: 12644, + 18: 5753, + 22: 10305, + 30: 10884, + 24: 12043, + 34: 5494, + 26: 13153, + 32: 8457, + 20: 8013, + 36: 3227, + 12: 1178, + 16: 3620, + 14: 2216, + 38: 1526, + 40: 457, + 42: 73, + 10: 585, + 8: 255, + 4: 32, + 6: 78, + 0: 4, + 2: 3, + }, + ("SumOfEvens", 7, 4): { + 34: 10022, + 20: 4695, + 36: 6630, + 38: 4042, + 30: 13018, + 26: 11605, + 24: 9234, + 22: 6948, + 32: 11907, + 28: 12907, + 40: 1978, + 10: 212, + 16: 1818, + 18: 3010, + 42: 424, + 14: 940, + 12: 482, + 8: 84, + 6: 33, + 2: 3, + 4: 7, + 0: 1, + }, + ("SumOfEvens", 7, 5): { + 34: 13412, + 36: 10366, + 24: 6303, + 30: 12713, + 26: 8816, + 40: 4734, + 22: 4347, + 38: 7212, + 32: 13273, + 28: 11561, + 20: 2543, + 18: 1526, + 42: 1564, + 14: 395, + 16: 920, + 12: 186, + 8: 31, + 10: 80, + 4: 4, + 6: 14, + }, + ("SumOfEvens", 7, 6): { + 40: 8464, + 32: 12798, + 36: 13346, + 28: 9389, + 38: 10011, + 24: 4176, + 34: 15385, + 30: 11291, + 26: 6057, + 22: 2683, + 42: 3605, + 20: 1359, + 18: 819, + 14: 148, + 16: 359, + 10: 32, + 12: 68, + 8: 4, + 6: 5, + 4: 1, + }, + ("SumOfEvens", 7, 7): { + 34: 15613, + 18: 390, + 42: 7149, + 36: 15702, + 38: 12021, + 30: 9525, + 40: 12478, + 32: 11106, + 26: 3913, + 28: 7007, + 20: 681, + 24: 2671, + 22: 1511, + 14: 69, + 16: 135, + 8: 2, + 12: 23, + 10: 3, + 6: 1, + }, + ("SumOfEvens", 7, 8): { + 40: 16137, + 26: 2459, + 36: 16970, + 30: 7669, + 38: 12599, + 32: 9076, + 42: 12085, + 34: 14812, + 24: 1645, + 28: 5058, + 22: 824, + 20: 339, + 18: 204, + 14: 24, + 16: 77, + 12: 18, + 10: 4, + }, + ("SumOfEvens", 8, 1): { + 24: 5501, + 14: 11696, + 26: 3771, + 28: 2435, + 16: 11862, + 18: 11145, + 10: 8598, + 32: 813, + 6: 4344, + 0: 373, + 12: 10648, + 2: 1020, + 22: 7414, + 20: 9463, + 8: 6532, + 30: 1376, + 4: 2316, + 38: 73, + 34: 408, + 36: 180, + 40: 24, + 42: 4, + 44: 3, + 46: 1, + }, + ("SumOfEvens", 8, 2): { + 38: 1519, + 26: 10879, + 16: 6135, + 20: 9772, + 30: 8043, + 32: 6058, + 28: 9711, + 18: 7865, + 24: 11148, + 34: 4215, + 22: 10922, + 10: 1536, + 14: 4098, + 36: 2718, + 12: 2761, + 8: 772, + 6: 386, + 42: 342, + 40: 769, + 4: 141, + 2: 45, + 44: 107, + 46: 37, + 0: 17, + 48: 4, + }, + ("SumOfEvens", 8, 3): { + 30: 12249, + 28: 11561, + 24: 8306, + 36: 7860, + 16: 1616, + 40: 3315, + 22: 6221, + 38: 5627, + 34: 10070, + 18: 2630, + 32: 11747, + 20: 4428, + 26: 10158, + 42: 1741, + 14: 874, + 44: 669, + 12: 430, + 46: 173, + 10: 187, + 8: 65, + 4: 5, + 6: 39, + 48: 28, + 2: 1, + }, + ("SumOfEvens", 8, 4): { + 40: 7009, + 34: 12243, + 28: 9047, + 32: 12344, + 38: 9623, + 30: 10811, + 16: 621, + 42: 4569, + 26: 6864, + 44: 2425, + 18: 1160, + 36: 11307, + 22: 3304, + 48: 216, + 24: 4882, + 10: 59, + 46: 1035, + 20: 1982, + 14: 294, + 6: 8, + 12: 167, + 8: 26, + 2: 2, + 4: 1, + 0: 1, + }, + ("SumOfEvens", 8, 5): { + 40: 10958, + 36: 12458, + 30: 8178, + 34: 12180, + 38: 12260, + 24: 2712, + 42: 7933, + 28: 6229, + 32: 10485, + 14: 108, + 22: 1654, + 46: 2920, + 26: 4229, + 20: 918, + 44: 5192, + 48: 814, + 16: 222, + 18: 467, + 8: 11, + 6: 3, + 4: 1, + 10: 17, + 12: 51, + }, + ("SumOfEvens", 8, 6): { + 36: 12064, + 48: 2382, + 26: 2376, + 24: 1455, + 44: 8361, + 28: 3916, + 40: 13920, + 42: 11359, + 38: 12862, + 32: 7846, + 46: 5912, + 30: 5727, + 34: 10367, + 18: 208, + 16: 78, + 22: 753, + 20: 361, + 14: 30, + 10: 6, + 12: 15, + 6: 1, + 8: 1, + }, + ("SumOfEvens", 8, 7): { + 34: 8619, + 42: 13899, + 32: 5303, + 36: 10651, + 30: 3778, + 46: 10004, + 28: 2390, + 38: 12089, + 40: 14999, + 44: 10574, + 48: 5042, + 8: 3, + 26: 1228, + 24: 767, + 22: 381, + 18: 74, + 20: 152, + 16: 27, + 12: 5, + 14: 11, + 10: 4, + }, + ("SumOfEvens", 8, 8): { + 40: 14996, + 38: 10354, + 46: 13670, + 42: 16214, + 48: 9039, + 30: 2458, + 32: 3565, + 36: 8996, + 44: 11803, + 34: 6358, + 26: 611, + 28: 1321, + 24: 352, + 22: 163, + 18: 36, + 20: 51, + 16: 6, + 14: 3, + 10: 4, + }, + ("DoubleThreesAndFours", 1, 1): {6: 16591, 8: 16660, 0: 66749}, + ("DoubleThreesAndFours", 1, 2): {0: 44675, 6: 27694, 8: 27631}, + ("DoubleThreesAndFours", 1, 3): {8: 35147, 6: 35261, 0: 29592}, + ("DoubleThreesAndFours", 1, 4): {8: 45993, 0: 24601, 6: 29406}, + ("DoubleThreesAndFours", 1, 5): {0: 20499, 8: 55081, 6: 24420}, + ("DoubleThreesAndFours", 1, 6): {8: 62657, 6: 20227, 0: 17116}, + ("DoubleThreesAndFours", 1, 7): {8: 68747, 6: 17060, 0: 14193}, + ("DoubleThreesAndFours", 1, 8): {6: 13924, 8: 74099, 0: 11977}, + ("DoubleThreesAndFours", 2, 1): {0: 44382, 6: 22191, 14: 5568, 12: 2892, 8: 22251, 16: 2716}, + ("DoubleThreesAndFours", 2, 2): {14: 15403, 0: 19720, 6: 24652, 12: 7693, 8: 24891, 16: 7641}, + ("DoubleThreesAndFours", 2, 3): {8: 20929, 14: 24721, 16: 12376, 0: 8765, 12: 12201, 6: 21008}, + ("DoubleThreesAndFours", 2, 4): {14: 26935, 6: 14466, 16: 21136, 8: 22828, 12: 8471, 0: 6164}, + ("DoubleThreesAndFours", 2, 5): {8: 22620, 14: 26822, 12: 6057, 16: 30189, 6: 10005, 0: 4307}, + ("DoubleThreesAndFours", 2, 6): {14: 25326, 16: 39078, 0: 2879, 12: 4204, 8: 21466, 6: 7047}, + ("DoubleThreesAndFours", 2, 7): {16: 47373, 8: 19698, 14: 23404, 6: 4637, 12: 2846, 0: 2042}, + ("DoubleThreesAndFours", 2, 8): {16: 54542, 14: 20907, 0: 1385, 8: 17795, 6: 3373, 12: 1998}, + ("DoubleThreesAndFours", 3, 1): { + 8: 22138, + 0: 29378, + 24: 480, + 6: 22335, + 14: 11232, + 12: 5551, + 16: 5702, + 22: 1429, + 20: 1344, + 18: 411, + }, + ("DoubleThreesAndFours", 3, 2): { + 6: 16518, + 0: 8894, + 14: 20757, + 24: 2162, + 16: 10163, + 8: 16277, + 12: 10334, + 20: 6399, + 18: 2102, + 22: 6394, + }, + ("DoubleThreesAndFours", 3, 3): { + 20: 12900, + 6: 9270, + 18: 4335, + 8: 9252, + 22: 13101, + 14: 21922, + 12: 11066, + 16: 11045, + 0: 2643, + 24: 4466, + }, + ("DoubleThreesAndFours", 3, 4): { + 14: 20310, + 16: 15697, + 8: 8330, + 12: 6223, + 6: 5443, + 20: 11695, + 24: 9679, + 22: 18521, + 0: 1523, + 18: 2579, + }, + ("DoubleThreesAndFours", 3, 5): { + 24: 16491, + 14: 16545, + 12: 3700, + 20: 9740, + 22: 22168, + 16: 18825, + 8: 7038, + 6: 3180, + 18: 1468, + 0: 845, + }, + ("DoubleThreesAndFours", 3, 6): { + 24: 24494, + 22: 23876, + 14: 12995, + 16: 20078, + 20: 7959, + 8: 5456, + 12: 2033, + 6: 1774, + 18: 836, + 0: 499, + }, + ("DoubleThreesAndFours", 3, 7): { + 14: 9997, + 24: 32693, + 22: 24010, + 16: 20149, + 20: 5970, + 6: 1005, + 8: 4244, + 0: 293, + 12: 1190, + 18: 449, + }, + ("DoubleThreesAndFours", 3, 8): { + 22: 23158, + 24: 40426, + 20: 4456, + 16: 19616, + 6: 598, + 14: 7514, + 8: 3029, + 12: 736, + 18: 289, + 0: 178, + }, + ("DoubleThreesAndFours", 4, 1): { + 0: 19809, + 22: 3661, + 6: 19538, + 14: 14835, + 8: 19765, + 16: 7377, + 12: 7513, + 20: 3787, + 24: 1312, + 18: 1239, + 28: 426, + 30: 317, + 32: 89, + 26: 332, + }, + ("DoubleThreesAndFours", 4, 2): { + 14: 18494, + 12: 9152, + 8: 9681, + 6: 9759, + 32: 582, + 20: 11442, + 24: 4411, + 16: 9182, + 22: 11245, + 28: 3481, + 30: 2486, + 18: 3796, + 26: 2317, + 0: 3972, + }, + ("DoubleThreesAndFours", 4, 3): { + 30: 6209, + 16: 6563, + 20: 15371, + 26: 6250, + 14: 12957, + 32: 1553, + 22: 15441, + 18: 5181, + 28: 9263, + 24: 6812, + 12: 6446, + 6: 3580, + 8: 3629, + 0: 745, + }, + ("DoubleThreesAndFours", 4, 4): { + 22: 18508, + 14: 10057, + 30: 11372, + 20: 11583, + 16: 7710, + 24: 10280, + 26: 4741, + 18: 2466, + 6: 1737, + 28: 10883, + 32: 4475, + 8: 2754, + 0: 371, + 12: 3063, + }, + ("DoubleThreesAndFours", 4, 5): { + 30: 16244, + 28: 10930, + 24: 14117, + 14: 6844, + 12: 1523, + 32: 9165, + 8: 1901, + 6: 827, + 22: 18097, + 16: 7733, + 0: 163, + 20: 8048, + 26: 3189, + 18: 1219, + }, + ("DoubleThreesAndFours", 4, 6): { + 24: 16773, + 22: 16364, + 30: 19782, + 32: 15340, + 26: 2088, + 28: 9736, + 16: 6958, + 12: 735, + 20: 5399, + 8: 1284, + 14: 4451, + 6: 427, + 18: 584, + 0: 79, + }, + ("DoubleThreesAndFours", 4, 7): { + 32: 22360, + 16: 5625, + 24: 18879, + 28: 8204, + 22: 13634, + 14: 2915, + 30: 22055, + 8: 804, + 20: 3378, + 26: 1283, + 18: 284, + 12: 341, + 6: 189, + 0: 49, + }, + ("DoubleThreesAndFours", 4, 8): { + 20: 2145, + 32: 29918, + 30: 22891, + 22: 10960, + 24: 19444, + 28: 6551, + 26: 825, + 16: 4633, + 14: 1776, + 8: 471, + 12: 162, + 6: 81, + 18: 123, + 0: 20, + }, + ("DoubleThreesAndFours", 5, 1): { + 12: 8304, + 6: 16411, + 16: 8295, + 18: 2097, + 22: 6092, + 14: 16464, + 0: 13122, + 20: 6145, + 24: 2291, + 8: 16451, + 28: 1554, + 26: 1026, + 30: 1078, + 34: 123, + 32: 320, + 36: 136, + 38: 72, + 40: 19, + }, + ("DoubleThreesAndFours", 5, 2): { + 22: 12832, + 16: 6786, + 14: 13562, + 28: 7847, + 34: 1650, + 20: 12668, + 6: 5469, + 12: 6656, + 0: 1676, + 26: 5358, + 18: 4316, + 8: 5318, + 32: 2093, + 24: 5636, + 30: 5450, + 36: 1673, + 38: 832, + 40: 178, + }, + ("DoubleThreesAndFours", 5, 3): { + 20: 11385, + 26: 9086, + 24: 6096, + 30: 9486, + 14: 6384, + 12: 3259, + 28: 13665, + 22: 11613, + 36: 5338, + 38: 2707, + 6: 1334, + 18: 3897, + 32: 4914, + 0: 223, + 34: 5404, + 8: 1388, + 16: 3268, + 40: 553, + }, + ("DoubleThreesAndFours", 5, 4): { + 30: 14319, + 14: 4130, + 22: 11374, + 20: 7322, + 26: 5595, + 28: 13488, + 24: 6778, + 34: 5245, + 38: 6576, + 36: 8341, + 8: 836, + 40: 2124, + 32: 7169, + 16: 3174, + 18: 1558, + 12: 1337, + 6: 539, + 0: 95, + }, + ("DoubleThreesAndFours", 5, 5): { + 34: 4446, + 28: 11201, + 30: 16810, + 32: 10248, + 24: 7483, + 38: 11129, + 36: 9980, + 20: 4128, + 26: 3289, + 40: 5010, + 14: 2318, + 22: 9485, + 8: 529, + 16: 2532, + 12: 537, + 18: 608, + 6: 229, + 0: 38, + }, + ("DoubleThreesAndFours", 5, 6): { + 30: 17020, + 38: 15569, + 34: 3326, + 40: 9391, + 24: 7336, + 32: 13519, + 36: 10243, + 22: 7062, + 28: 8349, + 16: 2019, + 20: 2231, + 26: 1815, + 12: 201, + 14: 1301, + 8: 260, + 18: 256, + 6: 86, + 0: 16, + }, + ("DoubleThreesAndFours", 5, 7): { + 34: 2268, + 38: 19248, + 32: 16368, + 16: 1354, + 40: 15233, + 24: 6675, + 18: 105, + 22: 4805, + 36: 9333, + 30: 15652, + 28: 5843, + 26: 957, + 8: 123, + 20: 1203, + 14: 710, + 12: 85, + 6: 31, + 0: 7, + }, + ("DoubleThreesAndFours", 5, 8): { + 40: 21990, + 36: 8113, + 24: 5723, + 32: 18163, + 38: 21064, + 30: 13694, + 28: 3938, + 22: 3183, + 34: 1518, + 16: 957, + 26: 458, + 14: 358, + 20: 677, + 8: 62, + 12: 38, + 18: 44, + 6: 18, + 0: 2, + }, + ("DoubleThreesAndFours", 6, 1): { + 0: 8738, + 22: 8265, + 20: 8158, + 28: 3123, + 8: 12988, + 26: 2034, + 24: 3198, + 6: 13463, + 12: 8147, + 14: 16506, + 30: 2139, + 16: 8267, + 18: 2801, + 32: 737, + 38: 251, + 36: 521, + 34: 482, + 42: 45, + 44: 31, + 40: 89, + 46: 16, + 48: 1, + }, + ("DoubleThreesAndFours", 6, 2): { + 20: 11349, + 18: 3691, + 30: 7553, + 40: 1118, + 16: 4479, + 26: 6877, + 8: 2801, + 14: 8843, + 22: 11356, + 28: 10790, + 24: 5588, + 34: 4398, + 6: 2934, + 42: 878, + 32: 3974, + 36: 4501, + 12: 4564, + 38: 2498, + 0: 784, + 46: 267, + 44: 700, + 48: 57, + }, + ("DoubleThreesAndFours", 6, 3): { + 30: 9057, + 28: 12114, + 38: 6065, + 36: 9738, + 34: 9548, + 6: 498, + 14: 2851, + 18: 2245, + 40: 3765, + 42: 3710, + 20: 6930, + 26: 8000, + 24: 4357, + 32: 6825, + 12: 1466, + 46: 1087, + 22: 6770, + 16: 1434, + 44: 2808, + 8: 492, + 0: 72, + 48: 168, + }, + ("DoubleThreesAndFours", 6, 4): { + 14: 1534, + 38: 10194, + 18: 698, + 30: 10836, + 32: 6720, + 42: 4836, + 36: 12511, + 40: 5366, + 26: 4164, + 44: 5640, + 46: 3626, + 34: 7926, + 24: 3611, + 28: 10039, + 20: 3603, + 6: 160, + 22: 5673, + 16: 1101, + 48: 992, + 8: 255, + 12: 491, + 0: 24, + }, + ("DoubleThreesAndFours", 6, 5): { + 40: 7833, + 28: 6985, + 46: 7219, + 36: 12190, + 38: 14163, + 34: 5449, + 32: 7047, + 30: 10494, + 44: 8161, + 24: 3099, + 42: 4738, + 26: 2099, + 22: 3827, + 48: 2739, + 16: 877, + 18: 244, + 20: 1755, + 14: 771, + 0: 8, + 12: 144, + 8: 113, + 6: 45, + }, + ("DoubleThreesAndFours", 6, 6): { + 38: 16439, + 44: 9477, + 36: 10342, + 40: 10795, + 48: 5932, + 30: 8697, + 42: 4008, + 26: 994, + 46: 11631, + 16: 539, + 28: 4300, + 22: 2383, + 32: 7204, + 20: 762, + 34: 3427, + 24: 2528, + 18: 96, + 14: 311, + 6: 19, + 8: 60, + 0: 4, + 12: 52, + }, + ("DoubleThreesAndFours", 6, 7): { + 32: 7113, + 42: 3210, + 44: 9660, + 46: 15581, + 38: 16374, + 48: 10353, + 40: 13795, + 30: 6708, + 36: 8028, + 24: 1921, + 34: 1922, + 20: 355, + 28: 2646, + 26: 437, + 22: 1401, + 16: 278, + 14: 145, + 8: 28, + 18: 31, + 6: 2, + 12: 11, + 0: 1, + }, + ("DoubleThreesAndFours", 6, 8): { + 46: 18638, + 30: 4988, + 40: 16076, + 24: 1352, + 38: 15017, + 48: 16432, + 36: 5846, + 32: 6450, + 44: 9045, + 20: 143, + 28: 1404, + 42: 2271, + 34: 1121, + 26: 160, + 16: 162, + 22: 812, + 14: 61, + 12: 9, + 8: 9, + 18: 4, + }, + ("DoubleThreesAndFours", 7, 1): { + 16: 7739, + 6: 10242, + 22: 9715, + 20: 9418, + 14: 15252, + 8: 10404, + 24: 4020, + 12: 7634, + 44: 141, + 0: 5803, + 18: 3195, + 30: 3270, + 40: 276, + 28: 4897, + 32: 1409, + 34: 1182, + 36: 1226, + 38: 668, + 42: 226, + 26: 3173, + 46: 71, + 48: 17, + 50: 16, + 54: 1, + 52: 5, + }, + ("DoubleThreesAndFours", 7, 2): { + 20: 8788, + 12: 2776, + 28: 11132, + 44: 2245, + 38: 4228, + 34: 6959, + 42: 2873, + 18: 2867, + 36: 7000, + 32: 5286, + 0: 357, + 30: 7900, + 40: 2927, + 26: 7287, + 16: 2846, + 22: 8736, + 46: 1083, + 24: 4687, + 14: 5631, + 6: 1500, + 48: 593, + 8: 1462, + 50: 446, + 56: 17, + 52: 276, + 54: 98, + }, + ("DoubleThreesAndFours", 7, 3): { + 42: 7821, + 36: 10081, + 34: 10088, + 30: 6641, + 38: 7494, + 50: 2457, + 28: 8269, + 26: 5630, + 32: 6333, + 40: 6987, + 52: 1356, + 44: 6306, + 20: 3613, + 16: 593, + 24: 2466, + 48: 2709, + 46: 3838, + 18: 1218, + 12: 568, + 22: 3517, + 6: 177, + 8: 170, + 54: 442, + 14: 1144, + 0: 14, + 56: 68, + }, + ("DoubleThreesAndFours", 7, 4): { + 46: 7244, + 48: 4033, + 30: 6379, + 44: 10218, + 20: 1553, + 42: 8597, + 28: 5838, + 52: 3713, + 38: 9398, + 50: 3948, + 32: 4601, + 40: 6630, + 36: 10741, + 34: 6715, + 22: 2413, + 24: 1659, + 26: 2455, + 54: 1886, + 16: 409, + 12: 175, + 56: 464, + 14: 499, + 18: 333, + 8: 51, + 6: 43, + 0: 5, + }, + ("DoubleThreesAndFours", 7, 5): { + 44: 11990, + 48: 5993, + 32: 3707, + 36: 8930, + 28: 3284, + 18: 109, + 42: 6888, + 50: 4653, + 38: 10182, + 52: 6259, + 46: 11137, + 54: 4781, + 34: 3996, + 56: 1472, + 22: 1391, + 40: 6767, + 26: 963, + 24: 1144, + 16: 242, + 30: 5190, + 20: 603, + 6: 16, + 14: 225, + 8: 23, + 12: 49, + 0: 6, + }, + ("DoubleThreesAndFours", 7, 6): { + 38: 9755, + 52: 8339, + 46: 14027, + 30: 3572, + 36: 6292, + 40: 7116, + 54: 8347, + 50: 4510, + 34: 2079, + 56: 3697, + 42: 5017, + 44: 11451, + 48: 8688, + 28: 1705, + 22: 755, + 24: 789, + 32: 3005, + 14: 65, + 20: 239, + 16: 134, + 26: 357, + 18: 36, + 8: 10, + 12: 15, + }, + ("DoubleThreesAndFours", 7, 7): { + 50: 3831, + 46: 15829, + 44: 9719, + 36: 4015, + 38: 8195, + 40: 7156, + 42: 3220, + 30: 2281, + 54: 12409, + 56: 7255, + 32: 2381, + 52: 9257, + 48: 11561, + 26: 133, + 22: 341, + 34: 923, + 28: 853, + 24: 452, + 20: 81, + 16: 60, + 18: 9, + 14: 27, + 12: 5, + 8: 5, + 6: 2, + }, + ("DoubleThreesAndFours", 7, 8): { + 56: 12116, + 52: 9418, + 38: 6452, + 48: 14055, + 32: 1809, + 54: 16183, + 30: 1357, + 50: 3002, + 36: 2363, + 46: 15616, + 40: 6757, + 42: 1859, + 44: 7554, + 24: 285, + 16: 30, + 34: 481, + 22: 175, + 14: 10, + 28: 379, + 20: 42, + 26: 55, + 8: 1, + 12: 1, + }, + ("DoubleThreesAndFours", 8, 1): { + 24: 4614, + 16: 6920, + 34: 2175, + 14: 13657, + 30: 4504, + 0: 3982, + 20: 10167, + 12: 6731, + 22: 10162, + 36: 2120, + 28: 6414, + 32: 2079, + 18: 3314, + 26: 4302, + 6: 7946, + 8: 7712, + 44: 379, + 38: 1218, + 40: 633, + 42: 533, + 50: 59, + 48: 108, + 46: 204, + 56: 7, + 52: 39, + 60: 1, + 54: 15, + 58: 5, + }, + ("DoubleThreesAndFours", 8, 2): { + 30: 7306, + 42: 5074, + 28: 9769, + 44: 4004, + 26: 6631, + 40: 4617, + 12: 1685, + 20: 6475, + 22: 6445, + 50: 1654, + 36: 8364, + 32: 5644, + 16: 1623, + 14: 3393, + 46: 2396, + 6: 749, + 34: 8035, + 24: 3639, + 38: 5473, + 54: 537, + 18: 2090, + 48: 1840, + 52: 1069, + 8: 735, + 58: 188, + 62: 29, + 56: 294, + 0: 161, + 60: 80, + 64: 1, + }, + ("DoubleThreesAndFours", 8, 3): { + 44: 8078, + 34: 8086, + 42: 9356, + 36: 8106, + 38: 6904, + 28: 4918, + 40: 7729, + 30: 4044, + 32: 4752, + 46: 5989, + 50: 5725, + 52: 4060, + 48: 6119, + 58: 1298, + 54: 2440, + 24: 1345, + 22: 1657, + 26: 3379, + 20: 1620, + 56: 1856, + 18: 582, + 6: 58, + 14: 525, + 64: 31, + 62: 167, + 60: 670, + 8: 53, + 12: 214, + 16: 233, + 0: 6, + }, + ("DoubleThreesAndFours", 8, 4): { + 42: 8437, + 48: 6657, + 44: 10354, + 54: 4862, + 36: 7211, + 34: 4515, + 50: 7755, + 52: 7763, + 56: 3204, + 60: 2271, + 30: 3188, + 20: 611, + 46: 8005, + 38: 6651, + 32: 2521, + 40: 5753, + 58: 2769, + 22: 950, + 24: 729, + 26: 1214, + 28: 2819, + 16: 151, + 62: 1044, + 14: 161, + 18: 137, + 64: 176, + 12: 56, + 8: 22, + 0: 1, + 6: 13, + }, + ("DoubleThreesAndFours", 8, 5): { + 52: 10531, + 60: 4703, + 54: 8556, + 40: 4470, + 44: 9760, + 36: 4863, + 18: 29, + 42: 5705, + 50: 7637, + 58: 4174, + 48: 6812, + 28: 1342, + 56: 4701, + 46: 9599, + 30: 2068, + 64: 852, + 38: 5795, + 62: 3095, + 24: 376, + 32: 1531, + 22: 458, + 34: 2192, + 26: 394, + 16: 60, + 20: 226, + 12: 12, + 14: 51, + 8: 6, + 6: 2, + }, + ("DoubleThreesAndFours", 8, 6): { + 62: 6075, + 44: 7896, + 50: 6139, + 54: 12058, + 60: 6904, + 64: 2228, + 58: 4472, + 38: 4423, + 46: 9936, + 48: 6877, + 52: 11631, + 56: 6986, + 42: 3493, + 36: 2900, + 40: 3520, + 22: 198, + 28: 607, + 30: 1238, + 34: 915, + 32: 1017, + 24: 216, + 26: 152, + 18: 8, + 20: 65, + 16: 27, + 14: 14, + 0: 2, + 12: 3, + }, + ("DoubleThreesAndFours", 8, 7): { + 56: 9724, + 60: 8403, + 54: 14541, + 38: 3201, + 50: 4302, + 52: 10602, + 44: 5588, + 40: 2855, + 46: 9100, + 58: 4125, + 62: 9808, + 36: 1437, + 48: 7192, + 32: 687, + 42: 1827, + 64: 5089, + 24: 110, + 30: 659, + 28: 234, + 22: 81, + 26: 28, + 34: 363, + 14: 6, + 16: 10, + 20: 24, + 8: 1, + 12: 1, + 6: 1, + 18: 1, + }, + ("DoubleThreesAndFours", 8, 8): { + 62: 13539, + 52: 8871, + 48: 7127, + 60: 9206, + 64: 9203, + 50: 2679, + 46: 7646, + 56: 12383, + 54: 15467, + 42: 851, + 30: 298, + 44: 3621, + 38: 2026, + 58: 3339, + 40: 2268, + 36: 703, + 32: 421, + 16: 4, + 34: 150, + 28: 99, + 22: 36, + 20: 4, + 24: 46, + 26: 12, + 8: 1, + }, + ("QuadrupleOnesAndTwos", 1, 1): {8: 16630, 0: 66567, 4: 16803}, + ("QuadrupleOnesAndTwos", 1, 2): {4: 27448, 0: 44809, 8: 27743}, + ("QuadrupleOnesAndTwos", 1, 3): {0: 37100, 4: 23184, 8: 39716}, + ("QuadrupleOnesAndTwos", 1, 4): {0: 30963, 8: 49816, 4: 19221}, + ("QuadrupleOnesAndTwos", 1, 5): {8: 58605, 4: 16079, 0: 25316}, + ("QuadrupleOnesAndTwos", 1, 6): {0: 21505, 8: 65258, 4: 13237}, + ("QuadrupleOnesAndTwos", 1, 7): {0: 17676, 8: 71224, 4: 11100}, + ("QuadrupleOnesAndTwos", 1, 8): {0: 14971, 8: 75706, 4: 9323}, + ("QuadrupleOnesAndTwos", 2, 1): {0: 44566, 4: 22273, 8: 24842, 16: 2834, 12: 5485}, + ("QuadrupleOnesAndTwos", 2, 2): {0: 19963, 12: 15172, 16: 7713, 4: 24890, 8: 32262}, + ("QuadrupleOnesAndTwos", 2, 3): {0: 13766, 8: 34907, 16: 15630, 4: 17158, 12: 18539}, + ("QuadrupleOnesAndTwos", 2, 4): {8: 34465, 12: 19108, 16: 24903, 0: 9543, 4: 11981}, + ("QuadrupleOnesAndTwos", 2, 5): {16: 34144, 4: 8302, 8: 32470, 12: 18612, 0: 6472}, + ("QuadrupleOnesAndTwos", 2, 6): {16: 42762, 8: 29716, 12: 17216, 0: 4569, 4: 5737}, + ("QuadrupleOnesAndTwos", 2, 7): {12: 15756, 16: 50635, 8: 26489, 4: 3974, 0: 3146}, + ("QuadrupleOnesAndTwos", 2, 8): {12: 14167, 16: 57266, 0: 2265, 8: 23578, 4: 2724}, + ("QuadrupleOnesAndTwos", 3, 1): {12: 11557, 0: 29440, 8: 27747, 4: 22574, 16: 6892, 24: 459, 20: 1331}, + ("QuadrupleOnesAndTwos", 3, 2): {8: 26434, 0: 8857, 12: 22986, 4: 16295, 16: 16799, 24: 2148, 20: 6481}, + ("QuadrupleOnesAndTwos", 3, 3): {20: 11167, 12: 21685, 4: 9447, 0: 5063, 16: 24084, 8: 22255, 24: 6299}, + ("QuadrupleOnesAndTwos", 3, 4): {24: 12448, 4: 5531, 8: 17681, 12: 18400, 16: 28524, 20: 14552, 0: 2864}, + ("QuadrupleOnesAndTwos", 3, 5): {16: 30427, 24: 19843, 12: 14755, 8: 13478, 20: 16602, 0: 1676, 4: 3219}, + ("QuadrupleOnesAndTwos", 3, 6): {24: 27625, 12: 11326, 16: 31125, 4: 1758, 8: 10259, 20: 16984, 0: 923}, + ("QuadrupleOnesAndTwos", 3, 7): {24: 35548, 12: 8769, 16: 29367, 20: 17085, 0: 586, 8: 7543, 4: 1102}, + ("QuadrupleOnesAndTwos", 3, 8): {24: 43483, 20: 16170, 12: 6388, 16: 27741, 8: 5277, 4: 607, 0: 334}, + ("QuadrupleOnesAndTwos", 4, 1): { + 12: 16126, + 20: 3979, + 0: 19691, + 8: 27288, + 4: 19657, + 16: 11167, + 24: 1705, + 28: 307, + 32: 80, + }, + ("QuadrupleOnesAndTwos", 4, 2): { + 4: 9776, + 8: 19015, + 16: 20986, + 12: 22094, + 0: 4023, + 20: 13805, + 24: 7340, + 28: 2393, + 32: 568, + }, + ("QuadrupleOnesAndTwos", 4, 3): { + 12: 16853, + 4: 4705, + 0: 1848, + 16: 22831, + 8: 12411, + 28: 5902, + 20: 18400, + 32: 2570, + 24: 14480, + }, + ("QuadrupleOnesAndTwos", 4, 4): { + 16: 21220, + 24: 20615, + 12: 12063, + 20: 19266, + 4: 2291, + 0: 930, + 32: 6088, + 8: 8084, + 28: 9443, + }, + ("QuadrupleOnesAndTwos", 4, 5): { + 24: 25474, + 20: 17910, + 32: 11370, + 28: 12864, + 16: 18209, + 12: 7649, + 0: 424, + 8: 4963, + 4: 1137, + }, + ("QuadrupleOnesAndTwos", 4, 6): { + 32: 18156, + 24: 28256, + 20: 15416, + 12: 4931, + 28: 14675, + 16: 14796, + 8: 3048, + 4: 532, + 0: 190, + }, + ("QuadrupleOnesAndTwos", 4, 7): { + 20: 12289, + 12: 3189, + 28: 16052, + 32: 25512, + 24: 29181, + 16: 11547, + 8: 1871, + 4: 244, + 0: 115, + }, + ("QuadrupleOnesAndTwos", 4, 8): { + 24: 28785, + 32: 33333, + 16: 8888, + 28: 16180, + 12: 1909, + 20: 9679, + 8: 1062, + 4: 114, + 0: 50, + }, + ("QuadrupleOnesAndTwos", 5, 1): { + 0: 13112, + 8: 24718, + 4: 16534, + 12: 18558, + 16: 14547, + 20: 7055, + 24: 3810, + 28: 1194, + 32: 390, + 36: 66, + 40: 16, + }, + ("QuadrupleOnesAndTwos", 5, 2): { + 4: 5529, + 20: 18149, + 12: 17687, + 24: 12849, + 16: 20808, + 28: 6991, + 32: 2980, + 36: 871, + 8: 12216, + 0: 1764, + 40: 156, + }, + ("QuadrupleOnesAndTwos", 5, 3): { + 36: 2946, + 24: 18643, + 32: 7960, + 20: 19002, + 28: 12827, + 12: 11074, + 16: 17322, + 8: 6362, + 4: 2161, + 0: 719, + 40: 984, + }, + ("QuadrupleOnesAndTwos", 5, 4): { + 32: 14218, + 40: 2982, + 28: 16398, + 4: 847, + 24: 20749, + 16: 12913, + 20: 15867, + 36: 5931, + 12: 6581, + 8: 3209, + 0: 305, + }, + ("QuadrupleOnesAndTwos", 5, 5): { + 40: 6767, + 24: 20010, + 36: 9319, + 20: 12037, + 16: 8863, + 32: 19789, + 28: 17568, + 4: 340, + 8: 1729, + 12: 3480, + 0: 98, + }, + ("QuadrupleOnesAndTwos", 5, 6): { + 24: 17830, + 36: 12115, + 40: 11918, + 20: 8436, + 32: 24246, + 16: 5734, + 28: 16864, + 12: 1793, + 4: 156, + 8: 870, + 0: 38, + }, + ("QuadrupleOnesAndTwos", 5, 7): { + 32: 27238, + 36: 14094, + 28: 14969, + 24: 14936, + 40: 17918, + 20: 5684, + 16: 3712, + 12: 924, + 8: 445, + 4: 51, + 0: 29, + }, + ("QuadrupleOnesAndTwos", 5, 8): { + 28: 12517, + 36: 15339, + 32: 28388, + 40: 25046, + 24: 11929, + 16: 2344, + 20: 3690, + 12: 481, + 8: 241, + 4: 21, + 0: 4, + }, + ("QuadrupleOnesAndTwos", 6, 1): { + 4: 13011, + 8: 21357, + 24: 6249, + 0: 8646, + 16: 17008, + 12: 19385, + 20: 10409, + 28: 2502, + 36: 289, + 32: 1041, + 40: 96, + 44: 6, + 48: 1, + }, + ("QuadrupleOnesAndTwos", 6, 2): { + 8: 7435, + 20: 18814, + 28: 11889, + 16: 17480, + 12: 12792, + 24: 16492, + 32: 6893, + 0: 844, + 36: 3013, + 4: 2876, + 40: 1124, + 44: 304, + 48: 44, + }, + ("QuadrupleOnesAndTwos", 6, 3): { + 32: 13314, + 12: 6431, + 36: 8034, + 28: 16506, + 20: 15584, + 24: 17967, + 16: 11685, + 40: 4204, + 8: 3203, + 48: 429, + 44: 1402, + 0: 264, + 4: 977, + }, + ("QuadrupleOnesAndTwos", 6, 4): { + 28: 17174, + 36: 12820, + 16: 6727, + 40: 9289, + 32: 17787, + 24: 15746, + 44: 3499, + 20: 10562, + 8: 1361, + 4: 301, + 12: 3077, + 48: 1574, + 0: 83, + }, + ("QuadrupleOnesAndTwos", 6, 5): { + 32: 19588, + 24: 12264, + 44: 6410, + 40: 14682, + 36: 16002, + 28: 14810, + 20: 6466, + 48: 3921, + 16: 3781, + 12: 1344, + 4: 106, + 8: 590, + 0: 36, + }, + ("QuadrupleOnesAndTwos", 6, 6): { + 40: 19906, + 32: 19145, + 36: 16864, + 24: 8774, + 8: 238, + 48: 7617, + 28: 11481, + 44: 9386, + 16: 2094, + 12: 594, + 20: 3849, + 4: 40, + 0: 12, + }, + ("QuadrupleOnesAndTwos", 6, 7): { + 36: 16148, + 32: 17207, + 44: 11862, + 40: 24051, + 48: 12836, + 24: 6015, + 28: 8372, + 16: 1032, + 20: 2123, + 12: 240, + 8: 96, + 4: 15, + 0: 3, + }, + ("QuadrupleOnesAndTwos", 6, 8): { + 36: 14585, + 32: 14489, + 24: 3868, + 40: 26779, + 28: 5738, + 44: 13821, + 48: 18879, + 8: 40, + 20: 1118, + 16: 559, + 12: 121, + 0: 1, + 4: 2, + }, + ("QuadrupleOnesAndTwos", 7, 1): { + 24: 8617, + 12: 18364, + 8: 17905, + 4: 10185, + 16: 18160, + 0: 5780, + 32: 2221, + 28: 4458, + 20: 13115, + 36: 827, + 44: 77, + 40: 266, + 48: 23, + 52: 2, + }, + ("QuadrupleOnesAndTwos", 7, 2): { + 28: 15061, + 24: 17562, + 12: 8501, + 16: 13204, + 20: 16895, + 4: 1436, + 32: 11122, + 40: 3259, + 8: 4327, + 44: 1279, + 36: 6507, + 0: 359, + 52: 86, + 48: 388, + 56: 14, + }, + ("QuadrupleOnesAndTwos", 7, 3): { + 12: 3419, + 20: 11008, + 36: 12681, + 44: 4707, + 24: 14839, + 40: 8773, + 8: 1544, + 16: 7076, + 32: 16118, + 28: 16393, + 48: 2126, + 0: 84, + 52: 637, + 4: 437, + 56: 158, + }, + ("QuadrupleOnesAndTwos", 7, 4): { + 20: 6250, + 48: 5741, + 32: 16527, + 36: 15938, + 28: 13596, + 40: 14071, + 24: 10535, + 44: 9192, + 12: 1277, + 8: 548, + 16: 3362, + 56: 733, + 52: 2105, + 4: 109, + 0: 16, + }, + ("QuadrupleOnesAndTwos", 7, 5): { + 28: 9400, + 44: 13369, + 32: 14443, + 36: 15955, + 20: 3100, + 56: 2291, + 48: 10702, + 40: 17820, + 16: 1506, + 24: 6337, + 52: 4316, + 8: 185, + 12: 538, + 4: 35, + 0: 3, + }, + ("QuadrupleOnesAndTwos", 7, 6): { + 40: 19063, + 56: 4910, + 48: 15867, + 32: 11398, + 44: 15587, + 52: 7202, + 36: 13738, + 24: 3747, + 28: 5988, + 20: 1535, + 16: 694, + 12: 199, + 8: 63, + 4: 8, + 0: 1, + }, + ("QuadrupleOnesAndTwos", 7, 7): { + 24: 2129, + 52: 9969, + 44: 16470, + 36: 10801, + 40: 18184, + 56: 9078, + 48: 20467, + 28: 3595, + 32: 8275, + 20: 673, + 16: 270, + 12: 66, + 8: 17, + 4: 4, + 0: 2, + }, + ("QuadrupleOnesAndTwos", 7, 8): { + 48: 24388, + 44: 15477, + 52: 12403, + 28: 2117, + 56: 14425, + 40: 16197, + 32: 5715, + 16: 107, + 24: 1063, + 36: 7770, + 20: 307, + 12: 24, + 8: 6, + 0: 1, + }, + ("QuadrupleOnesAndTwos", 8, 1): { + 12: 17214, + 8: 14638, + 20: 14651, + 4: 7682, + 16: 18191, + 24: 10976, + 36: 1607, + 0: 3811, + 32: 3601, + 28: 6591, + 44: 234, + 40: 725, + 48: 64, + 52: 14, + 56: 1, + }, + ("QuadrupleOnesAndTwos", 8, 2): { + 52: 470, + 40: 6198, + 28: 16246, + 32: 14131, + 24: 16213, + 20: 13623, + 36: 10076, + 8: 2413, + 16: 9421, + 48: 1427, + 12: 5355, + 44: 3336, + 4: 770, + 0: 136, + 56: 160, + 60: 21, + 64: 4, + }, + ("QuadrupleOnesAndTwos", 8, 3): { + 32: 15751, + 40: 12409, + 20: 7201, + 28: 13934, + 16: 4021, + 12: 1804, + 36: 14882, + 44: 8920, + 56: 1006, + 48: 5462, + 24: 10733, + 52: 2606, + 64: 51, + 8: 716, + 60: 280, + 4: 191, + 0: 33, + }, + ("QuadrupleOnesAndTwos", 8, 4): { + 48: 10706, + 36: 14756, + 44: 13795, + 40: 15851, + 32: 12990, + 28: 9073, + 16: 1518, + 8: 194, + 20: 3103, + 24: 6057, + 52: 6310, + 56: 3456, + 60: 1207, + 64: 403, + 12: 542, + 4: 35, + 0: 4, + }, + ("QuadrupleOnesAndTwos", 8, 5): { + 44: 15382, + 56: 7377, + 40: 15561, + 48: 15278, + 60: 2918, + 32: 8993, + 52: 10629, + 28: 5327, + 24: 2989, + 36: 12039, + 64: 1326, + 12: 178, + 20: 1300, + 16: 627, + 4: 14, + 8: 60, + 0: 2, + }, + ("QuadrupleOnesAndTwos", 8, 6): { + 56: 12425, + 52: 14024, + 48: 17731, + 36: 8463, + 60: 5446, + 44: 14818, + 64: 3333, + 40: 13177, + 32: 5606, + 28: 2711, + 24: 1484, + 20: 520, + 12: 63, + 16: 174, + 8: 23, + 4: 2, + }, + ("QuadrupleOnesAndTwos", 8, 7): { + 52: 15549, + 36: 5454, + 56: 17187, + 40: 10276, + 44: 12582, + 32: 3399, + 48: 18487, + 60: 8149, + 64: 6573, + 28: 1363, + 24: 681, + 20: 212, + 16: 65, + 12: 22, + 8: 1, + }, + ("QuadrupleOnesAndTwos", 8, 8): { + 40: 7484, + 64: 11129, + 52: 15898, + 48: 17080, + 44: 9727, + 56: 21877, + 60: 10773, + 36: 3224, + 32: 1803, + 24: 259, + 28: 651, + 20: 66, + 16: 27, + 8: 1, + 12: 1, + }, + ("MicroStraight", 1, 1): {0: 100000}, + ("MicroStraight", 1, 2): {0: 100000}, + ("MicroStraight", 1, 3): {0: 100000}, + ("MicroStraight", 1, 4): {0: 100000}, + ("MicroStraight", 1, 5): {0: 100000}, + ("MicroStraight", 1, 6): {0: 100000}, + ("MicroStraight", 1, 7): {0: 100000}, + ("MicroStraight", 1, 8): {0: 100000}, + ("MicroStraight", 2, 1): {0: 72326, 10: 27674}, + ("MicroStraight", 2, 2): {0: 48546, 10: 51454}, + ("MicroStraight", 2, 3): {10: 67381, 0: 32619}, + ("MicroStraight", 2, 4): {10: 78341, 0: 21659}, + ("MicroStraight", 2, 5): {10: 85712, 0: 14288}, + ("MicroStraight", 2, 6): {10: 90118, 0: 9882}, + ("MicroStraight", 2, 7): {10: 93498, 0: 6502}, + ("MicroStraight", 2, 8): {10: 95839, 0: 4161}, + ("MicroStraight", 3, 1): {10: 58057, 0: 41943}, + ("MicroStraight", 3, 2): {10: 84476, 0: 15524}, + ("MicroStraight", 3, 3): {10: 94300, 0: 5700}, + ("MicroStraight", 3, 4): {10: 97873, 0: 2127}, + ("MicroStraight", 3, 5): {10: 99256, 0: 744}, + ("MicroStraight", 3, 6): {10: 99740, 0: 260}, + ("MicroStraight", 3, 7): {10: 99885, 0: 115}, + ("MicroStraight", 3, 8): {10: 99966, 0: 34}, + ("MicroStraight", 4, 1): {10: 77693, 0: 22307}, + ("MicroStraight", 4, 2): {10: 95580, 0: 4420}, + ("MicroStraight", 4, 3): {10: 99194, 0: 806}, + ("MicroStraight", 4, 4): {10: 99795, 0: 205}, + ("MicroStraight", 4, 5): {10: 99980, 0: 20}, + ("MicroStraight", 4, 6): {10: 99995, 0: 5}, + ("MicroStraight", 4, 7): {10: 99999, 0: 1}, + ("MicroStraight", 4, 8): {10: 99999, 0: 1}, + ("MicroStraight", 5, 1): {10: 88315, 0: 11685}, + ("MicroStraight", 5, 2): {10: 98859, 0: 1141}, + ("MicroStraight", 5, 3): {10: 99881, 0: 119}, + ("MicroStraight", 5, 4): {10: 99989, 0: 11}, + ("MicroStraight", 5, 5): {10: 99999, 0: 1}, + ("MicroStraight", 5, 6): {10: 100000}, + ("MicroStraight", 5, 7): {10: 100000}, + ("MicroStraight", 5, 8): {10: 100000}, + ("MicroStraight", 6, 1): {10: 94063, 0: 5937}, + ("MicroStraight", 6, 2): {10: 99693, 0: 307}, + ("MicroStraight", 6, 3): {10: 99991, 0: 9}, + ("MicroStraight", 6, 4): {10: 99999, 0: 1}, + ("MicroStraight", 6, 5): {10: 100000}, + ("MicroStraight", 6, 6): {10: 100000}, + ("MicroStraight", 6, 7): {10: 100000}, + ("MicroStraight", 6, 8): {10: 100000}, + ("MicroStraight", 7, 1): {10: 96928, 0: 3072}, + ("MicroStraight", 7, 2): {10: 99915, 0: 85}, + ("MicroStraight", 7, 3): {10: 99998, 0: 2}, + ("MicroStraight", 7, 4): {10: 100000}, + ("MicroStraight", 7, 5): {10: 100000}, + ("MicroStraight", 7, 6): {10: 100000}, + ("MicroStraight", 7, 7): {10: 100000}, + ("MicroStraight", 7, 8): {10: 100000}, + ("MicroStraight", 8, 1): {10: 98456, 0: 1544}, + ("MicroStraight", 8, 2): {10: 99985, 0: 15}, + ("MicroStraight", 8, 3): {10: 100000}, + ("MicroStraight", 8, 4): {10: 100000}, + ("MicroStraight", 8, 5): {10: 100000}, + ("MicroStraight", 8, 6): {10: 100000}, + ("MicroStraight", 8, 7): {10: 100000}, + ("MicroStraight", 8, 8): {10: 100000}, + ("ThreeOdds", 1, 1): {0: 100000}, + ("ThreeOdds", 1, 2): {0: 100000}, + ("ThreeOdds", 1, 3): {0: 100000}, + ("ThreeOdds", 1, 4): {0: 100000}, + ("ThreeOdds", 1, 5): {0: 100000}, + ("ThreeOdds", 1, 6): {0: 100000}, + ("ThreeOdds", 1, 7): {0: 100000}, + ("ThreeOdds", 1, 8): {0: 100000}, + ("ThreeOdds", 2, 1): {0: 100000}, + ("ThreeOdds", 2, 2): {0: 100000}, + ("ThreeOdds", 2, 3): {0: 100000}, + ("ThreeOdds", 2, 4): {0: 100000}, + ("ThreeOdds", 2, 5): {0: 100000}, + ("ThreeOdds", 2, 6): {0: 100000}, + ("ThreeOdds", 2, 7): {0: 100000}, + ("ThreeOdds", 2, 8): {0: 100000}, + ("ThreeOdds", 3, 1): {0: 87592, 20: 12408}, + ("ThreeOdds", 3, 2): {20: 42145, 0: 57855}, + ("ThreeOdds", 3, 3): {20: 67332, 0: 32668}, + ("ThreeOdds", 3, 4): {0: 17508, 20: 82492}, + ("ThreeOdds", 3, 5): {20: 90844, 0: 9156}, + ("ThreeOdds", 3, 6): {20: 95428, 0: 4572}, + ("ThreeOdds", 3, 7): {20: 97675, 0: 2325}, + ("ThreeOdds", 3, 8): {20: 98884, 0: 1116}, + ("ThreeOdds", 4, 1): {20: 31331, 0: 68669}, + ("ThreeOdds", 4, 2): {0: 26140, 20: 73860}, + ("ThreeOdds", 4, 3): {20: 92163, 0: 7837}, + ("ThreeOdds", 4, 4): {20: 97831, 0: 2169}, + ("ThreeOdds", 4, 5): {20: 99484, 0: 516}, + ("ThreeOdds", 4, 6): {20: 99844, 0: 156}, + ("ThreeOdds", 4, 7): {20: 99960, 0: 40}, + ("ThreeOdds", 4, 8): {20: 99988, 0: 12}, + ("ThreeOdds", 5, 1): {0: 49908, 20: 50092}, + ("ThreeOdds", 5, 2): {20: 89627, 0: 10373}, + ("ThreeOdds", 5, 3): {20: 98360, 0: 1640}, + ("ThreeOdds", 5, 4): {20: 99777, 0: 223}, + ("ThreeOdds", 5, 5): {20: 99976, 0: 24}, + ("ThreeOdds", 5, 6): {20: 99997, 0: 3}, + ("ThreeOdds", 5, 7): {20: 99999, 0: 1}, + ("ThreeOdds", 5, 8): {20: 100000}, + ("ThreeOdds", 6, 1): {20: 65434, 0: 34566}, + ("ThreeOdds", 6, 2): {20: 96234, 0: 3766}, + ("ThreeOdds", 6, 3): {20: 99709, 0: 291}, + ("ThreeOdds", 6, 4): {20: 99978, 0: 22}, + ("ThreeOdds", 6, 5): {20: 100000}, + ("ThreeOdds", 6, 6): {20: 100000}, + ("ThreeOdds", 6, 7): {20: 100000}, + ("ThreeOdds", 6, 8): {20: 100000}, + ("ThreeOdds", 7, 1): {20: 77278, 0: 22722}, + ("ThreeOdds", 7, 2): {20: 98709, 0: 1291}, + ("ThreeOdds", 7, 3): {20: 99962, 0: 38}, + ("ThreeOdds", 7, 4): {20: 99998, 0: 2}, + ("ThreeOdds", 7, 5): {20: 100000}, + ("ThreeOdds", 7, 6): {20: 100000}, + ("ThreeOdds", 7, 7): {20: 100000}, + ("ThreeOdds", 7, 8): {20: 100000}, + ("ThreeOdds", 8, 1): {20: 85444, 0: 14556}, + ("ThreeOdds", 8, 2): {20: 99570, 0: 430}, + ("ThreeOdds", 8, 3): {20: 99997, 0: 3}, + ("ThreeOdds", 8, 4): {20: 100000}, + ("ThreeOdds", 8, 5): {20: 100000}, + ("ThreeOdds", 8, 6): {20: 100000}, + ("ThreeOdds", 8, 7): {20: 100000}, + ("ThreeOdds", 8, 8): {20: 100000}, + ("OneTwoOneConsecutive", 1, 1): {0: 100000}, + ("OneTwoOneConsecutive", 1, 2): {0: 100000}, + ("OneTwoOneConsecutive", 1, 3): {0: 100000}, + ("OneTwoOneConsecutive", 1, 4): {0: 100000}, + ("OneTwoOneConsecutive", 1, 5): {0: 100000}, + ("OneTwoOneConsecutive", 1, 6): {0: 100000}, + ("OneTwoOneConsecutive", 1, 7): {0: 100000}, + ("OneTwoOneConsecutive", 1, 8): {0: 100000}, + ("OneTwoOneConsecutive", 2, 1): {0: 100000}, + ("OneTwoOneConsecutive", 2, 2): {0: 100000}, + ("OneTwoOneConsecutive", 2, 3): {0: 100000}, + ("OneTwoOneConsecutive", 2, 4): {0: 100000}, + ("OneTwoOneConsecutive", 2, 5): {0: 100000}, + ("OneTwoOneConsecutive", 2, 6): {0: 100000}, + ("OneTwoOneConsecutive", 2, 7): {0: 100000}, + ("OneTwoOneConsecutive", 2, 8): {0: 100000}, + ("OneTwoOneConsecutive", 3, 1): {0: 100000}, + ("OneTwoOneConsecutive", 3, 2): {0: 100000}, + ("OneTwoOneConsecutive", 3, 3): {0: 100000}, + ("OneTwoOneConsecutive", 3, 4): {0: 100000}, + ("OneTwoOneConsecutive", 3, 5): {0: 100000}, + ("OneTwoOneConsecutive", 3, 6): {0: 100000}, + ("OneTwoOneConsecutive", 3, 7): {0: 100000}, + ("OneTwoOneConsecutive", 3, 8): {0: 100000}, + ("OneTwoOneConsecutive", 4, 1): {0: 96371, 30: 3629}, + ("OneTwoOneConsecutive", 4, 2): {30: 13395, 0: 86605}, + ("OneTwoOneConsecutive", 4, 3): {0: 75037, 30: 24963}, + ("OneTwoOneConsecutive", 4, 4): {30: 36344, 0: 63656}, + ("OneTwoOneConsecutive", 4, 5): {30: 46131, 0: 53869}, + ("OneTwoOneConsecutive", 4, 6): {30: 54869, 0: 45131}, + ("OneTwoOneConsecutive", 4, 7): {30: 62465, 0: 37535}, + ("OneTwoOneConsecutive", 4, 8): {30: 68575, 0: 31425}, + ("OneTwoOneConsecutive", 5, 1): {0: 86632, 30: 13368}, + ("OneTwoOneConsecutive", 5, 2): {0: 62779, 30: 37221}, + ("OneTwoOneConsecutive", 5, 3): {30: 53966, 0: 46034}, + ("OneTwoOneConsecutive", 5, 4): {0: 34983, 30: 65017}, + ("OneTwoOneConsecutive", 5, 5): {0: 28056, 30: 71944}, + ("OneTwoOneConsecutive", 5, 6): {30: 76850, 0: 23150}, + ("OneTwoOneConsecutive", 5, 7): {30: 80423, 0: 19577}, + ("OneTwoOneConsecutive", 5, 8): {0: 17613, 30: 82387}, + ("OneTwoOneConsecutive", 6, 1): {0: 71928, 30: 28072}, + ("OneTwoOneConsecutive", 6, 2): {0: 40724, 30: 59276}, + ("OneTwoOneConsecutive", 6, 3): {30: 73277, 0: 26723}, + ("OneTwoOneConsecutive", 6, 4): {0: 19685, 30: 80315}, + ("OneTwoOneConsecutive", 6, 5): {30: 84540, 0: 15460}, + ("OneTwoOneConsecutive", 6, 6): {30: 87474, 0: 12526}, + ("OneTwoOneConsecutive", 6, 7): {30: 89986, 0: 10014}, + ("OneTwoOneConsecutive", 6, 8): {30: 91749, 0: 8251}, + ("OneTwoOneConsecutive", 7, 1): {0: 55544, 30: 44456}, + ("OneTwoOneConsecutive", 7, 2): {30: 75160, 0: 24840}, + ("OneTwoOneConsecutive", 7, 3): {30: 84898, 0: 15102}, + ("OneTwoOneConsecutive", 7, 4): {30: 89459, 0: 10541}, + ("OneTwoOneConsecutive", 7, 5): {30: 92280, 0: 7720}, + ("OneTwoOneConsecutive", 7, 6): {30: 94446, 0: 5554}, + ("OneTwoOneConsecutive", 7, 7): {30: 95894, 0: 4106}, + ("OneTwoOneConsecutive", 7, 8): {30: 96975, 0: 3025}, + ("OneTwoOneConsecutive", 8, 1): {30: 59307, 0: 40693}, + ("OneTwoOneConsecutive", 8, 2): {0: 14827, 30: 85173}, + ("OneTwoOneConsecutive", 8, 3): {30: 91805, 0: 8195}, + ("OneTwoOneConsecutive", 8, 4): {30: 94617, 0: 5383}, + ("OneTwoOneConsecutive", 8, 5): {30: 96605, 0: 3395}, + ("OneTwoOneConsecutive", 8, 6): {30: 97701, 0: 2299}, + ("OneTwoOneConsecutive", 8, 7): {30: 98588, 0: 1412}, + ("OneTwoOneConsecutive", 8, 8): {30: 99128, 0: 872}, + ("ThreeDistinctDice", 1, 1): {0: 100000}, + ("ThreeDistinctDice", 1, 2): {0: 100000}, + ("ThreeDistinctDice", 1, 3): {0: 100000}, + ("ThreeDistinctDice", 1, 4): {0: 100000}, + ("ThreeDistinctDice", 1, 5): {0: 100000}, + ("ThreeDistinctDice", 1, 6): {0: 100000}, + ("ThreeDistinctDice", 1, 7): {0: 100000}, + ("ThreeDistinctDice", 1, 8): {0: 100000}, + ("ThreeDistinctDice", 2, 1): {0: 100000}, + ("ThreeDistinctDice", 2, 2): {0: 100000}, + ("ThreeDistinctDice", 2, 3): {0: 100000}, + ("ThreeDistinctDice", 2, 4): {0: 100000}, + ("ThreeDistinctDice", 2, 5): {0: 100000}, + ("ThreeDistinctDice", 2, 6): {0: 100000}, + ("ThreeDistinctDice", 2, 7): {0: 100000}, + ("ThreeDistinctDice", 2, 8): {0: 100000}, + ("ThreeDistinctDice", 3, 1): {20: 55293, 0: 44707}, + ("ThreeDistinctDice", 3, 2): {0: 15078, 20: 84922}, + ("ThreeDistinctDice", 3, 3): {20: 94944, 0: 5056}, + ("ThreeDistinctDice", 3, 4): {0: 1688, 20: 98312}, + ("ThreeDistinctDice", 3, 5): {20: 99484, 0: 516}, + ("ThreeDistinctDice", 3, 6): {20: 99818, 0: 182}, + ("ThreeDistinctDice", 3, 7): {20: 99944, 0: 56}, + ("ThreeDistinctDice", 3, 8): {20: 99985, 0: 15}, + ("ThreeDistinctDice", 4, 1): {20: 83279, 0: 16721}, + ("ThreeDistinctDice", 4, 2): {20: 98174, 0: 1826}, + ("ThreeDistinctDice", 4, 3): {20: 99797, 0: 203}, + ("ThreeDistinctDice", 4, 4): {20: 99982, 0: 18}, + ("ThreeDistinctDice", 4, 5): {20: 99997, 0: 3}, + ("ThreeDistinctDice", 4, 6): {20: 100000}, + ("ThreeDistinctDice", 4, 7): {20: 100000}, + ("ThreeDistinctDice", 4, 8): {20: 100000}, + ("ThreeDistinctDice", 5, 1): {0: 5904, 20: 94096}, + ("ThreeDistinctDice", 5, 2): {20: 99764, 0: 236}, + ("ThreeDistinctDice", 5, 3): {20: 99988, 0: 12}, + ("ThreeDistinctDice", 5, 4): {20: 100000}, + ("ThreeDistinctDice", 5, 5): {20: 100000}, + ("ThreeDistinctDice", 5, 6): {20: 100000}, + ("ThreeDistinctDice", 5, 7): {20: 100000}, + ("ThreeDistinctDice", 5, 8): {20: 100000}, + ("ThreeDistinctDice", 6, 1): {20: 98008, 0: 1992}, + ("ThreeDistinctDice", 6, 2): {20: 99979, 0: 21}, + ("ThreeDistinctDice", 6, 3): {20: 100000}, + ("ThreeDistinctDice", 6, 4): {20: 100000}, + ("ThreeDistinctDice", 6, 5): {20: 100000}, + ("ThreeDistinctDice", 6, 6): {20: 100000}, + ("ThreeDistinctDice", 6, 7): {20: 100000}, + ("ThreeDistinctDice", 6, 8): {20: 100000}, + ("ThreeDistinctDice", 7, 1): {20: 99308, 0: 692}, + ("ThreeDistinctDice", 7, 2): {20: 99996, 0: 4}, + ("ThreeDistinctDice", 7, 3): {20: 100000}, + ("ThreeDistinctDice", 7, 4): {20: 100000}, + ("ThreeDistinctDice", 7, 5): {20: 100000}, + ("ThreeDistinctDice", 7, 6): {20: 100000}, + ("ThreeDistinctDice", 7, 7): {20: 100000}, + ("ThreeDistinctDice", 7, 8): {20: 100000}, + ("ThreeDistinctDice", 8, 1): {20: 99757, 0: 243}, + ("ThreeDistinctDice", 8, 2): {20: 99999, 0: 1}, + ("ThreeDistinctDice", 8, 3): {20: 100000}, + ("ThreeDistinctDice", 8, 4): {20: 100000}, + ("ThreeDistinctDice", 8, 5): {20: 100000}, + ("ThreeDistinctDice", 8, 6): {20: 100000}, + ("ThreeDistinctDice", 8, 7): {20: 100000}, + ("ThreeDistinctDice", 8, 8): {20: 100000}, + ("TwoPair", 1, 1): {0: 100000}, + ("TwoPair", 1, 2): {0: 100000}, + ("TwoPair", 1, 3): {0: 100000}, + ("TwoPair", 1, 4): {0: 100000}, + ("TwoPair", 1, 5): {0: 100000}, + ("TwoPair", 1, 6): {0: 100000}, + ("TwoPair", 1, 7): {0: 100000}, + ("TwoPair", 1, 8): {0: 100000}, + ("TwoPair", 2, 1): {0: 100000}, + ("TwoPair", 2, 2): {0: 100000}, + ("TwoPair", 2, 3): {0: 100000}, + ("TwoPair", 2, 4): {0: 100000}, + ("TwoPair", 2, 5): {0: 100000}, + ("TwoPair", 2, 6): {0: 100000}, + ("TwoPair", 2, 7): {0: 100000}, + ("TwoPair", 2, 8): {0: 100000}, + ("TwoPair", 3, 1): {0: 100000}, + ("TwoPair", 3, 2): {0: 100000}, + ("TwoPair", 3, 3): {0: 100000}, + ("TwoPair", 3, 4): {0: 100000}, + ("TwoPair", 3, 5): {0: 100000}, + ("TwoPair", 3, 6): {0: 100000}, + ("TwoPair", 3, 7): {0: 100000}, + ("TwoPair", 3, 8): {0: 100000}, + ("TwoPair", 4, 1): {0: 93065, 30: 6935}, + ("TwoPair", 4, 2): {0: 82102, 30: 17898}, + ("TwoPair", 4, 3): {0: 71209, 30: 28791}, + ("TwoPair", 4, 4): {0: 61609, 30: 38391}, + ("TwoPair", 4, 5): {30: 46964, 0: 53036}, + ("TwoPair", 4, 6): {0: 45705, 30: 54295}, + ("TwoPair", 4, 7): {0: 39398, 30: 60602}, + ("TwoPair", 4, 8): {30: 66327, 0: 33673}, + ("TwoPair", 5, 1): {30: 27153, 0: 72847}, + ("TwoPair", 5, 2): {30: 53241, 0: 46759}, + ("TwoPair", 5, 3): {30: 70538, 0: 29462}, + ("TwoPair", 5, 4): {30: 81649, 0: 18351}, + ("TwoPair", 5, 5): {30: 88207, 0: 11793}, + ("TwoPair", 5, 6): {30: 92615, 0: 7385}, + ("TwoPair", 5, 7): {30: 95390, 0: 4610}, + ("TwoPair", 5, 8): {30: 97062, 0: 2938}, + ("TwoPair", 6, 1): {30: 55569, 0: 44431}, + ("TwoPair", 6, 2): {30: 82817, 0: 17183}, + ("TwoPair", 6, 3): {30: 93241, 0: 6759}, + ("TwoPair", 6, 4): {30: 97438, 0: 2562}, + ("TwoPair", 6, 5): {30: 99052, 0: 948}, + ("TwoPair", 6, 6): {30: 99625, 0: 375}, + ("TwoPair", 6, 7): {30: 99862, 0: 138}, + ("TwoPair", 6, 8): {30: 99943, 0: 57}, + ("TwoPair", 7, 1): {0: 19888, 30: 80112}, + ("TwoPair", 7, 2): {30: 96065, 0: 3935}, + ("TwoPair", 7, 3): {30: 99199, 0: 801}, + ("TwoPair", 7, 4): {30: 99825, 0: 175}, + ("TwoPair", 7, 5): {30: 99969, 0: 31}, + ("TwoPair", 7, 6): {30: 99993, 0: 7}, + ("TwoPair", 7, 7): {30: 99998, 0: 2}, + ("TwoPair", 7, 8): {30: 100000}, + ("TwoPair", 8, 1): {30: 93209, 0: 6791}, + ("TwoPair", 8, 2): {30: 99412, 0: 588}, + ("TwoPair", 8, 3): {30: 99939, 0: 61}, + ("TwoPair", 8, 4): {30: 99994, 0: 6}, + ("TwoPair", 8, 5): {30: 100000}, + ("TwoPair", 8, 6): {30: 100000}, + ("TwoPair", 8, 7): {30: 100000}, + ("TwoPair", 8, 8): {30: 100000}, + ("TwoOneTwoConsecutive", 1, 1): {0: 100000}, + ("TwoOneTwoConsecutive", 1, 2): {0: 100000}, + ("TwoOneTwoConsecutive", 1, 3): {0: 100000}, + ("TwoOneTwoConsecutive", 1, 4): {0: 100000}, + ("TwoOneTwoConsecutive", 1, 5): {0: 100000}, + ("TwoOneTwoConsecutive", 1, 6): {0: 100000}, + ("TwoOneTwoConsecutive", 1, 7): {0: 100000}, + ("TwoOneTwoConsecutive", 1, 8): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 1): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 2): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 3): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 4): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 5): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 6): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 7): {0: 100000}, + ("TwoOneTwoConsecutive", 2, 8): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 1): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 2): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 3): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 4): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 5): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 6): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 7): {0: 100000}, + ("TwoOneTwoConsecutive", 3, 8): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 1): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 2): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 3): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 4): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 5): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 6): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 7): {0: 100000}, + ("TwoOneTwoConsecutive", 4, 8): {0: 100000}, + ("TwoOneTwoConsecutive", 5, 1): {0: 98403, 40: 1597}, + ("TwoOneTwoConsecutive", 5, 2): {0: 90651, 40: 9349}, + ("TwoOneTwoConsecutive", 5, 3): {0: 80100, 40: 19900}, + ("TwoOneTwoConsecutive", 5, 4): {0: 69131, 40: 30869}, + ("TwoOneTwoConsecutive", 5, 5): {0: 58252, 40: 41748}, + ("TwoOneTwoConsecutive", 5, 6): {0: 49405, 40: 50595}, + ("TwoOneTwoConsecutive", 5, 7): {40: 58415, 0: 41585}, + ("TwoOneTwoConsecutive", 5, 8): {40: 65048, 0: 34952}, + ("TwoOneTwoConsecutive", 6, 1): {0: 93465, 40: 6535}, + ("TwoOneTwoConsecutive", 6, 2): {40: 26584, 0: 73416}, + ("TwoOneTwoConsecutive", 6, 3): {40: 45959, 0: 54041}, + ("TwoOneTwoConsecutive", 6, 4): {40: 61465, 0: 38535}, + ("TwoOneTwoConsecutive", 6, 5): {40: 72634, 0: 27366}, + ("TwoOneTwoConsecutive", 6, 6): {0: 18924, 40: 81076}, + ("TwoOneTwoConsecutive", 6, 7): {40: 86613, 0: 13387}, + ("TwoOneTwoConsecutive", 6, 8): {40: 90866, 0: 9134}, + ("TwoOneTwoConsecutive", 7, 1): {0: 84168, 40: 15832}, + ("TwoOneTwoConsecutive", 7, 2): {0: 52659, 40: 47341}, + ("TwoOneTwoConsecutive", 7, 3): {40: 69565, 0: 30435}, + ("TwoOneTwoConsecutive", 7, 4): {40: 82523, 0: 17477}, + ("TwoOneTwoConsecutive", 7, 5): {40: 90218, 0: 9782}, + ("TwoOneTwoConsecutive", 7, 6): {40: 94684, 0: 5316}, + ("TwoOneTwoConsecutive", 7, 7): {40: 97005, 0: 2995}, + ("TwoOneTwoConsecutive", 7, 8): {40: 98311, 0: 1689}, + ("TwoOneTwoConsecutive", 8, 1): {0: 71089, 40: 28911}, + ("TwoOneTwoConsecutive", 8, 2): {0: 33784, 40: 66216}, + ("TwoOneTwoConsecutive", 8, 3): {40: 85180, 0: 14820}, + ("TwoOneTwoConsecutive", 8, 4): {40: 93735, 0: 6265}, + ("TwoOneTwoConsecutive", 8, 5): {40: 97400, 0: 2600}, + ("TwoOneTwoConsecutive", 8, 6): {40: 98845, 0: 1155}, + ("TwoOneTwoConsecutive", 8, 7): {40: 99513, 0: 487}, + ("TwoOneTwoConsecutive", 8, 8): {40: 99810, 0: 190}, + ("FiveDistinctDice", 1, 1): {0: 100000}, + ("FiveDistinctDice", 1, 2): {0: 100000}, + ("FiveDistinctDice", 1, 3): {0: 100000}, + ("FiveDistinctDice", 1, 4): {0: 100000}, + ("FiveDistinctDice", 1, 5): {0: 100000}, + ("FiveDistinctDice", 1, 6): {0: 100000}, + ("FiveDistinctDice", 1, 7): {0: 100000}, + ("FiveDistinctDice", 1, 8): {0: 100000}, + ("FiveDistinctDice", 2, 1): {0: 100000}, + ("FiveDistinctDice", 2, 2): {0: 100000}, + ("FiveDistinctDice", 2, 3): {0: 100000}, + ("FiveDistinctDice", 2, 4): {0: 100000}, + ("FiveDistinctDice", 2, 5): {0: 100000}, + ("FiveDistinctDice", 2, 6): {0: 100000}, + ("FiveDistinctDice", 2, 7): {0: 100000}, + ("FiveDistinctDice", 2, 8): {0: 100000}, + ("FiveDistinctDice", 3, 1): {0: 100000}, + ("FiveDistinctDice", 3, 2): {0: 100000}, + ("FiveDistinctDice", 3, 3): {0: 100000}, + ("FiveDistinctDice", 3, 4): {0: 100000}, + ("FiveDistinctDice", 3, 5): {0: 100000}, + ("FiveDistinctDice", 3, 6): {0: 100000}, + ("FiveDistinctDice", 3, 7): {0: 100000}, + ("FiveDistinctDice", 3, 8): {0: 100000}, + ("FiveDistinctDice", 4, 1): {0: 100000}, + ("FiveDistinctDice", 4, 2): {0: 100000}, + ("FiveDistinctDice", 4, 3): {0: 100000}, + ("FiveDistinctDice", 4, 4): {0: 100000}, + ("FiveDistinctDice", 4, 5): {0: 100000}, + ("FiveDistinctDice", 4, 6): {0: 100000}, + ("FiveDistinctDice", 4, 7): {0: 100000}, + ("FiveDistinctDice", 4, 8): {0: 100000}, + ("FiveDistinctDice", 5, 1): {0: 90907, 25: 9093}, + ("FiveDistinctDice", 5, 2): {25: 31980, 0: 68020}, + ("FiveDistinctDice", 5, 3): {0: 47692, 25: 52308}, + ("FiveDistinctDice", 5, 4): {0: 32383, 25: 67617}, + ("FiveDistinctDice", 5, 5): {25: 78369, 0: 21631}, + ("FiveDistinctDice", 5, 6): {25: 85634, 0: 14366}, + ("FiveDistinctDice", 5, 7): {25: 90432, 0: 9568}, + ("FiveDistinctDice", 5, 8): {0: 6360, 25: 93640}, + ("FiveDistinctDice", 6, 1): {0: 75051, 25: 24949}, + ("FiveDistinctDice", 6, 2): {25: 61591, 0: 38409}, + ("FiveDistinctDice", 6, 3): {25: 82495, 0: 17505}, + ("FiveDistinctDice", 6, 4): {25: 92138, 0: 7862}, + ("FiveDistinctDice", 6, 5): {25: 96462, 0: 3538}, + ("FiveDistinctDice", 6, 6): {25: 98355, 0: 1645}, + ("FiveDistinctDice", 6, 7): {25: 99286, 0: 714}, + ("FiveDistinctDice", 6, 8): {25: 99659, 0: 341}, + ("FiveDistinctDice", 7, 1): {0: 58588, 25: 41412}, + ("FiveDistinctDice", 7, 2): {25: 80513, 0: 19487}, + ("FiveDistinctDice", 7, 3): {25: 93957, 0: 6043}, + ("FiveDistinctDice", 7, 4): {25: 98201, 0: 1799}, + ("FiveDistinctDice", 7, 5): {25: 99456, 0: 544}, + ("FiveDistinctDice", 7, 6): {25: 99831, 0: 169}, + ("FiveDistinctDice", 7, 7): {25: 99941, 0: 59}, + ("FiveDistinctDice", 7, 8): {25: 99989, 0: 11}, + ("FiveDistinctDice", 8, 1): {0: 43586, 25: 56414}, + ("FiveDistinctDice", 8, 2): {25: 90385, 0: 9615}, + ("FiveDistinctDice", 8, 3): {25: 98056, 0: 1944}, + ("FiveDistinctDice", 8, 4): {25: 99617, 0: 383}, + ("FiveDistinctDice", 8, 5): {25: 99923, 0: 77}, + ("FiveDistinctDice", 8, 6): {25: 99982, 0: 18}, + ("FiveDistinctDice", 8, 7): {25: 99997, 0: 3}, + ("FiveDistinctDice", 8, 8): {25: 99998, 0: 2}, + ("FourAndFiveFullHouse", 1, 1): {0: 100000}, + ("FourAndFiveFullHouse", 1, 2): {0: 100000}, + ("FourAndFiveFullHouse", 1, 3): {0: 100000}, + ("FourAndFiveFullHouse", 1, 4): {0: 100000}, + ("FourAndFiveFullHouse", 1, 5): {0: 100000}, + ("FourAndFiveFullHouse", 1, 6): {0: 100000}, + ("FourAndFiveFullHouse", 1, 7): {0: 100000}, + ("FourAndFiveFullHouse", 1, 8): {0: 100000}, + ("FourAndFiveFullHouse", 2, 1): {0: 100000}, + ("FourAndFiveFullHouse", 2, 2): {0: 100000}, + ("FourAndFiveFullHouse", 2, 3): {0: 100000}, + ("FourAndFiveFullHouse", 2, 4): {0: 100000}, + ("FourAndFiveFullHouse", 2, 5): {0: 100000}, + ("FourAndFiveFullHouse", 2, 6): {0: 100000}, + ("FourAndFiveFullHouse", 2, 7): {0: 100000}, + ("FourAndFiveFullHouse", 2, 8): {0: 100000}, + ("FourAndFiveFullHouse", 3, 1): {0: 100000}, + ("FourAndFiveFullHouse", 3, 2): {0: 100000}, + ("FourAndFiveFullHouse", 3, 3): {0: 100000}, + ("FourAndFiveFullHouse", 3, 4): {0: 100000}, + ("FourAndFiveFullHouse", 3, 5): {0: 100000}, + ("FourAndFiveFullHouse", 3, 6): {0: 100000}, + ("FourAndFiveFullHouse", 3, 7): {0: 100000}, + ("FourAndFiveFullHouse", 3, 8): {0: 100000}, + ("FourAndFiveFullHouse", 4, 1): {0: 100000}, + ("FourAndFiveFullHouse", 4, 2): {0: 100000}, + ("FourAndFiveFullHouse", 4, 3): {0: 100000}, + ("FourAndFiveFullHouse", 4, 4): {0: 100000}, + ("FourAndFiveFullHouse", 4, 5): {0: 100000}, + ("FourAndFiveFullHouse", 4, 6): {0: 100000}, + ("FourAndFiveFullHouse", 4, 7): {0: 100000}, + ("FourAndFiveFullHouse", 4, 8): {0: 100000}, + ("FourAndFiveFullHouse", 5, 1): {0: 99724, 50: 276}, + ("FourAndFiveFullHouse", 5, 2): {0: 96607, 50: 3393}, + ("FourAndFiveFullHouse", 5, 3): {0: 88788, 50: 11212}, + ("FourAndFiveFullHouse", 5, 4): {0: 77799, 50: 22201}, + ("FourAndFiveFullHouse", 5, 5): {50: 34203, 0: 65797}, + ("FourAndFiveFullHouse", 5, 6): {50: 45452, 0: 54548}, + ("FourAndFiveFullHouse", 5, 7): {50: 55102, 0: 44898}, + ("FourAndFiveFullHouse", 5, 8): {50: 63119, 0: 36881}, + ("FourAndFiveFullHouse", 6, 1): {0: 98841, 50: 1159}, + ("FourAndFiveFullHouse", 6, 2): {0: 88680, 50: 11320}, + ("FourAndFiveFullHouse", 6, 3): {50: 29785, 0: 70215}, + ("FourAndFiveFullHouse", 6, 4): {50: 49199, 0: 50801}, + ("FourAndFiveFullHouse", 6, 5): {50: 64244, 0: 35756}, + ("FourAndFiveFullHouse", 6, 6): {50: 75302, 0: 24698}, + ("FourAndFiveFullHouse", 6, 7): {50: 82855, 0: 17145}, + ("FourAndFiveFullHouse", 6, 8): {50: 88154, 0: 11846}, + ("FourAndFiveFullHouse", 7, 1): {0: 97090, 50: 2910}, + ("FourAndFiveFullHouse", 7, 2): {50: 22560, 0: 77440}, + ("FourAndFiveFullHouse", 7, 3): {50: 48628, 0: 51372}, + ("FourAndFiveFullHouse", 7, 4): {50: 69434, 0: 30566}, + ("FourAndFiveFullHouse", 7, 5): {50: 82134, 0: 17866}, + ("FourAndFiveFullHouse", 7, 6): {50: 89479, 0: 10521}, + ("FourAndFiveFullHouse", 7, 7): {50: 93796, 0: 6204}, + ("FourAndFiveFullHouse", 7, 8): {50: 96330, 0: 3670}, + ("FourAndFiveFullHouse", 8, 1): {0: 94172, 50: 5828}, + ("FourAndFiveFullHouse", 8, 2): {0: 64693, 50: 35307}, + ("FourAndFiveFullHouse", 8, 3): {0: 35293, 50: 64707}, + ("FourAndFiveFullHouse", 8, 4): {50: 82251, 0: 17749}, + ("FourAndFiveFullHouse", 8, 5): {50: 91260, 0: 8740}, + ("FourAndFiveFullHouse", 8, 6): {50: 95450, 0: 4550}, + ("FourAndFiveFullHouse", 8, 7): {50: 97782, 0: 2218}, + ("FourAndFiveFullHouse", 8, 8): {50: 98916, 0: 1084}, +} + +import time + +def process_dictionary(input_dict): + # Sort the dictionary by keys + sorted_dict = dict(sorted(input_dict.items())) + keep = sorted_dict + + added_to_keys = {} # Dictionary to keep track of keys and their addition counts + # Function to process the dictionary + def process_dict(d): + keys = list(d.keys()) + modified = False + + a = mean_value(input_dict) + b = mean_value(sorted_dict) + + if abs(a-b) < 1: + for i in range(len(keys) - 1): + key1, key2 = keys[i], keys[i + 1] + val1, val2 = d[key1], d[key2] + + # if added_to_keys.get(key1, 0) < 3 or added_to_keys.get(key2, 0) < 3: + # continue # Skip if either key has already been added to 3 times + + if val1 < val2 and val1 * (key2 - key1) < 1000 and (len(keys) > 3 or i > 0): + d[key2] += val1 + added_to_keys[key2] = added_to_keys.get(key2, 0) + 1 # Mark key2 as added to + del d[key1] + modified = True + break + elif val2 <= val1 and val2 * (key2 - key1) < 30000 and i < len(keys) - 2: + d[key1] += val2 + added_to_keys[key1] = added_to_keys.get(key1, 0) + 1 # Mark key1 as added to + del d[key2] + modified = True + break + + return d, modified + + + modified = True + while modified: + sorted_dict, modified = process_dict(sorted_dict) + + # Check if the sum of all values is 100000 + total_sum = sum(sorted_dict.values()) + if total_sum != 100000: + raise ValueError(f"The total sum of values is {total_sum}, which does not equal 100000.") + if input_dict != sorted_dict: + a = mean_value(input_dict) + b = mean_value(sorted_dict) + if abs(a-b) > 2: + print(f"{dict(sorted(input_dict.items()))} -> {sorted_dict}\n {mean_value(input_dict)} {mean_value(sorted_dict)}\n\n") + + return sorted_dict + +def mean_value(dictt): + summ = 0 + for key, value in dictt.items(): + summ += key * value + return summ/100000 + + +def combine_rounded_keys(yacht_weights): + new_yacht_weights = {} + for main_key, sub_dict in yacht_weights.items(): + new_yacht_weights[main_key] = process_dictionary(sub_dict) + return new_yacht_weights + + +yacht_weights = combine_rounded_keys(yacht_weights) \ No newline at end of file