Archipelago/worlds/yachtdice/YachtWeights.py

# 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: ("Category 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 "Category Choice", with 2 dice and 2 rolls.
# 13639 out of 100000 times, a score of 8 was achieved for example.
yacht_weights = {
    ("Category Ones", 0, 0): {0: 100000},
    ("Category Ones", 0, 1): {0: 100000},
    ("Category Ones", 0, 2): {0: 100000},
    ("Category Ones", 0, 3): {0: 100000},
    ("Category Ones", 0, 4): {0: 100000},
    ("Category Ones", 0, 5): {0: 100000},
    ("Category Ones", 0, 6): {0: 100000},
    ("Category Ones", 0, 7): {0: 100000},
    ("Category Ones", 0, 8): {0: 100000},
    ("Category Ones", 1, 0): {0: 100000},
    ("Category Ones", 1, 1): {0: 100000},
    ("Category Ones", 1, 2): {0: 100000},
    ("Category Ones", 1, 3): {0: 100000},
    ("Category Ones", 1, 4): {0: 100000},
    ("Category Ones", 1, 5): {0: 100000},
    ("Category Ones", 1, 6): {0: 33491, 1: 66509},
    ("Category Ones", 1, 7): {0: 27838, 1: 72162},
    ("Category Ones", 1, 8): {0: 23094, 1: 76906},
    ("Category Ones", 2, 0): {0: 100000},
    ("Category Ones", 2, 1): {0: 100000},
    ("Category Ones", 2, 2): {0: 100000},
    ("Category Ones", 2, 3): {0: 33544, 1: 66456},
    ("Category Ones", 2, 4): {0: 23342, 1: 76658},
    ("Category Ones", 2, 5): {0: 16036, 2: 83964},
    ("Category Ones", 2, 6): {0: 11355, 2: 88645},
    ("Category Ones", 2, 7): {0: 7812, 2: 92188},
    ("Category Ones", 2, 8): {0: 5395, 2: 94605},
    ("Category Ones", 3, 0): {0: 100000},
    ("Category Ones", 3, 1): {0: 100000},
    ("Category Ones", 3, 2): {0: 33327, 1: 66673},
    ("Category Ones", 3, 3): {0: 19432, 2: 80568},
    ("Category Ones", 3, 4): {0: 11191, 2: 88809},
    ("Category Ones", 3, 5): {0: 35427, 2: 64573},
    ("Category Ones", 3, 6): {0: 26198, 2: 73802},
    ("Category Ones", 3, 7): {0: 18851, 3: 81149},
    ("Category Ones", 3, 8): {0: 13847, 3: 86153},
    ("Category Ones", 4, 0): {0: 100000},
    ("Category Ones", 4, 1): {0: 100000},
    ("Category Ones", 4, 2): {0: 23349, 2: 76651},
    ("Category Ones", 4, 3): {0: 11366, 2: 88634},
    ("Category Ones", 4, 4): {0: 28572, 3: 71428},
    ("Category Ones", 4, 5): {0: 17976, 3: 82024},
    ("Category Ones", 4, 6): {0: 1253, 3: 98747},
    ("Category Ones", 4, 7): {0: 31228, 3: 68772},
    ("Category Ones", 4, 8): {0: 23273, 4: 76727},
    ("Category Ones", 5, 0): {0: 100000},
    ("Category Ones", 5, 1): {0: 100000},
    ("Category Ones", 5, 2): {0: 16212, 2: 83788},
    ("Category Ones", 5, 3): {0: 30104, 3: 69896},
    ("Category Ones", 5, 4): {0: 2552, 3: 97448},
    ("Category Ones", 5, 5): {0: 32028, 4: 67972},
    ("Category Ones", 5, 6): {0: 21215, 4: 78785},
    ("Category Ones", 5, 7): {0: 2295, 4: 97705},
    ("Category Ones", 5, 8): {0: 1167, 4: 98833},
    ("Category Ones", 6, 0): {0: 100000},
    ("Category Ones", 6, 1): {0: 33501, 1: 66499},
    ("Category Ones", 6, 2): {0: 40705, 2: 59295},
    ("Category Ones", 6, 3): {0: 3764, 3: 96236},
    ("Category Ones", 6, 4): {0: 9324, 4: 90676},
    ("Category Ones", 6, 5): {0: 4208, 4: 95792},
    ("Category Ones", 6, 6): {0: 158, 5: 99842},
    ("Category Ones", 6, 7): {0: 5503, 5: 94497},
    ("Category Ones", 6, 8): {0: 2896, 5: 97104},
    ("Category Ones", 7, 0): {0: 100000},
    ("Category Ones", 7, 1): {0: 27838, 2: 72162},
    ("Category Ones", 7, 2): {0: 7796, 3: 92204},
    ("Category Ones", 7, 3): {0: 13389, 4: 86611},
    ("Category Ones", 7, 4): {0: 5252, 4: 94748},
    ("Category Ones", 7, 5): {0: 9854, 5: 90146},
    ("Category Ones", 7, 6): {0: 4625, 5: 95375},
    ("Category Ones", 7, 7): {0: 30339, 6: 69661},
    ("Category Ones", 7, 8): {0: 5519, 6: 94481},
    ("Category Ones", 8, 0): {0: 100000},
    ("Category Ones", 8, 1): {0: 23156, 2: 76844},
    ("Category Ones", 8, 2): {0: 5472, 3: 94528},
    ("Category Ones", 8, 3): {0: 8661, 4: 91339},
    ("Category Ones", 8, 4): {0: 12125, 5: 87875},
    ("Category Ones", 8, 5): {0: 5173, 5: 94827},
    ("Category Ones", 8, 6): {0: 8872, 6: 91128},
    ("Category Ones", 8, 7): {0: 4236, 6: 95764},
    ("Category Ones", 8, 8): {0: 9107, 7: 90893},
    ("Category Twos", 0, 0): {0: 100000},
    ("Category Twos", 0, 1): {0: 100000},
    ("Category Twos", 0, 2): {0: 100000},
    ("Category Twos", 0, 3): {0: 100000},
    ("Category Twos", 0, 4): {0: 100000},
    ("Category Twos", 0, 5): {0: 100000},
    ("Category Twos", 0, 6): {0: 100000},
    ("Category Twos", 0, 7): {0: 100000},
    ("Category Twos", 0, 8): {0: 100000},
    ("Category Twos", 1, 0): {0: 100000},
    ("Category Twos", 1, 1): {0: 100000},
    ("Category Twos", 1, 2): {0: 100000},
    ("Category Twos", 1, 3): {0: 57818, 2: 42182},
    ("Category Twos", 1, 4): {0: 48418, 2: 51582},
    ("Category Twos", 1, 5): {0: 40301, 2: 59699},
    ("Category Twos", 1, 6): {0: 33558, 2: 66442},
    ("Category Twos", 1, 7): {0: 28182, 2: 71818},
    ("Category Twos", 1, 8): {0: 23406, 2: 76594},
    ("Category Twos", 2, 0): {0: 100000},
    ("Category Twos", 2, 1): {0: 100000},
    ("Category Twos", 2, 2): {0: 48238, 2: 51762},
    ("Category Twos", 2, 3): {0: 33290, 4: 66710},
    ("Category Twos", 2, 4): {0: 23136, 4: 76864},
    ("Category Twos", 2, 5): {0: 16146, 4: 83854},
    ("Category Twos", 2, 6): {0: 11083, 4: 88917},
    ("Category Twos", 2, 7): {0: 7662, 4: 92338},
    ("Category Twos", 2, 8): {0: 5354, 4: 94646},
    ("Category Twos", 3, 0): {0: 100000},
    ("Category Twos", 3, 1): {0: 58021, 2: 41979},
    ("Category Twos", 3, 2): {0: 33548, 4: 66452},
    ("Category Twos", 3, 3): {0: 19375, 4: 80625},
    ("Category Twos", 3, 4): {0: 10998, 4: 89002},
    ("Category Twos", 3, 5): {0: 6519, 6: 93481},
    ("Category Twos", 3, 6): {0: 3619, 6: 96381},
    ("Category Twos", 3, 7): {0: 2195, 6: 97805},
    ("Category Twos", 3, 8): {0: 13675, 6: 86325},
    ("Category Twos", 4, 0): {0: 100000},
    ("Category Twos", 4, 1): {0: 48235, 2: 51765},
    ("Category Twos", 4, 2): {0: 23289, 4: 76711},
    ("Category Twos", 4, 3): {0: 11177, 6: 88823},
    ("Category Twos", 4, 4): {0: 5499, 6: 94501},
    ("Category Twos", 4, 5): {0: 18356, 6: 81644},
    ("Category Twos", 4, 6): {0: 11169, 8: 88831},
    ("Category Twos", 4, 7): {0: 6945, 8: 93055},
    ("Category Twos", 4, 8): {0: 4091, 8: 95909},
    ("Category Twos", 5, 0): {0: 100000},
    ("Category Twos", 5, 1): {0: 40028, 4: 59972},
    ("Category Twos", 5, 2): {0: 16009, 6: 83991},
    ("Category Twos", 5, 3): {0: 6489, 6: 93511},
    ("Category Twos", 5, 4): {0: 16690, 8: 83310},
    ("Category Twos", 5, 5): {0: 9016, 8: 90984},
    ("Category Twos", 5, 6): {0: 4602, 8: 95398},
    ("Category Twos", 5, 7): {0: 13627, 10: 86373},
    ("Category Twos", 5, 8): {0: 8742, 10: 91258},
    ("Category Twos", 6, 0): {0: 100000},
    ("Category Twos", 6, 1): {0: 33502, 4: 66498},
    ("Category Twos", 6, 2): {0: 11210, 6: 88790},
    ("Category Twos", 6, 3): {0: 3673, 6: 96327},
    ("Category Twos", 6, 4): {0: 9291, 8: 90709},
    ("Category Twos", 6, 5): {0: 441, 8: 99559},
    ("Category Twos", 6, 6): {0: 10255, 10: 89745},
    ("Category Twos", 6, 7): {0: 5646, 10: 94354},
    ("Category Twos", 6, 8): {0: 14287, 12: 85713},
    ("Category Twos", 7, 0): {0: 100000},
    ("Category Twos", 7, 1): {0: 27683, 4: 72317},
    ("Category Twos", 7, 2): {0: 7824, 6: 92176},
    ("Category Twos", 7, 3): {0: 13167, 8: 86833},
    ("Category Twos", 7, 4): {0: 564, 10: 99436},
    ("Category Twos", 7, 5): {0: 9824, 10: 90176},
    ("Category Twos", 7, 6): {0: 702, 12: 99298},
    ("Category Twos", 7, 7): {0: 10186, 12: 89814},
    ("Category Twos", 7, 8): {0: 942, 12: 99058},
    ("Category Twos", 8, 0): {0: 100000},
    ("Category Twos", 8, 1): {0: 23378, 4: 76622},
    ("Category Twos", 8, 2): {0: 5420, 8: 94580},
    ("Category Twos", 8, 3): {0: 8560, 10: 91440},
    ("Category Twos", 8, 4): {0: 12199, 12: 87801},
    ("Category Twos", 8, 5): {0: 879, 12: 99121},
    ("Category Twos", 8, 6): {0: 9033, 14: 90967},
    ("Category Twos", 8, 7): {0: 15767, 14: 84233},
    ("Category Twos", 8, 8): {2: 9033, 14: 90967},
    ("Category Threes", 0, 0): {0: 100000},
    ("Category Threes", 0, 1): {0: 100000},
    ("Category Threes", 0, 2): {0: 100000},
    ("Category Threes", 0, 3): {0: 100000},
    ("Category Threes", 0, 4): {0: 100000},
    ("Category Threes", 0, 5): {0: 100000},
    ("Category Threes", 0, 6): {0: 100000},
    ("Category Threes", 0, 7): {0: 100000},
    ("Category Threes", 0, 8): {0: 100000},
    ("Category Threes", 1, 0): {0: 100000},
    ("Category Threes", 1, 1): {0: 100000},
    ("Category Threes", 1, 2): {0: 69569, 3: 30431},
    ("Category Threes", 1, 3): {0: 57872, 3: 42128},
    ("Category Threes", 1, 4): {0: 48081, 3: 51919},
    ("Category Threes", 1, 5): {0: 40271, 3: 59729},
    ("Category Threes", 1, 6): {0: 33201, 3: 66799},
    ("Category Threes", 1, 7): {0: 27903, 3: 72097},
    ("Category Threes", 1, 8): {0: 23240, 3: 76760},
    ("Category Threes", 2, 0): {0: 100000},
    ("Category Threes", 2, 1): {0: 69419, 3: 30581},
    ("Category Threes", 2, 2): {0: 48202, 3: 51798},
    ("Category Threes", 2, 3): {0: 33376, 6: 66624},
    ("Category Threes", 2, 4): {0: 23276, 6: 76724},
    ("Category Threes", 2, 5): {0: 16092, 6: 83908},
    ("Category Threes", 2, 6): {0: 11232, 6: 88768},
    ("Category Threes", 2, 7): {0: 7589, 6: 92411},
    ("Category Threes", 2, 8): {0: 5447, 6: 94553},
    ("Category Threes", 3, 0): {0: 100000},
    ("Category Threes", 3, 1): {0: 57964, 3: 42036},
    ("Category Threes", 3, 2): {0: 33637, 6: 66363},
    ("Category Threes", 3, 3): {0: 19520, 6: 80480},
    ("Category Threes", 3, 4): {0: 11265, 6: 88735},
    ("Category Threes", 3, 5): {0: 6419, 6: 72177, 9: 21404},
    ("Category Threes", 3, 6): {0: 3810, 6: 66884, 9: 29306},
    ("Category Threes", 3, 7): {0: 2174, 6: 60595, 9: 37231},
    ("Category Threes", 3, 8): {0: 1237, 6: 53693, 9: 45070},
    ("Category Threes", 4, 0): {0: 100000},
    ("Category Threes", 4, 1): {0: 48121, 6: 51879},
    ("Category Threes", 4, 2): {0: 23296, 6: 76704},
    ("Category Threes", 4, 3): {0: 11233, 6: 68363, 9: 20404},
    ("Category Threes", 4, 4): {0: 5463, 6: 60738, 9: 33799},
    ("Category Threes", 4, 5): {0: 2691, 6: 50035, 12: 47274},
    ("Category Threes", 4, 6): {0: 11267, 9: 88733},
    ("Category Threes", 4, 7): {0: 6921, 9: 66034, 12: 27045},
    ("Category Threes", 4, 8): {0: 4185, 9: 61079, 12: 34736},
    ("Category Threes", 5, 0): {0: 100000},
    ("Category Threes", 5, 1): {0: 40183, 6: 59817},
    ("Category Threes", 5, 2): {0: 16197, 6: 83803},
    ("Category Threes", 5, 3): {0: 6583, 6: 57826, 9: 35591},
    ("Category Threes", 5, 4): {0: 2636, 9: 76577, 12: 20787},
    ("Category Threes", 5, 5): {0: 8879, 9: 57821, 12: 33300},
    ("Category Threes", 5, 6): {0: 4652, 12: 95348},
    ("Category Threes", 5, 7): {0: 2365, 12: 97635},
    ("Category Threes", 5, 8): {0: 8671, 12: 64865, 15: 26464},
    ("Category Threes", 6, 0): {0: 100000},
    ("Category Threes", 6, 1): {0: 33473, 6: 66527},
    ("Category Threes", 6, 2): {0: 11147, 6: 62222, 9: 26631},
    ("Category Threes", 6, 3): {0: 3628, 9: 75348, 12: 21024},
    ("Category Threes", 6, 4): {0: 9498, 9: 52940, 15: 37562},
    ("Category Threes", 6, 5): {0: 4236, 12: 72944, 15: 22820},
    ("Category Threes", 6, 6): {0: 10168, 12: 55072, 15: 34760},
    ("Category Threes", 6, 7): {0: 5519, 15: 94481},
    ("Category Threes", 6, 8): {0: 2968, 15: 76504, 18: 20528},
    ("Category Threes", 7, 0): {0: 100000},
    ("Category Threes", 7, 1): {0: 27933, 6: 72067},
    ("Category Threes", 7, 2): {0: 7794, 6: 55728, 12: 36478},
    ("Category Threes", 7, 3): {0: 2138, 9: 64554, 15: 33308},
    ("Category Threes", 7, 4): {0: 5238, 12: 69214, 15: 25548},
    ("Category Threes", 7, 5): {0: 9894, 15: 90106},
    ("Category Threes", 7, 6): {0: 4656, 15: 69353, 18: 25991},
    ("Category Threes", 7, 7): {0: 10005, 15: 52430, 18: 37565},
    ("Category Threes", 7, 8): {0: 5710, 18: 94290},
    ("Category Threes", 8, 0): {0: 100000},
    ("Category Threes", 8, 1): {0: 23337, 6: 76663},
    ("Category Threes", 8, 2): {0: 5310, 9: 74178, 12: 20512},
    ("Category Threes", 8, 3): {0: 8656, 12: 70598, 15: 20746},
    ("Category Threes", 8, 4): {0: 291, 12: 59487, 18: 40222},
    ("Category Threes", 8, 5): {0: 5145, 15: 63787, 18: 31068},
    ("Category Threes", 8, 6): {0: 8804, 18: 91196},
    ("Category Threes", 8, 7): {0: 4347, 18: 65663, 21: 29990},
    ("Category Threes", 8, 8): {0: 9252, 21: 90748},
    ("Category Fours", 0, 0): {0: 100000},
    ("Category Fours", 0, 1): {0: 100000},
    ("Category Fours", 0, 2): {0: 100000},
    ("Category Fours", 0, 3): {0: 100000},
    ("Category Fours", 0, 4): {0: 100000},
    ("Category Fours", 0, 5): {0: 100000},
    ("Category Fours", 0, 6): {0: 100000},
    ("Category Fours", 0, 7): {0: 100000},
    ("Category Fours", 0, 8): {0: 100000},
    ("Category Fours", 1, 0): {0: 100000},
    ("Category Fours", 1, 1): {0: 83260, 4: 16740},
    ("Category Fours", 1, 2): {0: 69514, 4: 30486},
    ("Category Fours", 1, 3): {0: 58017, 4: 41983},
    ("Category Fours", 1, 4): {0: 48389, 4: 51611},
    ("Category Fours", 1, 5): {0: 40201, 4: 59799},
    ("Category Fours", 1, 6): {0: 33496, 4: 66504},
    ("Category Fours", 1, 7): {0: 28052, 4: 71948},
    ("Category Fours", 1, 8): {0: 23431, 4: 76569},
    ("Category Fours", 2, 0): {0: 100000},
    ("Category Fours", 2, 1): {0: 69379, 4: 30621},
    ("Category Fours", 2, 2): {0: 48538, 4: 51462},
    ("Category Fours", 2, 3): {0: 33756, 4: 48555, 8: 17689},
    ("Category Fours", 2, 4): {0: 23070, 4: 49916, 8: 27014},
    ("Category Fours", 2, 5): {0: 16222, 4: 48009, 8: 35769},
    ("Category Fours", 2, 6): {0: 11125, 4: 44400, 8: 44475},
    ("Category Fours", 2, 7): {0: 7919, 4: 40216, 8: 51865},
    ("Category Fours", 2, 8): {0: 5348, 8: 94652},
    ("Category Fours", 3, 0): {0: 100000},
    ("Category Fours", 3, 1): {0: 57914, 4: 42086},
    ("Category Fours", 3, 2): {0: 33621, 4: 44110, 8: 22269},
    ("Category Fours", 3, 3): {0: 19153, 4: 42425, 8: 38422},
    ("Category Fours", 3, 4): {0: 11125, 8: 88875},
    ("Category Fours", 3, 5): {0: 6367, 8: 72308, 12: 21325},
    ("Category Fours", 3, 6): {0: 3643, 8: 66934, 12: 29423},
    ("Category Fours", 3, 7): {0: 2178, 8: 60077, 12: 37745},
    ("Category Fours", 3, 8): {0: 1255, 8: 53433, 12: 45312},
    ("Category Fours", 4, 0): {0: 100000},
    ("Category Fours", 4, 1): {0: 48465, 4: 51535},
    ("Category Fours", 4, 2): {0: 23296, 4: 40911, 12: 35793},
    ("Category Fours", 4, 3): {0: 11200, 8: 68528, 12: 20272},
    ("Category Fours", 4, 4): {0: 5447, 8: 60507, 12: 34046},
    ("Category Fours", 4, 5): {0: 2533, 8: 50449, 16: 47018},
    ("Category Fours", 4, 6): {0: 1314, 8: 39851, 12: 39425, 16: 19410},
    ("Category Fours", 4, 7): {0: 6823, 12: 66167, 16: 27010},
    ("Category Fours", 4, 8): {0: 4189, 12: 61034, 16: 34777},
    ("Category Fours", 5, 0): {0: 100000},
    ("Category Fours", 5, 1): {0: 40215, 4: 40127, 8: 19658},
    ("Category Fours", 5, 2): {0: 15946, 8: 66737, 12: 17317},
    ("Category Fours", 5, 3): {0: 6479, 8: 58280, 16: 35241},
    ("Category Fours", 5, 4): {0: 2635, 8: 43968, 16: 53397},
    ("Category Fours", 5, 5): {0: 8916, 12: 57586, 16: 33498},
    ("Category Fours", 5, 6): {0: 4682, 12: 49435, 20: 45883},
    ("Category Fours", 5, 7): {0: 2291, 12: 40537, 16: 37701, 20: 19471},
    ("Category Fours", 5, 8): {0: 75, 16: 73483, 20: 26442},
    ("Category Fours", 6, 0): {0: 100000},
    ("Category Fours", 6, 1): {0: 33632, 4: 39856, 8: 26512},
    ("Category Fours", 6, 2): {0: 11175, 8: 62205, 12: 26620},
    ("Category Fours", 6, 3): {0: 3698, 8: 46268, 16: 50034},
    ("Category Fours", 6, 4): {0: 9173, 12: 52855, 20: 37972},
    ("Category Fours", 6, 5): {0: 4254, 12: 41626, 20: 54120},
    ("Category Fours", 6, 6): {0: 1783, 16: 63190, 24: 35027},
    ("Category Fours", 6, 7): {0: 5456, 16: 47775, 24: 46769},
    ("Category Fours", 6, 8): {0: 2881, 16: 39229, 24: 57890},
    ("Category Fours", 7, 0): {0: 100000},
    ("Category Fours", 7, 1): {0: 27821, 4: 39289, 12: 32890},
    ("Category Fours", 7, 2): {0: 7950, 8: 55659, 16: 36391},
    ("Category Fours", 7, 3): {0: 2194, 12: 64671, 20: 33135},
    ("Category Fours", 7, 4): {0: 5063, 12: 41118, 20: 53819},
    ("Category Fours", 7, 5): {0: 171, 16: 57977, 24: 41852},
    ("Category Fours", 7, 6): {0: 4575, 16: 38694, 24: 56731},
    ("Category Fours", 7, 7): {0: 252, 20: 62191, 28: 37557},
    ("Category Fours", 7, 8): {4: 5576, 20: 45351, 28: 49073},
    ("Category Fours", 8, 0): {0: 100000},
    ("Category Fours", 8, 1): {0: 23275, 8: 76725},
    ("Category Fours", 8, 2): {0: 5421, 8: 48273, 16: 46306},
    ("Category Fours", 8, 3): {0: 8626, 12: 45516, 20: 45858},
    ("Category Fours", 8, 4): {0: 2852, 16: 56608, 24: 40540},
    ("Category Fours", 8, 5): {0: 5049, 20: 63834, 28: 31117},
    ("Category Fours", 8, 6): {0: 269, 20: 53357, 28: 46374},
    ("Category Fours", 8, 7): {0: 4394, 24: 65785, 28: 29821},
    ("Category Fours", 8, 8): {0: 266, 24: 58443, 32: 41291},
    ("Category Fives", 0, 0): {0: 100000},
    ("Category Fives", 0, 1): {0: 100000},
    ("Category Fives", 0, 2): {0: 100000},
    ("Category Fives", 0, 3): {0: 100000},
    ("Category Fives", 0, 4): {0: 100000},
    ("Category Fives", 0, 5): {0: 100000},
    ("Category Fives", 0, 6): {0: 100000},
    ("Category Fives", 0, 7): {0: 100000},
    ("Category Fives", 0, 8): {0: 100000},
    ("Category Fives", 1, 0): {0: 100000},
    ("Category Fives", 1, 1): {0: 83338, 5: 16662},
    ("Category Fives", 1, 2): {0: 69499, 5: 30501},
    ("Category Fives", 1, 3): {0: 57799, 5: 42201},
    ("Category Fives", 1, 4): {0: 48311, 5: 51689},
    ("Category Fives", 1, 5): {0: 40084, 5: 59916},
    ("Category Fives", 1, 6): {0: 33440, 5: 66560},
    ("Category Fives", 1, 7): {0: 27730, 5: 72270},
    ("Category Fives", 1, 8): {0: 23210, 5: 76790},
    ("Category Fives", 2, 0): {0: 100000},
    ("Category Fives", 2, 1): {0: 69299, 5: 30701},
    ("Category Fives", 2, 2): {0: 48156, 5: 51844},
    ("Category Fives", 2, 3): {0: 33225, 5: 49153, 10: 17622},
    ("Category Fives", 2, 4): {0: 23218, 5: 50075, 10: 26707},
    ("Category Fives", 2, 5): {0: 15939, 5: 48313, 10: 35748},
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    ("Category Large Straight", 0, 1): {0: 100000},
    ("Category Large Straight", 0, 2): {0: 100000},
    ("Category Large Straight", 0, 3): {0: 100000},
    ("Category Large Straight", 0, 4): {0: 100000},
    ("Category Large Straight", 0, 5): {0: 100000},
    ("Category Large Straight", 0, 6): {0: 100000},
    ("Category Large Straight", 0, 7): {0: 100000},
    ("Category Large Straight", 0, 8): {0: 100000},
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    ("Category Large Straight", 1, 1): {0: 100000},
    ("Category Large Straight", 1, 2): {0: 100000},
    ("Category Large Straight", 1, 3): {0: 100000},
    ("Category Large Straight", 1, 4): {0: 100000},
    ("Category Large Straight", 1, 5): {0: 100000},
    ("Category Large Straight", 1, 6): {0: 100000},
    ("Category Large Straight", 1, 7): {0: 100000},
    ("Category Large Straight", 1, 8): {0: 100000},
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    ("Category Large Straight", 2, 1): {0: 100000},
    ("Category Large Straight", 2, 2): {0: 100000},
    ("Category Large Straight", 2, 3): {0: 100000},
    ("Category Large Straight", 2, 4): {0: 100000},
    ("Category Large Straight", 2, 5): {0: 100000},
    ("Category Large Straight", 2, 6): {0: 100000},
    ("Category Large Straight", 2, 7): {0: 100000},
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    ("Category Large Straight", 3, 1): {0: 100000},
    ("Category Large Straight", 3, 2): {0: 100000},
    ("Category Large Straight", 3, 3): {0: 100000},
    ("Category Large Straight", 3, 4): {0: 100000},
    ("Category Large Straight", 3, 5): {0: 100000},
    ("Category Large Straight", 3, 6): {0: 100000},
    ("Category Large Straight", 3, 7): {0: 100000},
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    ("Category Large Straight", 4, 2): {0: 100000},
    ("Category Large Straight", 4, 3): {0: 100000},
    ("Category Large Straight", 4, 4): {0: 100000},
    ("Category Large Straight", 4, 5): {0: 100000},
    ("Category Large Straight", 4, 6): {0: 100000},
    ("Category Large Straight", 4, 7): {0: 100000},
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    ("Category Large Straight", 5, 2): {0: 87056, 40: 12944},
    ("Category Large Straight", 5, 3): {0: 75101, 40: 24899},
    ("Category Large Straight", 5, 4): {0: 63617, 40: 36383},
    ("Category Large Straight", 5, 5): {0: 53149, 40: 46851},
    ("Category Large Straight", 5, 6): {0: 44321, 40: 55679},
    ("Category Large Straight", 5, 7): {0: 36948, 40: 63052},
    ("Category Large Straight", 5, 8): {0: 30661, 40: 69339},
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    ("Category Large Straight", 6, 1): {0: 90756, 40: 9244},
    ("Category Large Straight", 6, 2): {0: 69805, 40: 30195},
    ("Category Large Straight", 6, 3): {0: 49814, 40: 50186},
    ("Category Large Straight", 6, 4): {0: 35102, 40: 64898},
    ("Category Large Straight", 6, 5): {0: 24385, 40: 75615},
    ("Category Large Straight", 6, 6): {0: 17018, 40: 82982},
    ("Category Large Straight", 6, 7): {0: 11739, 40: 88261},
    ("Category Large Straight", 6, 8): {0: 7972, 40: 92028},
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    ("Category Large Straight", 7, 1): {0: 82840, 40: 17160},
    ("Category Large Straight", 7, 2): {0: 52821, 40: 47179},
    ("Category Large Straight", 7, 3): {0: 31348, 40: 68652},
    ("Category Large Straight", 7, 4): {0: 18166, 40: 81834},
    ("Category Large Straight", 7, 5): {0: 10690, 40: 89310},
    ("Category Large Straight", 7, 6): {0: 6051, 40: 93949},
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    ("Category Large Straight", 7, 8): {0: 1941, 40: 98059},
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    ("Category Large Straight", 8, 1): {0: 73520, 40: 26480},
    ("Category Large Straight", 8, 2): {0: 39031, 40: 60969},
    ("Category Large Straight", 8, 3): {0: 19156, 40: 80844},
    ("Category Large Straight", 8, 4): {0: 9304, 40: 90696},
    ("Category Large Straight", 8, 5): {0: 4420, 40: 95580},
    ("Category Large Straight", 8, 6): {0: 2141, 40: 97859},
    ("Category Large Straight", 8, 7): {0: 1037, 40: 98963},
    ("Category Large Straight", 8, 8): {0: 511, 40: 99489},
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    ("Category Full House", 0, 1): {0: 100000},
    ("Category Full House", 0, 2): {0: 100000},
    ("Category Full House", 0, 3): {0: 100000},
    ("Category Full House", 0, 4): {0: 100000},
    ("Category Full House", 0, 5): {0: 100000},
    ("Category Full House", 0, 6): {0: 100000},
    ("Category Full House", 0, 7): {0: 100000},
    ("Category Full House", 0, 8): {0: 100000},
    ("Category Full House", 1, 0): {0: 100000},
    ("Category Full House", 1, 1): {0: 100000},
    ("Category Full House", 1, 2): {0: 100000},
    ("Category Full House", 1, 3): {0: 100000},
    ("Category Full House", 1, 4): {0: 100000},
    ("Category Full House", 1, 5): {0: 100000},
    ("Category Full House", 1, 6): {0: 100000},
    ("Category Full House", 1, 7): {0: 100000},
    ("Category Full House", 1, 8): {0: 100000},
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    ("Category Full House", 2, 1): {0: 100000},
    ("Category Full House", 2, 2): {0: 100000},
    ("Category Full House", 2, 3): {0: 100000},
    ("Category Full House", 2, 4): {0: 100000},
    ("Category Full House", 2, 5): {0: 100000},
    ("Category Full House", 2, 6): {0: 100000},
    ("Category Full House", 2, 7): {0: 100000},
    ("Category Full House", 2, 8): {0: 100000},
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    ("Category Full House", 3, 2): {0: 100000},
    ("Category Full House", 3, 3): {0: 100000},
    ("Category Full House", 3, 4): {0: 100000},
    ("Category Full House", 3, 5): {0: 100000},
    ("Category Full House", 3, 6): {0: 100000},
    ("Category Full House", 3, 7): {0: 100000},
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    ("Category Full House", 4, 1): {0: 100000},
    ("Category Full House", 4, 2): {0: 100000},
    ("Category Full House", 4, 3): {0: 100000},
    ("Category Full House", 4, 4): {0: 100000},
    ("Category Full House", 4, 5): {0: 100000},
    ("Category Full House", 4, 6): {0: 100000},
    ("Category Full House", 4, 7): {0: 100000},
    ("Category Full House", 4, 8): {0: 100000},
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    ("Category Full House", 5, 1): {0: 96155, 25: 3845},
    ("Category Full House", 5, 2): {0: 81391, 25: 18609},
    ("Category Full House", 5, 3): {0: 64300, 25: 35700},
    ("Category Full House", 5, 4): {0: 49669, 25: 50331},
    ("Category Full House", 5, 5): {0: 38019, 25: 61981},
    ("Category Full House", 5, 6): {0: 29751, 25: 70249},
    ("Category Full House", 5, 7): {0: 22960, 25: 77040},
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    ("Category Full House", 6, 1): {0: 82989, 25: 17011},
    ("Category Full House", 6, 2): {0: 47153, 25: 52847},
    ("Category Full House", 6, 3): {0: 24151, 25: 75849},
    ("Category Full House", 6, 4): {0: 12519, 25: 87481},
    ("Category Full House", 6, 5): {0: 6524, 25: 93476},
    ("Category Full House", 6, 6): {0: 3606, 25: 96394},
    ("Category Full House", 6, 7): {0: 1959, 25: 98041},
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    ("Category Full House", 7, 1): {0: 60232, 25: 39768},
    ("Category Full House", 7, 2): {0: 18894, 25: 81106},
    ("Category Full House", 7, 3): {0: 5682, 25: 94318},
    ("Category Full House", 7, 4): {0: 1706, 25: 98294},
    ("Category Full House", 7, 5): {0: 522, 25: 99478},
    ("Category Full House", 7, 6): {0: 146, 25: 99854},
    ("Category Full House", 7, 7): {0: 54, 25: 99946},
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    ("Category Full House", 8, 1): {0: 35909, 25: 64091},
    ("Category Full House", 8, 2): {0: 5712, 25: 94288},
    ("Category Full House", 8, 3): {0: 930, 25: 99070},
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    ("Category Full House", 8, 6): {0: 6, 25: 99994},
    ("Category Full House", 8, 7): {25: 100000},
    ("Category Full House", 8, 8): {25: 100000},
    ("Category Yacht", 0, 0): {0: 100000},
    ("Category Yacht", 0, 1): {0: 100000},
    ("Category Yacht", 0, 2): {0: 100000},
    ("Category Yacht", 0, 3): {0: 100000},
    ("Category Yacht", 0, 4): {0: 100000},
    ("Category Yacht", 0, 5): {0: 100000},
    ("Category Yacht", 0, 6): {0: 100000},
    ("Category Yacht", 0, 7): {0: 100000},
    ("Category Yacht", 0, 8): {0: 100000},
    ("Category Yacht", 1, 0): {0: 100000},
    ("Category Yacht", 1, 1): {0: 100000},
    ("Category Yacht", 1, 2): {0: 100000},
    ("Category Yacht", 1, 3): {0: 100000},
    ("Category Yacht", 1, 4): {0: 100000},
    ("Category Yacht", 1, 5): {0: 100000},
    ("Category Yacht", 1, 6): {0: 100000},
    ("Category Yacht", 1, 7): {0: 100000},
    ("Category Yacht", 1, 8): {0: 100000},
    ("Category Yacht", 2, 0): {0: 100000},
    ("Category Yacht", 2, 1): {0: 100000},
    ("Category Yacht", 2, 2): {0: 100000},
    ("Category Yacht", 2, 3): {0: 100000},
    ("Category Yacht", 2, 4): {0: 100000},
    ("Category Yacht", 2, 5): {0: 100000},
    ("Category Yacht", 2, 6): {0: 100000},
    ("Category Yacht", 2, 7): {0: 100000},
    ("Category Yacht", 2, 8): {0: 100000},
    ("Category Yacht", 3, 0): {0: 100000},
    ("Category Yacht", 3, 1): {0: 100000},
    ("Category Yacht", 3, 2): {0: 100000},
    ("Category Yacht", 3, 3): {0: 100000},
    ("Category Yacht", 3, 4): {0: 100000},
    ("Category Yacht", 3, 5): {0: 100000},
    ("Category Yacht", 3, 6): {0: 100000},
    ("Category Yacht", 3, 7): {0: 100000},
    ("Category Yacht", 3, 8): {0: 100000},
    ("Category Yacht", 4, 0): {0: 100000},
    ("Category Yacht", 4, 1): {0: 100000},
    ("Category Yacht", 4, 2): {0: 100000},
    ("Category Yacht", 4, 3): {0: 100000},
    ("Category Yacht", 4, 4): {0: 100000},
    ("Category Yacht", 4, 5): {0: 100000},
    ("Category Yacht", 4, 6): {0: 100000},
    ("Category Yacht", 4, 7): {0: 100000},
    ("Category Yacht", 4, 8): {0: 100000},
    ("Category Yacht", 5, 0): {0: 100000},
    ("Category Yacht", 5, 1): {0: 100000},
    ("Category Yacht", 5, 2): {0: 98727, 50: 1273},
    ("Category Yacht", 5, 3): {0: 95347, 50: 4653},
    ("Category Yacht", 5, 4): {0: 89969, 50: 10031},
    ("Category Yacht", 5, 5): {0: 83124, 50: 16876},
    ("Category Yacht", 5, 6): {0: 75023, 50: 24977},
    ("Category Yacht", 5, 7): {0: 67007, 50: 32993},
    ("Category Yacht", 5, 8): {0: 58618, 50: 41382},
    ("Category Yacht", 6, 0): {0: 100000},
    ("Category Yacht", 6, 1): {0: 100000},
    ("Category Yacht", 6, 2): {0: 94726, 50: 5274},
    ("Category Yacht", 6, 3): {0: 84366, 50: 15634},
    ("Category Yacht", 6, 4): {0: 70782, 50: 29218},
    ("Category Yacht", 6, 5): {0: 56573, 50: 43427},
    ("Category Yacht", 6, 6): {0: 44206, 50: 55794},
    ("Category Yacht", 6, 7): {0: 33578, 50: 66422},
    ("Category Yacht", 6, 8): {0: 25079, 50: 74921},
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    ("Category Yacht", 7, 1): {0: 100000},
    ("Category Yacht", 7, 2): {0: 87511, 50: 12489},
    ("Category Yacht", 7, 3): {0: 68252, 50: 31748},
    ("Category Yacht", 7, 4): {0: 49065, 50: 50935},
    ("Category Yacht", 7, 5): {0: 33364, 50: 66636},
    ("Category Yacht", 7, 6): {0: 21483, 50: 78517},
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    ("Category Yacht", 8, 1): {0: 97212, 50: 2788},
    ("Category Yacht", 8, 2): {0: 76962, 50: 23038},
    ("Category Yacht", 8, 3): {0: 50533, 50: 49467},
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    ("Category Yacht", 8, 5): {0: 16776, 50: 83224},
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    ("Category Distincts", 1, 2): {1: 100000},
    ("Category Distincts", 1, 3): {1: 100000},
    ("Category Distincts", 1, 4): {1: 100000},
    ("Category Distincts", 1, 5): {1: 100000},
    ("Category Distincts", 1, 6): {1: 100000},
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    ("Category Distincts", 1, 8): {1: 100000},
    ("Category Distincts", 2, 1): {1: 16804, 2: 83196},
    ("Category Distincts", 2, 2): {1: 2686, 2: 97314},
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    ("Category Distincts", 2, 4): {1: 66, 2: 99934},
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    ("Category Distincts", 2, 6): {1: 1, 2: 99999},
    ("Category Distincts", 2, 7): {2: 100000},
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    ("Category Distincts", 3, 1): {1: 2760, 3: 97240},
    ("Category Distincts", 3, 2): {1: 15014, 3: 84986},
    ("Category Distincts", 3, 3): {1: 4866, 3: 95134},
    ("Category Distincts", 3, 4): {2: 1659, 3: 98341},
    ("Category Distincts", 3, 5): {2: 575, 3: 99425},
    ("Category Distincts", 3, 6): {2: 200, 3: 99800},
    ("Category Distincts", 3, 7): {2: 69, 3: 99931},
    ("Category Distincts", 3, 8): {2: 22, 3: 99978},
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    ("Category Distincts", 4, 2): {1: 1893, 4: 98107},
    ("Category Distincts", 4, 3): {2: 19861, 4: 80139},
    ("Category Distincts", 4, 4): {2: 9879, 4: 90121},
    ("Category Distincts", 4, 5): {2: 4906, 4: 95094},
    ("Category Distincts", 4, 6): {3: 2494, 4: 97506},
    ("Category Distincts", 4, 7): {3: 1297, 4: 98703},
    ("Category Distincts", 4, 8): {3: 611, 4: 99389},
    ("Category Distincts", 5, 1): {1: 5798, 4: 94202},
    ("Category Distincts", 5, 2): {2: 11843, 4: 88157},
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    ("Category Distincts", 5, 4): {3: 32354, 5: 67646},
    ("Category Distincts", 5, 5): {3: 21606, 5: 78394},
    ("Category Distincts", 5, 6): {3: 14525, 5: 85475},
    ("Category Distincts", 5, 7): {3: 9660, 5: 90340},
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    ("Category Distincts", 6, 6): {4: 1557, 6: 98443},
    ("Category Distincts", 6, 7): {4: 728, 6: 99272},
    ("Category Distincts", 6, 8): {4: 321, 6: 99679},
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    ("Category Distincts", 7, 5): {4: 28257, 6: 71743},
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    ("Category Distincts", 7, 7): {4: 13618, 6: 86382},
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    ("Category Distincts", 8, 7): {4: 4179, 6: 95821},
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    ("Category Two times Ones", 0, 1): {0: 100000},
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    ("Category Two times Ones", 1, 3): {0: 57818, 2: 42182},
    ("Category Two times Ones", 1, 4): {0: 48418, 2: 51582},
    ("Category Two times Ones", 1, 5): {0: 40301, 2: 59699},
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    ("Category Two times Ones", 2, 3): {0: 33290, 4: 66710},
    ("Category Two times Ones", 2, 4): {0: 23136, 4: 76864},
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    ("Category Two times Ones", 3, 1): {0: 58021, 2: 41979},
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    ("Category Two times Ones", 7, 0): {0: 100000},
    ("Category Two times Ones", 7, 1): {0: 27683, 4: 72317},
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    ("Category Two times Ones", 7, 4): {0: 564, 10: 99436},
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    ("Category Two times Ones", 7, 6): {0: 702, 12: 99298},
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    ("Category Two times Ones", 8, 0): {0: 100000},
    ("Category Two times Ones", 8, 1): {0: 23378, 4: 76622},
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    ("Category Two times Ones", 8, 5): {0: 879, 12: 99121},
    ("Category Two times Ones", 8, 6): {0: 9033, 14: 90967},
    ("Category Two times Ones", 8, 7): {0: 15767, 14: 84233},
    ("Category Two times Ones", 8, 8): {2: 9033, 14: 90967},
    ("Category Half of Sixes", 0, 0): {0: 100000},
    ("Category Half of Sixes", 0, 1): {0: 100000},
    ("Category Half of Sixes", 0, 2): {0: 100000},
    ("Category Half of Sixes", 0, 3): {0: 100000},
    ("Category Half of Sixes", 0, 4): {0: 100000},
    ("Category Half of Sixes", 0, 5): {0: 100000},
    ("Category Half of Sixes", 0, 6): {0: 100000},
    ("Category Half of Sixes", 0, 7): {0: 100000},
    ("Category Half of Sixes", 0, 8): {0: 100000},
    ("Category Half of Sixes", 1, 0): {0: 100000},
    ("Category Half of Sixes", 1, 1): {0: 100000},
    ("Category Half of Sixes", 1, 2): {0: 69569, 3: 30431},
    ("Category Half of Sixes", 1, 3): {0: 57872, 3: 42128},
    ("Category Half of Sixes", 1, 4): {0: 48081, 3: 51919},
    ("Category Half of Sixes", 1, 5): {0: 40271, 3: 59729},
    ("Category Half of Sixes", 1, 6): {0: 33201, 3: 66799},
    ("Category Half of Sixes", 1, 7): {0: 27903, 3: 72097},
    ("Category Half of Sixes", 1, 8): {0: 23240, 3: 76760},
    ("Category Half of Sixes", 2, 0): {0: 100000},
    ("Category Half of Sixes", 2, 1): {0: 69419, 3: 30581},
    ("Category Half of Sixes", 2, 2): {0: 48202, 3: 51798},
    ("Category Half of Sixes", 2, 3): {0: 33376, 6: 66624},
    ("Category Half of Sixes", 2, 4): {0: 23276, 6: 76724},
    ("Category Half of Sixes", 2, 5): {0: 16092, 6: 83908},
    ("Category Half of Sixes", 2, 6): {0: 11232, 6: 88768},
    ("Category Half of Sixes", 2, 7): {0: 7589, 6: 92411},
    ("Category Half of Sixes", 2, 8): {0: 5447, 6: 94553},
    ("Category Half of Sixes", 3, 0): {0: 100000},
    ("Category Half of Sixes", 3, 1): {0: 57964, 3: 42036},
    ("Category Half of Sixes", 3, 2): {0: 33637, 6: 66363},
    ("Category Half of Sixes", 3, 3): {0: 19520, 6: 80480},
    ("Category Half of Sixes", 3, 4): {0: 11265, 6: 88735},
    ("Category Half of Sixes", 3, 5): {0: 6419, 6: 72177, 9: 21404},
    ("Category Half of Sixes", 3, 6): {0: 3810, 6: 66884, 9: 29306},
    ("Category Half of Sixes", 3, 7): {0: 2174, 6: 60595, 9: 37231},
    ("Category Half of Sixes", 3, 8): {0: 1237, 6: 53693, 9: 45070},
    ("Category Half of Sixes", 4, 0): {0: 100000},
    ("Category Half of Sixes", 4, 1): {0: 48121, 6: 51879},
    ("Category Half of Sixes", 4, 2): {0: 23296, 6: 76704},
    ("Category Half of Sixes", 4, 3): {0: 11233, 6: 68363, 9: 20404},
    ("Category Half of Sixes", 4, 4): {0: 5463, 6: 60738, 9: 33799},
    ("Category Half of Sixes", 4, 5): {0: 2691, 6: 50035, 12: 47274},
    ("Category Half of Sixes", 4, 6): {0: 11267, 9: 88733},
    ("Category Half of Sixes", 4, 7): {0: 6921, 9: 66034, 12: 27045},
    ("Category Half of Sixes", 4, 8): {0: 4185, 9: 61079, 12: 34736},
    ("Category Half of Sixes", 5, 0): {0: 100000},
    ("Category Half of Sixes", 5, 1): {0: 40183, 6: 59817},
    ("Category Half of Sixes", 5, 2): {0: 16197, 6: 83803},
    ("Category Half of Sixes", 5, 3): {0: 6583, 6: 57826, 9: 35591},
    ("Category Half of Sixes", 5, 4): {0: 2636, 9: 76577, 12: 20787},
    ("Category Half of Sixes", 5, 5): {0: 8879, 9: 57821, 12: 33300},
    ("Category Half of Sixes", 5, 6): {0: 4652, 12: 95348},
    ("Category Half of Sixes", 5, 7): {0: 2365, 12: 97635},
    ("Category Half of Sixes", 5, 8): {0: 8671, 12: 64865, 15: 26464},
    ("Category Half of Sixes", 6, 0): {0: 100000},
    ("Category Half of Sixes", 6, 1): {0: 33473, 6: 66527},
    ("Category Half of Sixes", 6, 2): {0: 11147, 6: 62222, 9: 26631},
    ("Category Half of Sixes", 6, 3): {0: 3628, 9: 75348, 12: 21024},
    ("Category Half of Sixes", 6, 4): {0: 9498, 9: 52940, 15: 37562},
    ("Category Half of Sixes", 6, 5): {0: 4236, 12: 72944, 15: 22820},
    ("Category Half of Sixes", 6, 6): {0: 10168, 12: 55072, 15: 34760},
    ("Category Half of Sixes", 6, 7): {0: 5519, 15: 94481},
    ("Category Half of Sixes", 6, 8): {0: 2968, 15: 76504, 18: 20528},
    ("Category Half of Sixes", 7, 0): {0: 100000},
    ("Category Half of Sixes", 7, 1): {0: 27933, 6: 72067},
    ("Category Half of Sixes", 7, 2): {0: 7794, 6: 55728, 12: 36478},
    ("Category Half of Sixes", 7, 3): {0: 2138, 9: 64554, 15: 33308},
    ("Category Half of Sixes", 7, 4): {0: 5238, 12: 69214, 15: 25548},
    ("Category Half of Sixes", 7, 5): {0: 9894, 15: 90106},
    ("Category Half of Sixes", 7, 6): {0: 4656, 15: 69353, 18: 25991},
    ("Category Half of Sixes", 7, 7): {0: 10005, 15: 52430, 18: 37565},
    ("Category Half of Sixes", 7, 8): {0: 5710, 18: 94290},
    ("Category Half of Sixes", 8, 0): {0: 100000},
    ("Category Half of Sixes", 8, 1): {0: 23337, 6: 76663},
    ("Category Half of Sixes", 8, 2): {0: 5310, 9: 74178, 12: 20512},
    ("Category Half of Sixes", 8, 3): {0: 8656, 12: 70598, 15: 20746},
    ("Category Half of Sixes", 8, 4): {0: 291, 12: 59487, 18: 40222},
    ("Category Half of Sixes", 8, 5): {0: 5145, 15: 63787, 18: 31068},
    ("Category Half of Sixes", 8, 6): {0: 8804, 18: 91196},
    ("Category Half of Sixes", 8, 7): {0: 4347, 18: 65663, 21: 29990},
    ("Category Half of Sixes", 8, 8): {0: 9252, 21: 90748},
    ("Category Twos and Threes", 1, 1): {0: 66466, 2: 33534},
    ("Category Twos and Threes", 1, 2): {0: 55640, 2: 44360},
    ("Category Twos and Threes", 1, 3): {0: 57822, 3: 42178},
    ("Category Twos and Threes", 1, 4): {0: 48170, 3: 51830},
    ("Category Twos and Threes", 1, 5): {0: 40294, 3: 59706},
    ("Category Twos and Threes", 1, 6): {0: 33417, 3: 66583},
    ("Category Twos and Threes", 1, 7): {0: 27852, 3: 72148},
    ("Category Twos and Threes", 1, 8): {0: 23364, 3: 76636},
    ("Category Twos and Threes", 2, 1): {0: 44565, 3: 55435},
    ("Category Twos and Threes", 2, 2): {0: 46335, 3: 53665},
    ("Category Twos and Threes", 2, 3): {0: 32347, 3: 67653},
    ("Category Twos and Threes", 2, 4): {0: 22424, 5: 77576},
    ("Category Twos and Threes", 2, 5): {0: 15661, 6: 84339},
    ("Category Twos and Threes", 2, 6): {0: 10775, 6: 89225},
    ("Category Twos and Threes", 2, 7): {0: 7375, 6: 92625},
    ("Category Twos and Threes", 2, 8): {0: 5212, 6: 94788},
    ("Category Twos and Threes", 3, 1): {0: 29892, 3: 70108},
    ("Category Twos and Threes", 3, 2): {0: 17285, 5: 82715},
    ("Category Twos and Threes", 3, 3): {0: 17436, 6: 82564},
    ("Category Twos and Threes", 3, 4): {0: 9962, 6: 90038},
    ("Category Twos and Threes", 3, 5): {0: 3347, 6: 96653},
    ("Category Twos and Threes", 3, 6): {0: 1821, 8: 98179},
    ("Category Twos and Threes", 3, 7): {0: 1082, 6: 61417, 9: 37501},
    ("Category Twos and Threes", 3, 8): {0: 13346, 9: 86654},
    ("Category Twos and Threes", 4, 1): {0: 19619, 5: 80381},
    ("Category Twos and Threes", 4, 2): {0: 18914, 6: 81086},
    ("Category Twos and Threes", 4, 3): {0: 4538, 5: 61859, 8: 33603},
    ("Category Twos and Threes", 4, 4): {0: 2183, 6: 62279, 9: 35538},
    ("Category Twos and Threes", 4, 5): {0: 16416, 9: 83584},
    ("Category Twos and Threes", 4, 6): {0: 6285, 9: 93715},
    ("Category Twos and Threes", 4, 7): {0: 30331, 11: 69669},
    ("Category Twos and Threes", 4, 8): {0: 22305, 12: 77695},
    ("Category Twos and Threes", 5, 1): {0: 13070, 5: 86930},
    ("Category Twos and Threes", 5, 2): {0: 5213, 5: 61441, 8: 33346},
    ("Category Twos and Threes", 5, 3): {0: 2126, 6: 58142, 9: 39732},
    ("Category Twos and Threes", 5, 4): {0: 848, 2: 30734, 11: 68418},
    ("Category Twos and Threes", 5, 5): {0: 29502, 12: 70498},
    ("Category Twos and Threes", 5, 6): {0: 123, 9: 52792, 12: 47085},
    ("Category Twos and Threes", 5, 7): {0: 8241, 12: 91759},
    ("Category Twos and Threes", 5, 8): {0: 13, 2: 31670, 14: 68317},
    ("Category Twos and Threes", 6, 1): {0: 22090, 6: 77910},
    ("Category Twos and Threes", 6, 2): {0: 2944, 6: 62394, 9: 34662},
    ("Category Twos and Threes", 6, 3): {0: 977, 2: 30626, 11: 68397},
    ("Category Twos and Threes", 6, 4): {0: 320, 8: 58370, 12: 41310},
    ("Category Twos and Threes", 6, 5): {0: 114, 2: 31718, 14: 68168},
    ("Category Twos and Threes", 6, 6): {0: 29669, 15: 70331},
    ("Category Twos and Threes", 6, 7): {0: 19855, 15: 80145},
    ("Category Twos and Threes", 6, 8): {0: 8524, 15: 91476},
    ("Category Twos and Threes", 7, 1): {0: 5802, 4: 54580, 7: 39618},
    ("Category Twos and Threes", 7, 2): {0: 1605, 6: 62574, 10: 35821},
    ("Category Twos and Threes", 7, 3): {0: 471, 8: 59691, 12: 39838},
    ("Category Twos and Threes", 7, 4): {0: 26620, 14: 73380},
    ("Category Twos and Threes", 7, 5): {0: 17308, 11: 37515, 15: 45177},
    ("Category Twos and Threes", 7, 6): {0: 30281, 17: 69719},
    ("Category Twos and Threes", 7, 7): {0: 28433, 18: 71567},
    ("Category Twos and Threes", 7, 8): {0: 13274, 18: 86726},
    ("Category Twos and Threes", 8, 1): {0: 3799, 5: 56614, 8: 39587},
    ("Category Twos and Threes", 8, 2): {0: 902, 7: 58003, 11: 41095},
    ("Category Twos and Threes", 8, 3): {0: 29391, 14: 70609},
    ("Category Twos and Threes", 8, 4): {0: 26041, 12: 40535, 16: 33424},
    ("Category Twos and Threes", 8, 5): {0: 26328, 14: 38760, 18: 34912},
    ("Category Twos and Threes", 8, 6): {0: 22646, 15: 45218, 19: 32136},
    ("Category Twos and Threes", 8, 7): {0: 25908, 20: 74092},
    ("Category Twos and Threes", 8, 8): {3: 18441, 17: 38826, 21: 42733},
    ("Category Sum of Odds", 1, 1): {0: 66572, 5: 33428},
    ("Category Sum of Odds", 1, 2): {0: 44489, 5: 55511},
    ("Category Sum of Odds", 1, 3): {0: 37185, 5: 62815},
    ("Category Sum of Odds", 1, 4): {0: 30917, 5: 69083},
    ("Category Sum of Odds", 1, 5): {0: 41833, 5: 58167},
    ("Category Sum of Odds", 1, 6): {0: 34902, 5: 65098},
    ("Category Sum of Odds", 1, 7): {0: 29031, 5: 70969},
    ("Category Sum of Odds", 1, 8): {0: 24051, 5: 75949},
    ("Category Sum of Odds", 2, 1): {0: 66460, 5: 33540},
    ("Category Sum of Odds", 2, 2): {0: 11216, 5: 65597, 8: 23187},
    ("Category Sum of Odds", 2, 3): {0: 30785, 8: 69215},
    ("Category Sum of Odds", 2, 4): {0: 21441, 10: 78559},
    ("Category Sum of Odds", 2, 5): {0: 14948, 10: 85052},
    ("Category Sum of Odds", 2, 6): {0: 4657, 3: 35569, 10: 59774},
    ("Category Sum of Odds", 2, 7): {0: 7262, 5: 42684, 10: 50054},
    ("Category Sum of Odds", 2, 8): {0: 4950, 5: 37432, 10: 57618},
    ("Category Sum of Odds", 3, 1): {0: 29203, 6: 70797},
    ("Category Sum of Odds", 3, 2): {0: 34454, 9: 65546},
    ("Category Sum of Odds", 3, 3): {0: 5022, 3: 32067, 8: 45663, 13: 17248},
    ("Category Sum of Odds", 3, 4): {0: 6138, 4: 33396, 13: 60466},
    ("Category Sum of Odds", 3, 5): {0: 29405, 15: 70595},
    ("Category Sum of Odds", 3, 6): {0: 21390, 15: 78610},
    ("Category Sum of Odds", 3, 7): {0: 8991, 8: 38279, 15: 52730},
    ("Category Sum of Odds", 3, 8): {0: 6340, 8: 34003, 15: 59657},
    ("Category Sum of Odds", 4, 1): {0: 28095, 4: 38198, 8: 33707},
    ("Category Sum of Odds", 4, 2): {0: 27003, 11: 72997},
    ("Category Sum of Odds", 4, 3): {0: 18712, 8: 40563, 13: 40725},
    ("Category Sum of Odds", 4, 4): {0: 30691, 15: 69309},
    ("Category Sum of Odds", 4, 5): {0: 433, 3: 32140, 13: 43150, 18: 24277},
    ("Category Sum of Odds", 4, 6): {0: 6549, 9: 32451, 15: 43220, 20: 17780},
    ("Category Sum of Odds", 4, 7): {0: 29215, 15: 45491, 20: 25294},
    ("Category Sum of Odds", 4, 8): {0: 11807, 13: 38927, 20: 49266},
    ("Category Sum of Odds", 5, 1): {0: 25139, 9: 74861},
    ("Category Sum of Odds", 5, 2): {0: 25110, 9: 40175, 14: 34715},
    ("Category Sum of Odds", 5, 3): {0: 23453, 11: 37756, 16: 38791},
    ("Category Sum of Odds", 5, 4): {0: 22993, 13: 37263, 18: 39744},
    ("Category Sum of Odds", 5, 5): {0: 25501, 15: 38407, 20: 36092},
    ("Category Sum of Odds", 5, 6): {0: 2542, 10: 32537, 18: 41122, 23: 23799},
    ("Category Sum of Odds", 5, 7): {0: 8228, 14: 32413, 20: 41289, 25: 18070},
    ("Category Sum of Odds", 5, 8): {0: 2, 2: 31173, 20: 43652, 25: 25173},
    ("Category Sum of Odds", 6, 1): {0: 23822, 6: 40166, 11: 36012},
    ("Category Sum of Odds", 6, 2): {0: 24182, 11: 37137, 16: 38681},
    ("Category Sum of Odds", 6, 3): {0: 27005, 14: 35759, 19: 37236},
    ("Category Sum of Odds", 6, 4): {0: 25133, 16: 35011, 21: 39856},
    ("Category Sum of Odds", 6, 5): {0: 24201, 18: 34934, 23: 40865},
    ("Category Sum of Odds", 6, 6): {0: 12978, 17: 32943, 23: 36836, 28: 17243},
    ("Category Sum of Odds", 6, 7): {0: 2314, 14: 32834, 23: 40134, 28: 24718},
    ("Category Sum of Odds", 6, 8): {0: 5464, 18: 34562, 25: 40735, 30: 19239},
    ("Category Sum of Odds", 7, 1): {0: 29329, 8: 37697, 13: 32974},
    ("Category Sum of Odds", 7, 2): {0: 29935, 14: 34878, 19: 35187},
    ("Category Sum of Odds", 7, 3): {0: 30638, 17: 33733, 22: 35629},
    ("Category Sum of Odds", 7, 4): {0: 163, 6: 32024, 20: 33870, 25: 33943},
    ("Category Sum of Odds", 7, 5): {0: 31200, 22: 35565, 27: 33235},
    ("Category Sum of Odds", 7, 6): {2: 30174, 24: 36670, 29: 33156},
    ("Category Sum of Odds", 7, 7): {4: 8712, 21: 35208, 28: 36799, 33: 19281},
    ("Category Sum of Odds", 7, 8): {0: 1447, 18: 32027, 28: 39941, 33: 26585},
    ("Category Sum of Odds", 8, 1): {0: 26931, 9: 35423, 14: 37646},
    ("Category Sum of Odds", 8, 2): {0: 29521, 16: 32919, 21: 37560},
    ("Category Sum of Odds", 8, 3): {0: 412, 7: 32219, 20: 32055, 25: 35314},
    ("Category Sum of Odds", 8, 4): {1: 27021, 22: 36376, 28: 36603},
    ("Category Sum of Odds", 8, 5): {1: 1069, 14: 32451, 26: 32884, 31: 33596},
    ("Category Sum of Odds", 8, 6): {4: 31598, 28: 33454, 33: 34948},
    ("Category Sum of Odds", 8, 7): {6: 27327, 29: 35647, 34: 37026},
    ("Category Sum of Odds", 8, 8): {4: 1, 26: 40489, 33: 37825, 38: 21685},
    ("Category Sum of Evens", 1, 1): {0: 49585, 6: 50415},
    ("Category Sum of Evens", 1, 2): {0: 44331, 6: 55669},
    ("Category Sum of Evens", 1, 3): {0: 29576, 6: 70424},
    ("Category Sum of Evens", 1, 4): {0: 24744, 6: 75256},
    ("Category Sum of Evens", 1, 5): {0: 20574, 6: 79426},
    ("Category Sum of Evens", 1, 6): {0: 17182, 6: 82818},
    ("Category Sum of Evens", 1, 7): {0: 14152, 6: 85848},
    ("Category Sum of Evens", 1, 8): {0: 8911, 6: 91089},
    ("Category Sum of Evens", 2, 1): {0: 25229, 8: 74771},
    ("Category Sum of Evens", 2, 2): {0: 18682, 6: 58078, 10: 23240},
    ("Category Sum of Evens", 2, 3): {0: 8099, 10: 91901},
    ("Category Sum of Evens", 2, 4): {0: 16906, 12: 83094},
    ("Category Sum of Evens", 2, 5): {0: 11901, 12: 88099},
    ("Category Sum of Evens", 2, 6): {0: 8054, 12: 91946},
    ("Category Sum of Evens", 2, 7): {0: 5695, 12: 94305},
    ("Category Sum of Evens", 2, 8): {0: 3950, 12: 96050},
    ("Category Sum of Evens", 3, 1): {0: 25054, 6: 51545, 10: 23401},
    ("Category Sum of Evens", 3, 2): {0: 17863, 10: 64652, 14: 17485},
    ("Category Sum of Evens", 3, 3): {0: 7748, 12: 75072, 16: 17180},
    ("Category Sum of Evens", 3, 4): {0: 1318, 12: 70339, 16: 28343},
    ("Category Sum of Evens", 3, 5): {0: 7680, 12: 53582, 18: 38738},
    ("Category Sum of Evens", 3, 6): {0: 1475, 12: 50152, 18: 48373},
    ("Category Sum of Evens", 3, 7): {0: 14328, 18: 85672},
    ("Category Sum of Evens", 3, 8): {0: 10001, 18: 89999},
    ("Category Sum of Evens", 4, 1): {0: 6214, 8: 67940, 12: 25846},
    ("Category Sum of Evens", 4, 2): {0: 16230, 12: 55675, 16: 28095},
    ("Category Sum of Evens", 4, 3): {0: 11069, 16: 70703, 20: 18228},
    ("Category Sum of Evens", 4, 4): {0: 13339, 20: 86661},
    ("Category Sum of Evens", 4, 5): {0: 8193, 18: 66423, 22: 25384},
    ("Category Sum of Evens", 4, 6): {0: 11127, 18: 53742, 22: 35131},
    ("Category Sum of Evens", 4, 7): {0: 7585, 18: 48073, 24: 44342},
    ("Category Sum of Evens", 4, 8): {0: 642, 18: 46588, 24: 52770},
    ("Category Sum of Evens", 5, 1): {0: 8373, 8: 50641, 16: 40986},
    ("Category Sum of Evens", 5, 2): {0: 7271, 12: 42254, 20: 50475},
    ("Category Sum of Evens", 5, 3): {0: 8350, 16: 44711, 24: 46939},
    ("Category Sum of Evens", 5, 4): {0: 8161, 18: 44426, 26: 47413},
    ("Category Sum of Evens", 5, 5): {0: 350, 8: 16033, 24: 67192, 28: 16425},
    ("Category Sum of Evens", 5, 6): {0: 10318, 24: 64804, 28: 24878},
    ("Category Sum of Evens", 5, 7): {0: 12783, 24: 52804, 28: 34413},
    ("Category Sum of Evens", 5, 8): {0: 1, 24: 56646, 30: 43353},
    ("Category Sum of Evens", 6, 1): {0: 10482, 10: 48137, 18: 41381},
    ("Category Sum of Evens", 6, 2): {0: 12446, 16: 43676, 24: 43878},
    ("Category Sum of Evens", 6, 3): {0: 11037, 20: 44249, 28: 44714},
    ("Category Sum of Evens", 6, 4): {0: 10005, 22: 42316, 30: 47679},
    ("Category Sum of Evens", 6, 5): {0: 9751, 24: 42204, 32: 48045},
    ("Category Sum of Evens", 6, 6): {0: 9692, 26: 45108, 34: 45200},
    ("Category Sum of Evens", 6, 7): {4: 1437, 26: 42351, 34: 56212},
    ("Category Sum of Evens", 6, 8): {4: 13017, 30: 51814, 36: 35169},
    ("Category Sum of Evens", 7, 1): {0: 12688, 12: 45275, 20: 42037},
    ("Category Sum of Evens", 7, 2): {0: 1433, 20: 60350, 28: 38217},
    ("Category Sum of Evens", 7, 3): {0: 13724, 24: 43514, 32: 42762},
    ("Category Sum of Evens", 7, 4): {0: 11285, 26: 40694, 34: 48021},
    ("Category Sum of Evens", 7, 5): {4: 5699, 28: 43740, 36: 50561},
    ("Category Sum of Evens", 7, 6): {4: 5478, 30: 43711, 38: 50811},
    ("Category Sum of Evens", 7, 7): {6: 9399, 32: 43251, 40: 47350},
    ("Category Sum of Evens", 7, 8): {10: 1490, 32: 40719, 40: 57791},
    ("Category Sum of Evens", 8, 1): {0: 14585, 14: 42804, 22: 42611},
    ("Category Sum of Evens", 8, 2): {0: 15891, 22: 39707, 30: 44402},
    ("Category Sum of Evens", 8, 3): {2: 297, 12: 16199, 28: 42274, 36: 41230},
    ("Category Sum of Evens", 8, 4): {0: 7625, 30: 43948, 38: 48427},
    ("Category Sum of Evens", 8, 5): {4: 413, 18: 16209, 34: 43301, 42: 40077},
    ("Category Sum of Evens", 8, 6): {6: 14927, 36: 43139, 44: 41934},
    ("Category Sum of Evens", 8, 7): {8: 5042, 36: 40440, 44: 54518},
    ("Category Sum of Evens", 8, 8): {10: 5005, 38: 44269, 46: 50726},
    ("Category Double Threes and Fours", 1, 1): {0: 66749, 8: 33251},
    ("Category Double Threes and Fours", 1, 2): {0: 44675, 8: 55325},
    ("Category Double Threes and Fours", 1, 3): {0: 29592, 8: 70408},
    ("Category Double Threes and Fours", 1, 4): {0: 24601, 8: 75399},
    ("Category Double Threes and Fours", 1, 5): {0: 20499, 8: 79501},
    ("Category Double Threes and Fours", 1, 6): {0: 17116, 8: 82884},
    ("Category Double Threes and Fours", 1, 7): {0: 14193, 8: 85807},
    ("Category Double Threes and Fours", 1, 8): {0: 11977, 8: 88023},
    ("Category Double Threes and Fours", 2, 1): {0: 44382, 8: 55618},
    ("Category Double Threes and Fours", 2, 2): {0: 19720, 8: 57236, 14: 23044},
    ("Category Double Threes and Fours", 2, 3): {0: 8765, 8: 41937, 14: 49298},
    ("Category Double Threes and Fours", 2, 4): {0: 6164, 16: 93836},
    ("Category Double Threes and Fours", 2, 5): {0: 4307, 8: 38682, 16: 57011},
    ("Category Double Threes and Fours", 2, 6): {0: 2879, 8: 32717, 16: 64404},
    ("Category Double Threes and Fours", 2, 7): {0: 6679, 16: 93321},
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    ("Category 1-2-1 Consecutive", 7, 7): {0: 4106, 30: 95894},
    ("Category 1-2-1 Consecutive", 7, 8): {0: 3025, 30: 96975},
    ("Category 1-2-1 Consecutive", 8, 1): {0: 40693, 30: 59307},
    ("Category 1-2-1 Consecutive", 8, 2): {0: 14827, 30: 85173},
    ("Category 1-2-1 Consecutive", 8, 3): {0: 8195, 30: 91805},
    ("Category 1-2-1 Consecutive", 8, 4): {0: 5383, 30: 94617},
    ("Category 1-2-1 Consecutive", 8, 5): {0: 3395, 30: 96605},
    ("Category 1-2-1 Consecutive", 8, 6): {0: 2299, 30: 97701},
    ("Category 1-2-1 Consecutive", 8, 7): {0: 1412, 30: 98588},
    ("Category 1-2-1 Consecutive", 8, 8): {0: 872, 30: 99128},
    ("Category Three Distinct Dice", 1, 1): {0: 100000},
    ("Category Three Distinct Dice", 1, 2): {0: 100000},
    ("Category Three Distinct Dice", 1, 3): {0: 100000},
    ("Category Three Distinct Dice", 1, 4): {0: 100000},
    ("Category Three Distinct Dice", 1, 5): {0: 100000},
    ("Category Three Distinct Dice", 1, 6): {0: 100000},
    ("Category Three Distinct Dice", 1, 7): {0: 100000},
    ("Category Three Distinct Dice", 1, 8): {0: 100000},
    ("Category Three Distinct Dice", 2, 1): {0: 100000},
    ("Category Three Distinct Dice", 2, 2): {0: 100000},
    ("Category Three Distinct Dice", 2, 3): {0: 100000},
    ("Category Three Distinct Dice", 2, 4): {0: 100000},
    ("Category Three Distinct Dice", 2, 5): {0: 100000},
    ("Category Three Distinct Dice", 2, 6): {0: 100000},
    ("Category Three Distinct Dice", 2, 7): {0: 100000},
    ("Category Three Distinct Dice", 2, 8): {0: 100000},
    ("Category Three Distinct Dice", 3, 1): {0: 44707, 20: 55293},
    ("Category Three Distinct Dice", 3, 2): {0: 15078, 20: 84922},
    ("Category Three Distinct Dice", 3, 3): {0: 5056, 20: 94944},
    ("Category Three Distinct Dice", 3, 4): {0: 1688, 20: 98312},
    ("Category Three Distinct Dice", 3, 5): {0: 516, 20: 99484},
    ("Category Three Distinct Dice", 3, 6): {0: 182, 20: 99818},
    ("Category Three Distinct Dice", 3, 7): {0: 56, 20: 99944},
    ("Category Three Distinct Dice", 3, 8): {0: 15, 20: 99985},
    ("Category Three Distinct Dice", 4, 1): {0: 16721, 20: 83279},
    ("Category Three Distinct Dice", 4, 2): {0: 1826, 20: 98174},
    ("Category Three Distinct Dice", 4, 3): {0: 203, 20: 99797},
    ("Category Three Distinct Dice", 4, 4): {0: 18, 20: 99982},
    ("Category Three Distinct Dice", 4, 5): {0: 3, 20: 99997},
    ("Category Three Distinct Dice", 4, 6): {20: 100000},
    ("Category Three Distinct Dice", 4, 7): {20: 100000},
    ("Category Three Distinct Dice", 4, 8): {20: 100000},
    ("Category Three Distinct Dice", 5, 1): {0: 5904, 20: 94096},
    ("Category Three Distinct Dice", 5, 2): {0: 236, 20: 99764},
    ("Category Three Distinct Dice", 5, 3): {0: 12, 20: 99988},
    ("Category Three Distinct Dice", 5, 4): {20: 100000},
    ("Category Three Distinct Dice", 5, 5): {20: 100000},
    ("Category Three Distinct Dice", 5, 6): {20: 100000},
    ("Category Three Distinct Dice", 5, 7): {20: 100000},
    ("Category Three Distinct Dice", 5, 8): {20: 100000},
    ("Category Three Distinct Dice", 6, 1): {0: 1992, 20: 98008},
    ("Category Three Distinct Dice", 6, 2): {0: 21, 20: 99979},
    ("Category Three Distinct Dice", 6, 3): {20: 100000},
    ("Category Three Distinct Dice", 6, 4): {20: 100000},
    ("Category Three Distinct Dice", 6, 5): {20: 100000},
    ("Category Three Distinct Dice", 6, 6): {20: 100000},
    ("Category Three Distinct Dice", 6, 7): {20: 100000},
    ("Category Three Distinct Dice", 6, 8): {20: 100000},
    ("Category Three Distinct Dice", 7, 1): {0: 692, 20: 99308},
    ("Category Three Distinct Dice", 7, 2): {0: 4, 20: 99996},
    ("Category Three Distinct Dice", 7, 3): {20: 100000},
    ("Category Three Distinct Dice", 7, 4): {20: 100000},
    ("Category Three Distinct Dice", 7, 5): {20: 100000},
    ("Category Three Distinct Dice", 7, 6): {20: 100000},
    ("Category Three Distinct Dice", 7, 7): {20: 100000},
    ("Category Three Distinct Dice", 7, 8): {20: 100000},
    ("Category Three Distinct Dice", 8, 1): {0: 243, 20: 99757},
    ("Category Three Distinct Dice", 8, 2): {0: 1, 20: 99999},
    ("Category Three Distinct Dice", 8, 3): {20: 100000},
    ("Category Three Distinct Dice", 8, 4): {20: 100000},
    ("Category Three Distinct Dice", 8, 5): {20: 100000},
    ("Category Three Distinct Dice", 8, 6): {20: 100000},
    ("Category Three Distinct Dice", 8, 7): {20: 100000},
    ("Category Three Distinct Dice", 8, 8): {20: 100000},
    ("Category Two Pair", 1, 1): {0: 100000},
    ("Category Two Pair", 1, 2): {0: 100000},
    ("Category Two Pair", 1, 3): {0: 100000},
    ("Category Two Pair", 1, 4): {0: 100000},
    ("Category Two Pair", 1, 5): {0: 100000},
    ("Category Two Pair", 1, 6): {0: 100000},
    ("Category Two Pair", 1, 7): {0: 100000},
    ("Category Two Pair", 1, 8): {0: 100000},
    ("Category Two Pair", 2, 1): {0: 100000},
    ("Category Two Pair", 2, 2): {0: 100000},
    ("Category Two Pair", 2, 3): {0: 100000},
    ("Category Two Pair", 2, 4): {0: 100000},
    ("Category Two Pair", 2, 5): {0: 100000},
    ("Category Two Pair", 2, 6): {0: 100000},
    ("Category Two Pair", 2, 7): {0: 100000},
    ("Category Two Pair", 2, 8): {0: 100000},
    ("Category Two Pair", 3, 1): {0: 100000},
    ("Category Two Pair", 3, 2): {0: 100000},
    ("Category Two Pair", 3, 3): {0: 100000},
    ("Category Two Pair", 3, 4): {0: 100000},
    ("Category Two Pair", 3, 5): {0: 100000},
    ("Category Two Pair", 3, 6): {0: 100000},
    ("Category Two Pair", 3, 7): {0: 100000},
    ("Category Two Pair", 3, 8): {0: 100000},
    ("Category Two Pair", 4, 1): {0: 93065, 30: 6935},
    ("Category Two Pair", 4, 2): {0: 82102, 30: 17898},
    ("Category Two Pair", 4, 3): {0: 71209, 30: 28791},
    ("Category Two Pair", 4, 4): {0: 61609, 30: 38391},
    ("Category Two Pair", 4, 5): {0: 53036, 30: 46964},
    ("Category Two Pair", 4, 6): {0: 45705, 30: 54295},
    ("Category Two Pair", 4, 7): {0: 39398, 30: 60602},
    ("Category Two Pair", 4, 8): {0: 33673, 30: 66327},
    ("Category Two Pair", 5, 1): {0: 72847, 30: 27153},
    ("Category Two Pair", 5, 2): {0: 46759, 30: 53241},
    ("Category Two Pair", 5, 3): {0: 29462, 30: 70538},
    ("Category Two Pair", 5, 4): {0: 18351, 30: 81649},
    ("Category Two Pair", 5, 5): {0: 11793, 30: 88207},
    ("Category Two Pair", 5, 6): {0: 7385, 30: 92615},
    ("Category Two Pair", 5, 7): {0: 4610, 30: 95390},
    ("Category Two Pair", 5, 8): {0: 2938, 30: 97062},
    ("Category Two Pair", 6, 1): {0: 44431, 30: 55569},
    ("Category Two Pair", 6, 2): {0: 17183, 30: 82817},
    ("Category Two Pair", 6, 3): {0: 6759, 30: 93241},
    ("Category Two Pair", 6, 4): {0: 2562, 30: 97438},
    ("Category Two Pair", 6, 5): {0: 948, 30: 99052},
    ("Category Two Pair", 6, 6): {0: 375, 30: 99625},
    ("Category Two Pair", 6, 7): {0: 138, 30: 99862},
    ("Category Two Pair", 6, 8): {0: 57, 30: 99943},
    ("Category Two Pair", 7, 1): {0: 19888, 30: 80112},
    ("Category Two Pair", 7, 2): {0: 3935, 30: 96065},
    ("Category Two Pair", 7, 3): {0: 801, 30: 99199},
    ("Category Two Pair", 7, 4): {0: 175, 30: 99825},
    ("Category Two Pair", 7, 5): {0: 31, 30: 99969},
    ("Category Two Pair", 7, 6): {0: 7, 30: 99993},
    ("Category Two Pair", 7, 7): {0: 2, 30: 99998},
    ("Category Two Pair", 7, 8): {30: 100000},
    ("Category Two Pair", 8, 1): {0: 6791, 30: 93209},
    ("Category Two Pair", 8, 2): {0: 588, 30: 99412},
    ("Category Two Pair", 8, 3): {0: 61, 30: 99939},
    ("Category Two Pair", 8, 4): {0: 6, 30: 99994},
    ("Category Two Pair", 8, 5): {30: 100000},
    ("Category Two Pair", 8, 6): {30: 100000},
    ("Category Two Pair", 8, 7): {30: 100000},
    ("Category Two Pair", 8, 8): {30: 100000},
    ("Category 2-1-2 Consecutive", 1, 1): {0: 100000},
    ("Category 2-1-2 Consecutive", 1, 2): {0: 100000},
    ("Category 2-1-2 Consecutive", 1, 3): {0: 100000},
    ("Category 2-1-2 Consecutive", 1, 4): {0: 100000},
    ("Category 2-1-2 Consecutive", 1, 5): {0: 100000},
    ("Category 2-1-2 Consecutive", 1, 6): {0: 100000},
    ("Category 2-1-2 Consecutive", 1, 7): {0: 100000},
    ("Category 2-1-2 Consecutive", 1, 8): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 1): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 2): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 3): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 4): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 5): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 6): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 7): {0: 100000},
    ("Category 2-1-2 Consecutive", 2, 8): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 1): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 2): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 3): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 4): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 5): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 6): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 7): {0: 100000},
    ("Category 2-1-2 Consecutive", 3, 8): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 1): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 2): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 3): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 4): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 5): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 6): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 7): {0: 100000},
    ("Category 2-1-2 Consecutive", 4, 8): {0: 100000},
    ("Category 2-1-2 Consecutive", 5, 1): {0: 98403, 40: 1597},
    ("Category 2-1-2 Consecutive", 5, 2): {0: 90651, 40: 9349},
    ("Category 2-1-2 Consecutive", 5, 3): {0: 80100, 40: 19900},
    ("Category 2-1-2 Consecutive", 5, 4): {0: 69131, 40: 30869},
    ("Category 2-1-2 Consecutive", 5, 5): {0: 58252, 40: 41748},
    ("Category 2-1-2 Consecutive", 5, 6): {0: 49405, 40: 50595},
    ("Category 2-1-2 Consecutive", 5, 7): {0: 41585, 40: 58415},
    ("Category 2-1-2 Consecutive", 5, 8): {0: 34952, 40: 65048},
    ("Category 2-1-2 Consecutive", 6, 1): {0: 93465, 40: 6535},
    ("Category 2-1-2 Consecutive", 6, 2): {0: 73416, 40: 26584},
    ("Category 2-1-2 Consecutive", 6, 3): {0: 54041, 40: 45959},
    ("Category 2-1-2 Consecutive", 6, 4): {0: 38535, 40: 61465},
    ("Category 2-1-2 Consecutive", 6, 5): {0: 27366, 40: 72634},
    ("Category 2-1-2 Consecutive", 6, 6): {0: 18924, 40: 81076},
    ("Category 2-1-2 Consecutive", 6, 7): {0: 13387, 40: 86613},
    ("Category 2-1-2 Consecutive", 6, 8): {0: 9134, 40: 90866},
    ("Category 2-1-2 Consecutive", 7, 1): {0: 84168, 40: 15832},
    ("Category 2-1-2 Consecutive", 7, 2): {0: 52659, 40: 47341},
    ("Category 2-1-2 Consecutive", 7, 3): {0: 30435, 40: 69565},
    ("Category 2-1-2 Consecutive", 7, 4): {0: 17477, 40: 82523},
    ("Category 2-1-2 Consecutive", 7, 5): {0: 9782, 40: 90218},
    ("Category 2-1-2 Consecutive", 7, 6): {0: 5316, 40: 94684},
    ("Category 2-1-2 Consecutive", 7, 7): {0: 2995, 40: 97005},
    ("Category 2-1-2 Consecutive", 7, 8): {0: 1689, 40: 98311},
    ("Category 2-1-2 Consecutive", 8, 1): {0: 71089, 40: 28911},
    ("Category 2-1-2 Consecutive", 8, 2): {0: 33784, 40: 66216},
    ("Category 2-1-2 Consecutive", 8, 3): {0: 14820, 40: 85180},
    ("Category 2-1-2 Consecutive", 8, 4): {0: 6265, 40: 93735},
    ("Category 2-1-2 Consecutive", 8, 5): {0: 2600, 40: 97400},
    ("Category 2-1-2 Consecutive", 8, 6): {0: 1155, 40: 98845},
    ("Category 2-1-2 Consecutive", 8, 7): {0: 487, 40: 99513},
    ("Category 2-1-2 Consecutive", 8, 8): {0: 190, 40: 99810},
    ("Category Five Distinct Dice", 1, 1): {0: 100000},
    ("Category Five Distinct Dice", 1, 2): {0: 100000},
    ("Category Five Distinct Dice", 1, 3): {0: 100000},
    ("Category Five Distinct Dice", 1, 4): {0: 100000},
    ("Category Five Distinct Dice", 1, 5): {0: 100000},
    ("Category Five Distinct Dice", 1, 6): {0: 100000},
    ("Category Five Distinct Dice", 1, 7): {0: 100000},
    ("Category Five Distinct Dice", 1, 8): {0: 100000},
    ("Category Five Distinct Dice", 2, 1): {0: 100000},
    ("Category Five Distinct Dice", 2, 2): {0: 100000},
    ("Category Five Distinct Dice", 2, 3): {0: 100000},
    ("Category Five Distinct Dice", 2, 4): {0: 100000},
    ("Category Five Distinct Dice", 2, 5): {0: 100000},
    ("Category Five Distinct Dice", 2, 6): {0: 100000},
    ("Category Five Distinct Dice", 2, 7): {0: 100000},
    ("Category Five Distinct Dice", 2, 8): {0: 100000},
    ("Category Five Distinct Dice", 3, 1): {0: 100000},
    ("Category Five Distinct Dice", 3, 2): {0: 100000},
    ("Category Five Distinct Dice", 3, 3): {0: 100000},
    ("Category Five Distinct Dice", 3, 4): {0: 100000},
    ("Category Five Distinct Dice", 3, 5): {0: 100000},
    ("Category Five Distinct Dice", 3, 6): {0: 100000},
    ("Category Five Distinct Dice", 3, 7): {0: 100000},
    ("Category Five Distinct Dice", 3, 8): {0: 100000},
    ("Category Five Distinct Dice", 4, 1): {0: 100000},
    ("Category Five Distinct Dice", 4, 2): {0: 100000},
    ("Category Five Distinct Dice", 4, 3): {0: 100000},
    ("Category Five Distinct Dice", 4, 4): {0: 100000},
    ("Category Five Distinct Dice", 4, 5): {0: 100000},
    ("Category Five Distinct Dice", 4, 6): {0: 100000},
    ("Category Five Distinct Dice", 4, 7): {0: 100000},
    ("Category Five Distinct Dice", 4, 8): {0: 100000},
    ("Category Five Distinct Dice", 5, 1): {0: 90907, 25: 9093},
    ("Category Five Distinct Dice", 5, 2): {0: 68020, 25: 31980},
    ("Category Five Distinct Dice", 5, 3): {0: 47692, 25: 52308},
    ("Category Five Distinct Dice", 5, 4): {0: 32383, 25: 67617},
    ("Category Five Distinct Dice", 5, 5): {0: 21631, 25: 78369},
    ("Category Five Distinct Dice", 5, 6): {0: 14366, 25: 85634},
    ("Category Five Distinct Dice", 5, 7): {0: 9568, 25: 90432},
    ("Category Five Distinct Dice", 5, 8): {0: 6360, 25: 93640},
    ("Category Five Distinct Dice", 6, 1): {0: 75051, 25: 24949},
    ("Category Five Distinct Dice", 6, 2): {0: 38409, 25: 61591},
    ("Category Five Distinct Dice", 6, 3): {0: 17505, 25: 82495},
    ("Category Five Distinct Dice", 6, 4): {0: 7862, 25: 92138},
    ("Category Five Distinct Dice", 6, 5): {0: 3538, 25: 96462},
    ("Category Five Distinct Dice", 6, 6): {0: 1645, 25: 98355},
    ("Category Five Distinct Dice", 6, 7): {0: 714, 25: 99286},
    ("Category Five Distinct Dice", 6, 8): {0: 341, 25: 99659},
    ("Category Five Distinct Dice", 7, 1): {0: 58588, 25: 41412},
    ("Category Five Distinct Dice", 7, 2): {0: 19487, 25: 80513},
    ("Category Five Distinct Dice", 7, 3): {0: 6043, 25: 93957},
    ("Category Five Distinct Dice", 7, 4): {0: 1799, 25: 98201},
    ("Category Five Distinct Dice", 7, 5): {0: 544, 25: 99456},
    ("Category Five Distinct Dice", 7, 6): {0: 169, 25: 99831},
    ("Category Five Distinct Dice", 7, 7): {0: 59, 25: 99941},
    ("Category Five Distinct Dice", 7, 8): {0: 11, 25: 99989},
    ("Category Five Distinct Dice", 8, 1): {0: 43586, 25: 56414},
    ("Category Five Distinct Dice", 8, 2): {0: 9615, 25: 90385},
    ("Category Five Distinct Dice", 8, 3): {0: 1944, 25: 98056},
    ("Category Five Distinct Dice", 8, 4): {0: 383, 25: 99617},
    ("Category Five Distinct Dice", 8, 5): {0: 77, 25: 99923},
    ("Category Five Distinct Dice", 8, 6): {0: 18, 25: 99982},
    ("Category Five Distinct Dice", 8, 7): {0: 3, 25: 99997},
    ("Category Five Distinct Dice", 8, 8): {0: 2, 25: 99998},
    ("Category 4&5 Full House", 1, 1): {0: 100000},
    ("Category 4&5 Full House", 1, 2): {0: 100000},
    ("Category 4&5 Full House", 1, 3): {0: 100000},
    ("Category 4&5 Full House", 1, 4): {0: 100000},
    ("Category 4&5 Full House", 1, 5): {0: 100000},
    ("Category 4&5 Full House", 1, 6): {0: 100000},
    ("Category 4&5 Full House", 1, 7): {0: 100000},
    ("Category 4&5 Full House", 1, 8): {0: 100000},
    ("Category 4&5 Full House", 2, 1): {0: 100000},
    ("Category 4&5 Full House", 2, 2): {0: 100000},
    ("Category 4&5 Full House", 2, 3): {0: 100000},
    ("Category 4&5 Full House", 2, 4): {0: 100000},
    ("Category 4&5 Full House", 2, 5): {0: 100000},
    ("Category 4&5 Full House", 2, 6): {0: 100000},
    ("Category 4&5 Full House", 2, 7): {0: 100000},
    ("Category 4&5 Full House", 2, 8): {0: 100000},
    ("Category 4&5 Full House", 3, 1): {0: 100000},
    ("Category 4&5 Full House", 3, 2): {0: 100000},
    ("Category 4&5 Full House", 3, 3): {0: 100000},
    ("Category 4&5 Full House", 3, 4): {0: 100000},
    ("Category 4&5 Full House", 3, 5): {0: 100000},
    ("Category 4&5 Full House", 3, 6): {0: 100000},
    ("Category 4&5 Full House", 3, 7): {0: 100000},
    ("Category 4&5 Full House", 3, 8): {0: 100000},
    ("Category 4&5 Full House", 4, 1): {0: 100000},
    ("Category 4&5 Full House", 4, 2): {0: 100000},
    ("Category 4&5 Full House", 4, 3): {0: 100000},
    ("Category 4&5 Full House", 4, 4): {0: 100000},
    ("Category 4&5 Full House", 4, 5): {0: 100000},
    ("Category 4&5 Full House", 4, 6): {0: 100000},
    ("Category 4&5 Full House", 4, 7): {0: 100000},
    ("Category 4&5 Full House", 4, 8): {0: 100000},
    ("Category 4&5 Full House", 5, 1): {0: 100000},
    ("Category 4&5 Full House", 5, 2): {0: 96607, 50: 3393},
    ("Category 4&5 Full House", 5, 3): {0: 88788, 50: 11212},
    ("Category 4&5 Full House", 5, 4): {0: 77799, 50: 22201},
    ("Category 4&5 Full House", 5, 5): {0: 65797, 50: 34203},
    ("Category 4&5 Full House", 5, 6): {0: 54548, 50: 45452},
    ("Category 4&5 Full House", 5, 7): {0: 44898, 50: 55102},
    ("Category 4&5 Full House", 5, 8): {0: 36881, 50: 63119},
    ("Category 4&5 Full House", 6, 1): {0: 100000},
    ("Category 4&5 Full House", 6, 2): {0: 88680, 50: 11320},
    ("Category 4&5 Full House", 6, 3): {0: 70215, 50: 29785},
    ("Category 4&5 Full House", 6, 4): {0: 50801, 50: 49199},
    ("Category 4&5 Full House", 6, 5): {0: 35756, 50: 64244},
    ("Category 4&5 Full House", 6, 6): {0: 24698, 50: 75302},
    ("Category 4&5 Full House", 6, 7): {0: 17145, 50: 82855},
    ("Category 4&5 Full House", 6, 8): {0: 11846, 50: 88154},
    ("Category 4&5 Full House", 7, 1): {0: 97090, 50: 2910},
    ("Category 4&5 Full House", 7, 2): {0: 77440, 50: 22560},
    ("Category 4&5 Full House", 7, 3): {0: 51372, 50: 48628},
    ("Category 4&5 Full House", 7, 4): {0: 30566, 50: 69434},
    ("Category 4&5 Full House", 7, 5): {0: 17866, 50: 82134},
    ("Category 4&5 Full House", 7, 6): {0: 10521, 50: 89479},
    ("Category 4&5 Full House", 7, 7): {0: 6204, 50: 93796},
    ("Category 4&5 Full House", 7, 8): {0: 3670, 50: 96330},
    ("Category 4&5 Full House", 8, 1): {0: 94172, 50: 5828},
    ("Category 4&5 Full House", 8, 2): {0: 64693, 50: 35307},
    ("Category 4&5 Full House", 8, 3): {0: 35293, 50: 64707},
    ("Category 4&5 Full House", 8, 4): {0: 17749, 50: 82251},
    ("Category 4&5 Full House", 8, 5): {0: 8740, 50: 91260},
    ("Category 4&5 Full House", 8, 6): {0: 4550, 50: 95450},
    ("Category 4&5 Full House", 8, 7): {0: 2218, 50: 97782},
    ("Category 4&5 Full House", 8, 8): {0: 1084, 50: 98916},
}