{"version":1,"generated":"2026-10-05","method":"NumPy Generator.multinomial; PCG64DXSM with SeedSequence independent spawn keys","numpy":"2.4.2","seed":2026100502,"sessionsPerCell":100000,"source":"https://wizardofodds.com/games/video-poker/tables/triple-double-bonus/","totalSessions":600000,"representedHands":330000000000,"quantiles":"inverse empirical CDF (nearest rank)","units":"Net total-wager units; multiply by USD wager per hand","models":[{"id":"triple-double-bonus-9-7","label":"9/7","mean":0.9957780871848453,"variance":98.28129547302376,"payouts":[800,50,800,400,160,80,50,9,7,4,2,1,1,0],"weights":[439463508,2348724720,1402364496,3440009028,2952442272,6376626780,31673324076,206321656284,311320443672,252218322636,1468173074448,2390581734264,3944045609748,11311936721268],"denominator":19933230517200,"results":[{"hands":100000,"sessions":100000,"spawnKey":[5,0,0],"meanNet":-419.56637,"median":-513,"q05":-5397,"q25":-2579,"q75":1635,"q95":4892,"minimum":-11584,"maximum":14530,"profitable":43385,"breakEven":9,"profitableCI":[0.43078086467070814,0.43692421738408677],"histogram":{"start":-11600,"width":100,"counts":[1,0,1,0,0,0,2,3,2,0,3,3,1,4,3,4,5,5,8,2,13,10,12,11,7,15,15,15,22,28,34,47,32,42,42,52,57,56,66,74,87,71,96,111,107,127,140,133,133,158,189,155,203,226,222,264,291,286,301,295,342,353,388,394,401,446,457,450,533,529,556,565,613,616,664,691,719,777,770,819,783,902,856,934,945,962,943,994,1031,1060,1128,1077,1053,1135,1189,1201,1173,1223,1212,1194,1223,1178,1309,1255,1256,1227,1281,1223,1256,1309,1261,1325,1296,1314,1280,1243,1178,1218,1200,1228,1222,1207,1158,1131,1114,1149,1092,1118,1034,1007,980,998,990,914,938,876,888,882,862,817,781,779,738,743,686,657,651,648,584,566,583,564,494,460,489,455,450,416,391,391,352,366,362,302,316,311,295,261,240,193,218,204,230,175,191,175,163,154,138,112,132,109,126,111,113,103,83,84,67,83,72,60,62,57,45,37,50,39,44,25,38,27,32,20,27,16,17,25,15,23,12,12,9,7,7,13,10,11,9,7,7,5,6,3,5,3,5,2,5,0,1,4,6,1,4,0,0,1,2,2,0,1,0,1,2,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1]},"deciles":[-4349,-3078,-2133,-1307,-513,282,1143,2186,3641],"worstFiveMean":-6525.9492,"worstFiveCount":5000},{"hands":1000000,"sessions":100000,"spawnKey":[5,0,1],"meanNet":-4265.31319,"median":-4366,"q05":-20336,"q25":-10967,"q75":2312,"q95":12155,"minimum":-46462,"maximum":40378,"profitable":33022,"breakEven":4,"profitableCI":[0.327311722785643,0.3331413207708658],"histogram":{"start":-46500,"width":300,"counts":[1,0,0,0,0,1,0,0,0,1,0,0,1,1,1,1,1,1,1,1,0,1,2,1,1,0,0,2,2,2,3,7,3,8,2,3,7,5,8,11,9,15,6,11,12,17,18,21,21,27,17,31,19,34,47,42,32,49,52,56,54,53,72,67,84,79,97,88,115,115,127,112,141,144,169,161,150,192,206,201,237,253,262,255,270,302,299,327,324,337,408,401,413,458,444,475,502,540,497,559,601,629,671,639,658,686,703,741,773,729,818,830,904,884,878,907,959,969,947,1000,1055,1031,1095,1079,1096,1095,1189,1179,1144,1132,1165,1145,1186,1133,1149,1225,1212,1209,1224,1226,1145,1295,1243,1153,1196,1149,1207,1160,1158,1177,1155,1116,1138,1111,1071,1087,1088,1099,1084,961,999,1014,953,1007,948,857,821,840,834,847,807,813,719,728,637,657,647,660,590,583,547,571,547,511,527,456,493,432,383,386,367,382,346,307,321,311,284,241,253,244,218,222,217,227,176,154,180,149,133,152,136,113,127,122,106,93,97,101,99,70,84,60,51,48,60,53,51,42,39,30,44,42,22,32,21,24,25,12,14,14,21,12,12,9,4,9,13,12,11,7,3,6,7,4,5,3,7,2,4,1,0,2,2,1,2,2,3,1,2,0,0,0,1,1,1,2,1,0,0,0,1,1,0,0,1,0,0,0,0,1]},"deciles":[-16825,-12598,-9518,-6878,-4366,-1855,825,3991,8450],"worstFiveMean":-24293.5486,"worstFiveCount":5000}]},{"id":"triple-double-bonus-9-6","label":"9/6","mean":0.9815399594207027,"variance":100.11477198714306,"payouts":[800,50,800,400,160,80,50,9,6,4,2,1,1,0],"weights":[41831018,184487158,116933150,286610393,247064430,531459920,2672839322,17363514183,21114215454,22473322760,123927226256,201675895074,341489045751,928978098231],"denominator":1661102543100,"results":[{"hands":100000,"sessions":100000,"spawnKey":[5,1,0],"meanNet":-1849.45285,"median":-1957,"q05":-6908,"q25":-4061,"q75":250,"q95":3543,"minimum":-13154,"maximum":13708,"profitable":27419,"breakEven":13,"profitableCI":[0.27143377573440447,0.27696357239550035],"histogram":{"start":-13200,"width":100,"counts":[1,1,2,2,1,1,1,3,4,4,0,2,4,3,6,2,2,2,6,6,4,6,18,10,19,20,19,21,25,30,17,30,36,35,37,53,55,59,66,81,72,58,67,101,97,99,129,148,146,159,140,199,178,187,227,221,265,248,284,310,282,326,404,358,389,414,429,463,480,464,532,524,592,579,619,654,682,704,741,771,749,792,881,851,890,932,1038,967,983,1025,1013,1058,1051,1057,1117,1075,1090,1118,1198,1144,1231,1183,1209,1270,1195,1305,1270,1241,1274,1295,1264,1254,1265,1283,1236,1176,1241,1200,1208,1216,1134,1149,1111,1106,1132,1186,1165,1121,1040,1051,1099,993,995,982,957,946,881,850,919,852,835,754,798,710,734,743,723,702,631,646,624,582,604,579,526,473,495,477,421,406,393,387,362,349,320,360,301,297,284,269,245,249,230,223,204,188,193,202,142,145,143,144,134,122,115,118,101,96,93,87,64,85,46,74,52,58,51,45,43,52,44,49,27,26,28,23,24,22,24,16,16,22,15,21,13,9,15,8,9,13,11,7,3,8,7,3,9,0,4,7,5,7,0,3,0,0,1,3,1,4,1,2,1,0,1,1,2,2,0,2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},"deciles":[-5845,-4558,-3592,-2746,-1957,-1136,-246,805,2275],"worstFiveMean":-8063.4218,"worstFiveCount":5000},{"hands":1000000,"sessions":100000,"spawnKey":[5,1,1],"meanNet":-18434.41662,"median":-18550,"q05":-34670,"q25":-25194,"q75":-11710,"q95":-1839,"minimum":-61105,"maximum":27374,"profitable":3415,"breakEven":2,"profitableCI":[0.033042137323229186,0.035293652173764435],"histogram":{"start":-61200,"width":300,"counts":[1,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,1,1,0,2,1,1,2,2,2,1,3,4,3,4,1,5,1,4,4,5,5,9,12,7,9,7,16,15,14,12,9,20,16,17,22,29,39,38,32,53,43,42,53,65,67,59,79,79,62,69,71,104,106,106,115,139,130,128,162,160,161,188,210,195,207,234,258,261,267,311,288,332,307,350,402,424,411,433,443,474,475,501,544,550,578,576,641,647,628,627,666,744,781,752,799,827,756,910,836,917,930,883,984,1005,970,1062,1063,1086,1091,1077,1155,1103,1121,1119,1170,1218,1165,1171,1180,1173,1163,1275,1182,1128,1127,1208,1262,1249,1202,1129,1110,1127,1154,1169,1208,1102,1121,1092,1103,1091,1082,1024,1046,959,962,937,955,963,999,877,916,880,841,816,803,806,768,760,728,694,688,638,632,621,595,575,561,511,538,456,459,439,441,464,423,382,382,335,352,311,298,291,291,252,280,203,239,206,191,201,179,160,178,142,141,144,124,113,125,117,109,102,78,81,69,63,64,71,46,39,55,42,40,52,33,35,28,39,34,28,21,22,29,35,19,19,15,10,10,15,7,9,9,7,2,6,3,3,2,7,4,2,4,4,3,5,1,2,0,0,1,2,1,0,1,0,3,1,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},"deciles":[-31164,-26839,-23748,-21101,-18550,-16003,-13272,-10030,-5555],"worstFiveMean":-38681.4142,"worstFiveCount":5000}]},{"id":"triple-double-bonus-8-5","label":"8/5","mean":0.9596865163248572,"variance":100.74684130251438,"payouts":[800,50,800,400,160,80,50,8,5,4,2,1,1,0],"weights":[525973572,2132054712,1406749692,3440617260,2984069232,6384180120,32257116156,209546245836,219262205916,273985033860,1497870521748,2438228332836,4196992500792,11048214915468],"denominator":19933230517200,"results":[{"hands":100000,"sessions":100000,"spawnKey":[5,2,0],"meanNet":-4029.90269,"median":-4124,"q05":-9105,"q25":-6248,"q75":-1927,"q95":1370,"minimum":-15155,"maximum":10986,"profitable":10596,"breakEven":3,"profitableCI":[0.10406746797067286,0.1078828046350916],"histogram":{"start":-15200,"width":100,"counts":[1,1,3,4,2,4,4,3,1,6,3,7,4,2,5,2,12,4,4,16,10,8,14,14,19,21,14,31,23,26,33,42,38,38,52,62,51,55,68,81,69,100,87,106,119,136,141,148,162,168,171,202,192,250,262,242,319,287,337,335,389,363,420,437,415,445,454,518,550,555,528,589,617,653,672,733,735,725,741,815,803,888,900,877,985,954,1001,1047,1045,999,1058,1054,1090,1122,1147,1099,1152,1140,1175,1204,1191,1250,1194,1205,1164,1171,1312,1248,1355,1217,1272,1251,1241,1253,1262,1201,1234,1198,1178,1151,1178,1167,1139,1161,1122,1112,1053,1040,1061,1030,980,993,939,962,933,856,930,805,850,870,825,762,795,717,682,697,686,570,586,579,538,520,519,494,510,468,468,430,410,396,363,349,347,352,290,293,287,265,234,234,238,222,193,185,197,176,181,157,159,156,123,140,135,98,113,104,79,87,78,78,83,61,70,67,41,47,40,45,39,43,30,30,27,30,29,30,23,22,17,14,14,14,15,18,21,7,8,12,11,5,4,7,2,5,16,4,3,8,2,2,4,2,0,0,2,2,2,3,4,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1]},"deciles":[-8049,-6744,-5782,-4931,-4124,-3310,-2424,-1369,117],"worstFiveMean":-10236.961,"worstFiveCount":5000},{"hands":1000000,"sessions":100000,"spawnKey":[5,2,1],"meanNet":-40279.25092,"median":-40371,"q05":-56687,"q25":-47086,"q75":-33597,"q95":-23620,"minimum":-83783,"maximum":5613,"profitable":7,"breakEven":0,"profitableCI":[3.390903779016499e-05,0.00014449869695711302],"histogram":{"start":-84000,"width":300,"counts":[1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,1,1,0,1,0,1,0,1,0,2,2,2,1,1,3,5,4,7,1,6,5,4,4,5,11,8,8,12,13,13,10,14,18,21,18,23,15,29,21,29,19,25,40,41,34,62,50,78,56,79,64,93,71,87,124,102,120,128,122,141,132,141,182,170,203,213,227,224,254,264,247,284,272,313,331,351,353,385,369,442,408,442,487,489,496,490,548,564,581,586,670,620,670,686,728,717,755,788,774,820,826,868,918,936,916,950,958,969,1009,1026,1048,1000,1024,1158,1117,1107,1131,1150,1147,1184,1191,1105,1171,1186,1184,1161,1276,1248,1227,1188,1173,1165,1236,1185,1131,1189,1172,1114,1081,1136,1147,1053,1045,1097,1056,1074,1014,1029,998,981,998,894,876,886,860,841,863,792,742,769,755,755,697,681,661,675,610,634,576,528,552,504,476,481,460,453,421,428,380,373,351,338,310,307,291,259,256,298,217,217,219,217,192,190,172,176,162,149,133,146,132,117,115,103,84,86,74,77,56,67,61,61,71,51,52,40,43,34,27,35,21,28,29,26,30,22,16,17,21,20,10,17,11,11,8,8,5,9,7,12,6,9,5,6,6,3,3,5,4,2,3,1,0,0,4,1,3,0,2,1,1,0,2,1,1,0,1,0,0,1,0,0,2,0,0,0,0,0,0,0,0,1]},"deciles":[-53114,-48742,-45589,-42896,-40371,-37839,-35091,-31885,-27381],"worstFiveMean":-60670.5044,"worstFiveCount":5000}]}],"categories":["Royal Flush","Straight Flush","Four Aces + 2\u20134","Four 2s\u20134s + A\u20134","Four Aces + 5\u2013K","Four 2s\u20134s + 5\u2013K","Four 5s\u2013Kings","Full House","Flush","Straight","Three of a Kind","Two Pair","Jacks or Better","Nothing"],"profitIntervalMethod":"Wilson two-sided 95%; UI uses exact one-sided 95% upper bound for zero observed profits"}