The great "Poker is rigged" debate - Collected threads edition
Site #0, 2 to 10 players, NL Hold'em, all stakes combined Using 25 equity bins. Number of hands analysed: 1630652 Preflop heads-up all-ins: 10149 (Once per 161 hands). FAVORITE'S Preflop equity Mean% Hands Wins Ties Actual% T-Test 5% Sig [0.98 - 1.00] . 0 0 0 . [0.96 - 0.98] . 0 0 0 . [0.94 - 0.96] 94.23% 7 7 0 100.00% 0.68 2.45 [0.92 - 0.94] 92.92% 217 200 3 92.86% -0.04 1.96 [0.90 - 0.92] 91.20% 37 34 1 93.24% 0.45 2.02 [0.88 - 0.90] 88.61% 21 19 1 92.86% 0.62 2.09 [0.86 - 0.88] 87.18% 147 131 2 89.80% 0.96 1.96 [0.84 - 0.86] 85.00% 68 57 1 84.56% -0.10 1.98 [0.82 - 0.84] 82.52% 288 229 6 80.56% -0.88 1.96 [0.80 - 0.82] 81.30% 1788 1439 31 81.35% 0.05 1.96 [0.78 - 0.80] 79.38% 73 59 2 82.19% 0.60 1.98 [0.76 - 0.78] 76.89% 28 21 0 75.00% -0.24 2.05 [0.74 - 0.76] 74.71% 581 407 34 72.98% -0.99 1.96 [0.72 - 0.74] 73.07% 481 316 38 69.65% -1.74 1.96 [0.70 - 0.72] 71.07% 740 511 33 71.28% 0.13 1.96 [0.68 - 0.70] 69.15% 677 425 46 66.17% -1.71 1.96 [0.66 - 0.68] 67.28% 387 254 10 66.93% -0.15 1.96 [0.64 - 0.66] 65.09% 348 225 9 65.95% 0.34 1.96 [0.62 - 0.64] 62.92% 255 165 4 65.49% 0.86 1.96 [0.60 - 0.62] 60.96% 230 136 5 60.22% -0.23 1.96 [0.58 - 0.60] 59.12% 258 155 6 61.24% 0.70 1.96 [0.56 - 0.58] 56.88% 895 487 16 55.31% -0.95 1.96 [0.54 - 0.56] 54.91% 913 472 17 52.63% -1.39 1.96 [0.52 - 0.54] 52.98% 853 347 194 52.05% -0.61 1.96 [0.50 - 0.52] 50.74% 505 146 212 49.90% -0.49 1.96 [ ALL ] 67.94% 9797 6242 671 67.14% -1.75 1.96 Using 23 valid bins, expected T-test deviations at 5% sig = 1.15 * Observed individual T-test deviations at or over 5% sig = 0 Chi-Square for Favorite = 4.22 w/ 22 degrees of freedom Critical numbers (.10 .05 .01) = 30.81 33.92 40.29 UNDERDOG'S Preflop equity Mean% Hands Wins Ties Actual% T-Test 5% Sig [0.48 - 0.50] 49.26% 505 147 212 50.10% 0.49 1.96 [0.46 - 0.48] 47.02% 853 312 194 47.95% 0.61 1.96 [0.44 - 0.46] 45.09% 913 424 17 47.37% 1.39 1.96 [0.42 - 0.44] 43.12% 895 392 16 44.69% 0.95 1.96 [0.40 - 0.42] 40.88% 258 97 6 38.76% -0.70 1.96 [0.38 - 0.40] 39.04% 230 89 5 39.78% 0.23 1.96 [0.36 - 0.38] 37.08% 255 86 4 34.51% -0.86 1.96 [0.34 - 0.36] 34.91% 348 114 9 34.05% -0.34 1.96 [0.32 - 0.34] 32.72% 387 123 10 33.07% 0.15 1.96 [0.30 - 0.32] 30.85% 677 206 46 33.83% 1.71 1.96 [0.28 - 0.30] 28.93% 740 196 33 28.72% -0.13 1.96 [0.26 - 0.28] 26.93% 481 127 38 30.35% 1.74 1.96 [0.24 - 0.26] 25.29% 581 140 34 27.02% 0.99 1.96 [0.22 - 0.24] 23.11% 28 7 0 25.00% 0.24 2.05 [0.20 - 0.22] 20.62% 73 12 2 17.81% -0.60 1.98 [0.18 - 0.20] 18.70% 1788 318 31 18.65% -0.05 1.96 [0.16 - 0.18] 17.48% 288 53 6 19.44% 0.88 1.96 [0.14 - 0.16] 15.00% 68 10 1 15.44% 0.10 1.98 [0.12 - 0.14] 12.82% 147 14 2 10.20% -0.96 1.96 [0.10 - 0.12] 11.39% 21 1 1 7.14% -0.62 2.09 [0.08 - 0.10] 8.80% 37 2 1 6.76% -0.45 2.02 [0.06 - 0.08] 7.08% 217 14 3 7.14% 0.04 1.96 [0.04 - 0.06] 5.77% 7 0 0 0.00% -0.68 2.45 [0.02 - 0.04] . 0 0 0 . [0.00 - 0.02] . 0 0 0 . [ ALL ] 32.06% 9797 2884 671 32.86% 1.75 1.96 Using 23 valid bins, expected T-test deviations at 5% sig = 1.15 * Observed individual T-test deviations at or over 5% sig = 0 Chi-Square for Underdog = 9.96 w/ 21 degrees of freedom Critical numbers (.10 .05 .01) = 29.62 32.67 38.93 NO FAVORITE HANDS Preflop equity Mean% Hands Wins Ties Actual% T-Test 5% Sig [exact 50/50] 50.00% 352 5 347 50.71% 0.27 --------------------------------------------------------------------
Site #0, 2 to 10 players, NL Hold'em, all stakes combined Using 25 equity bins. Number of hands analysed: 1630652 Preflop heads-up all-ins: 10149 (Once per 161 hands). FAVORITE'S Preflop equity Mean% Hands Wins Ties Actual% T-Test 5% Sig [0.98 - 1.00] . 0 0 0 . [0.96 - 0.98] . 0 0 0 . [0.94 - 0.96] 94.23% 7 7 0 100.00% 0.68 2.45 [0.92 - 0.94] 92.92% 217 200 3 92.86% -0.04 1.96 [0.90 - 0.92] 91.20% 37 34 1 93.24% 0.45 2.02 [0.88 - 0.90] 88.61% 21 19 1 92.86% 0.62 2.09 [0.86 - 0.88] 87.18% 147 131 2 89.80% 0.96 1.96 [0.84 - 0.86] 85.00% 68 57 1 84.56% -0.10 1.98 [0.82 - 0.84] 82.52% 288 229 6 80.56% -0.88 1.96 [0.80 - 0.82] 81.30% 1788 1439 31 81.35% 0.05 1.96 [0.78 - 0.80] 79.38% 73 59 2 82.19% 0.60 1.98 [0.76 - 0.78] 76.89% 28 21 0 75.00% -0.24 2.05 [0.74 - 0.76] 74.71% 581 407 34 72.98% -0.99 1.96 [0.72 - 0.74] 73.07% 481 316 38 69.65% -1.74 1.96 [0.70 - 0.72] 71.07% 740 511 33 71.28% 0.13 1.96 [0.68 - 0.70] 69.15% 677 425 46 66.17% -1.71 1.96 [0.66 - 0.68] 67.28% 387 254 10 66.93% -0.15 1.96 [0.64 - 0.66] 65.09% 348 225 9 65.95% 0.34 1.96 [0.62 - 0.64] 62.92% 255 165 4 65.49% 0.86 1.96 [0.60 - 0.62] 60.96% 230 136 5 60.22% -0.23 1.96 [0.58 - 0.60] 59.12% 258 155 6 61.24% 0.70 1.96 [0.56 - 0.58] 56.88% 895 487 16 55.31% -0.95 1.96 [0.54 - 0.56] 54.91% 913 472 17 52.63% -1.39 1.96 [0.52 - 0.54] 52.98% 853 347 194 52.05% -0.61 1.96 [0.50 - 0.52] 50.74% 505 146 212 49.90% -0.49 1.96 [ ALL ] 67.94% 9797 6242 671 67.14% -1.75 1.96 Using 23 valid bins, expected T-test deviations at 5% sig = 1.15 * Observed individual T-test deviations at or over 5% sig = 0 Chi-Square for Favorite = 4.22 w/ 22 degrees of freedom Critical numbers (.10 .05 .01) = 30.81 33.92 40.29 UNDERDOG'S Preflop equity Mean% Hands Wins Ties Actual% T-Test 5% Sig [0.48 - 0.50] 49.26% 505 147 212 50.10% 0.49 1.96 [0.46 - 0.48] 47.02% 853 312 194 47.95% 0.61 1.96 [0.44 - 0.46] 45.09% 913 424 17 47.37% 1.39 1.96 [0.42 - 0.44] 43.12% 895 392 16 44.69% 0.95 1.96 [0.40 - 0.42] 40.88% 258 97 6 38.76% -0.70 1.96 [0.38 - 0.40] 39.04% 230 89 5 39.78% 0.23 1.96 [0.36 - 0.38] 37.08% 255 86 4 34.51% -0.86 1.96 [0.34 - 0.36] 34.91% 348 114 9 34.05% -0.34 1.96 [0.32 - 0.34] 32.72% 387 123 10 33.07% 0.15 1.96 [0.30 - 0.32] 30.85% 677 206 46 33.83% 1.71 1.96 [0.28 - 0.30] 28.93% 740 196 33 28.72% -0.13 1.96 [0.26 - 0.28] 26.93% 481 127 38 30.35% 1.74 1.96 [0.24 - 0.26] 25.29% 581 140 34 27.02% 0.99 1.96 [0.22 - 0.24] 23.11% 28 7 0 25.00% 0.24 2.05 [0.20 - 0.22] 20.62% 73 12 2 17.81% -0.60 1.98 [0.18 - 0.20] 18.70% 1788 318 31 18.65% -0.05 1.96 [0.16 - 0.18] 17.48% 288 53 6 19.44% 0.88 1.96 [0.14 - 0.16] 15.00% 68 10 1 15.44% 0.10 1.98 [0.12 - 0.14] 12.82% 147 14 2 10.20% -0.96 1.96 [0.10 - 0.12] 11.39% 21 1 1 7.14% -0.62 2.09 [0.08 - 0.10] 8.80% 37 2 1 6.76% -0.45 2.02 [0.06 - 0.08] 7.08% 217 14 3 7.14% 0.04 1.96 [0.04 - 0.06] 5.77% 7 0 0 0.00% -0.68 2.45 [0.02 - 0.04] . 0 0 0 . [0.00 - 0.02] . 0 0 0 . [ ALL ] 32.06% 9797 2884 671 32.86% 1.75 1.96 Using 23 valid bins, expected T-test deviations at 5% sig = 1.15 * Observed individual T-test deviations at or over 5% sig = 0 Chi-Square for Underdog = 9.96 w/ 21 degrees of freedom Critical numbers (.10 .05 .01) = 29.62 32.67 38.93 NO FAVORITE HANDS Preflop equity Mean% Hands Wins Ties Actual% T-Test 5% Sig [exact 50/50] 50.00% 352 5 347 50.71% 0.27 --------------------------------------------------------------------