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| non-flush example | flush example |
| distribution of hand types | ||||
|---|---|---|---|---|
| distinct | combinations | probability | odds | |
| royal flush | 0 | 0 | impossible | impossible |
| straight flush | 0 | 0 | impossible | impossible |
| four of a kind | 0 | 0 | impossible | impossible |
| full house | 0 | 0 | impossible | impossible |
| flush | 45 | 180 | 0.29% | 1 : 344 |
| straight | 0 | 0 | impossible | impossible |
| three of a kind | 3 | 192 | 0.31% | 1 : 322 |
| two pairs | 3 | 432 | 0.70% | 1 : 143 |
| one pair | 40 | 15,360 | 24.75% | 1 : 3.04 |
| high card | 45 | 45,900 | 73.96% | 2.84 : 1 |
| total | 136 | 62,064 | 100 % | |
| ranking of all 136 distinct hole cards | |||||||
|---|---|---|---|---|---|---|---|
| hole cards | hand | category | combinations | probability | odds | equity | |
| nuts | AKs | AK932 | flush | 4 | 0.01% | 1 : 15515 | 100.00% |
| 2 | AQs | AQ932 | flush | 4 | 0.01% | 1 : 15515 | 99.99% |
| 3 | AJs | AJ932 | flush | 4 | 0.01% | 1 : 15515 | 99.99% |
| 4 | ATs | AT932 | flush | 4 | 0.01% | 1 : 15515 | 99.98% |
| 5 | A8s | A9832 | flush | 4 | 0.01% | 1 : 15515 | 99.97% |
| 6 | A7s | A9732 | flush | 4 | 0.01% | 1 : 15515 | 99.97% |
| 7 | A6s | A9632 | flush | 4 | 0.01% | 1 : 15515 | 99.96% |
| 8 | A5s | A9532 | flush | 4 | 0.01% | 1 : 15515 | 99.95% |
| 9 | A4s | A9432 | flush | 4 | 0.01% | 1 : 15515 | 99.95% |
| 10 | KQs | KQ932 | flush | 4 | 0.01% | 1 : 15515 | 99.94% |
| 11 | KJs | KJ932 | flush | 4 | 0.01% | 1 : 15515 | 99.94% |
| 12 | KTs | KT932 | flush | 4 | 0.01% | 1 : 15515 | 99.93% |
| 13 | K8s | K9832 | flush | 4 | 0.01% | 1 : 15515 | 99.92% |
| 14 | K7s | K9732 | flush | 4 | 0.01% | 1 : 15515 | 99.92% |
| 15 | K6s | K9632 | flush | 4 | 0.01% | 1 : 15515 | 99.91% |
| 16 | K5s | K9532 | flush | 4 | 0.01% | 1 : 15515 | 99.90% |
| 17 | K4s | K9432 | flush | 4 | 0.01% | 1 : 15515 | 99.90% |
| 18 | QJs | QJ932 | flush | 4 | 0.01% | 1 : 15515 | 99.89% |
| 19 | QTs | QT932 | flush | 4 | 0.01% | 1 : 15515 | 99.88% |
| 20 | Q8s | Q9832 | flush | 4 | 0.01% | 1 : 15515 | 99.88% |
| 21 | Q7s | Q9732 | flush | 4 | 0.01% | 1 : 15515 | 99.87% |
| 22 | Q6s | Q9632 | flush | 4 | 0.01% | 1 : 15515 | 99.86% |
| 23 | Q5s | Q9532 | flush | 4 | 0.01% | 1 : 15515 | 99.86% |
| 24 | Q4s | Q9432 | flush | 4 | 0.01% | 1 : 15515 | 99.85% |
| 25 | JTs | JT932 | flush | 4 | 0.01% | 1 : 15515 | 99.85% |
| 26 | J8s | J9832 | flush | 4 | 0.01% | 1 : 15515 | 99.84% |
| 27 | J7s | J9732 | flush | 4 | 0.01% | 1 : 15515 | 99.83% |
| 28 | J6s | J9632 | flush | 4 | 0.01% | 1 : 15515 | 99.83% |
| 29 | J5s | J9532 | flush | 4 | 0.01% | 1 : 15515 | 99.82% |
| 30 | J4s | J9432 | flush | 4 | 0.01% | 1 : 15515 | 99.81% |
| 31 | T8s | T9832 | flush | 4 | 0.01% | 1 : 15515 | 99.81% |
| 32 | T7s | T9732 | flush | 4 | 0.01% | 1 : 15515 | 99.80% |
| 33 | T6s | T9632 | flush | 4 | 0.01% | 1 : 15515 | 99.79% |
| 34 | T5s | T9532 | flush | 4 | 0.01% | 1 : 15515 | 99.79% |
| 35 | T4s | T9432 | flush | 4 | 0.01% | 1 : 15515 | 99.78% |
| 36 | 87s | 98732 | flush | 4 | 0.01% | 1 : 15515 | 99.77% |
| 37 | 86s | 98632 | flush | 4 | 0.01% | 1 : 15515 | 99.77% |
| 38 | 85s | 98532 | flush | 4 | 0.01% | 1 : 15515 | 99.76% |
| 39 | 84s | 98432 | flush | 4 | 0.01% | 1 : 15515 | 99.76% |
| 40 | 76s | 97632 | flush | 4 | 0.01% | 1 : 15515 | 99.75% |
| 41 | 75s | 97532 | flush | 4 | 0.01% | 1 : 15515 | 99.74% |
| 42 | 74s | 97432 | flush | 4 | 0.01% | 1 : 15515 | 99.74% |
| 43 | 65s | 96532 | flush | 4 | 0.01% | 1 : 15515 | 99.73% |
| 44 | 64s | 96432 | flush | 4 | 0.01% | 1 : 15515 | 99.72% |
| 45 | 54s | 95432 | flush | 4 | 0.01% | 1 : 15515 | 99.72% |
| 46 | 99 | 99932 | three of a kind | 64 | 0.10% | 1 : 969 | 99.71% |
| 47 | 33 | 93332 | three of a kind | 64 | 0.10% | 1 : 969 | 99.61% |
| 48 | 22 | 93222 | three of a kind | 64 | 0.10% | 1 : 969 | 99.50% |
| 49 | 93 | 99332 | two pairs | 144 | 0.23% | 1 : 430 | 99.40% |
| 50 | 92 | 99322 | two pairs | 144 | 0.23% | 1 : 430 | 99.17% |
| 51 | 32 | 93322 | two pairs | 144 | 0.23% | 1 : 430 | 98.94% |
| 52 | AA | AA932 | one pair | 384 | 0.62% | 1 : 161 | 98.70% |
| 53 | KK | KK932 | one pair | 384 | 0.62% | 1 : 161 | 98.09% |
| 54 | QQ932 | one pair | 384 | 0.62% | 1 : 161 | 97.47% | |
| 55 | JJ | JJ932 | one pair | 384 | 0.62% | 1 : 161 | 96.85% |
| 56 | TT | TT932 | one pair | 384 | 0.62% | 1 : 161 | 96.23% |
| 57 | A9 | A9932 | one pair | 384 | 0.62% | 1 : 161 | 95.61% |
| 58 | K9 | K9932 | one pair | 384 | 0.62% | 1 : 161 | 94.99% |
| 59 | Q9 | Q9932 | one pair | 384 | 0.62% | 1 : 161 | 94.37% |
| 60 | J9 | J9932 | one pair | 384 | 0.62% | 1 : 161 | 93.75% |
| 61 | T9 | T9932 | one pair | 384 | 0.62% | 1 : 161 | 93.14% |
| 62 | 98 | 99832 | one pair | 384 | 0.62% | 1 : 161 | 92.52% |
| 63 | 97 | 99732 | one pair | 384 | 0.62% | 1 : 161 | 91.90% |
| 64 | 96 | 99632 | one pair | 384 | 0.62% | 1 : 161 | 91.28% |
| 65 | 95 | 99532 | one pair | 384 | 0.62% | 1 : 161 | 90.66% |
| 66 | 94 | 99432 | one pair | 384 | 0.62% | 1 : 161 | 90.04% |
| 67 | 88 | 98832 | one pair | 384 | 0.62% | 1 : 161 | 89.42% |
| 68 | 77 | 97732 | one pair | 384 | 0.62% | 1 : 161 | 88.81% |
| 69 | 66 | 96632 | one pair | 384 | 0.62% | 1 : 161 | 88.19% |
| 70 | 55 | 95532 | one pair | 384 | 0.62% | 1 : 161 | 87.57% |
| 71 | 44 | 94432 | one pair | 384 | 0.62% | 1 : 161 | 86.95% |
| 72 | A3 | A9332 | one pair | 384 | 0.62% | 1 : 161 | 86.33% |
| 73 | K3 | K9332 | one pair | 384 | 0.62% | 1 : 161 | 85.71% |
| 74 | Q3 | Q9332 | one pair | 384 | 0.62% | 1 : 161 | 85.09% |
| 75 | J3 | J9332 | one pair | 384 | 0.62% | 1 : 161 | 84.47% |
| 76 | T3 | T9332 | one pair | 384 | 0.62% | 1 : 161 | 83.86% |
| 77 | 83 | 98332 | one pair | 384 | 0.62% | 1 : 161 | 83.24% |
| 78 | 73 | 97332 | one pair | 384 | 0.62% | 1 : 161 | 82.62% |
| 79 | 63 | 96332 | one pair | 384 | 0.62% | 1 : 161 | 82.00% |
| 80 | 53 | 95332 | one pair | 384 | 0.62% | 1 : 161 | 81.38% |
| 81 | 43 | 94332 | one pair | 384 | 0.62% | 1 : 161 | 80.76% |
| 82 | A2 | A9322 | one pair | 384 | 0.62% | 1 : 161 | 80.14% |
| 83 | K2 | K9322 | one pair | 384 | 0.62% | 1 : 161 | 79.52% |
| 84 | Q2 | Q9322 | one pair | 384 | 0.62% | 1 : 161 | 78.91% |
| 85 | J2 | J9322 | one pair | 384 | 0.62% | 1 : 161 | 78.29% |
| 86 | T2 | T9322 | one pair | 384 | 0.62% | 1 : 161 | 77.67% |
| 87 | 82 | 98322 | one pair | 384 | 0.62% | 1 : 161 | 77.05% |
| 88 | 72 | 97322 | one pair | 384 | 0.62% | 1 : 161 | 76.43% |
| 89 | 62 | 96322 | one pair | 384 | 0.62% | 1 : 161 | 75.81% |
| 90 | 52 | 95322 | one pair | 384 | 0.62% | 1 : 161 | 75.19% |
| 91 | 42 | 94322 | one pair | 384 | 0.62% | 1 : 161 | 74.57% |
| 92 | AK | AK932 | high card | 1,020 | 1.64% | 1 : 59.8 | 73.96% |
| 93 | AQ | AQ932 | high card | 1,020 | 1.64% | 1 : 59.8 | 72.31% |
| 94 | AJ | AJ932 | high card | 1,020 | 1.64% | 1 : 59.8 | 70.67% |
| 95 | AT | AT932 | high card | 1,020 | 1.64% | 1 : 59.8 | 69.03% |
| 96 | A8 | A9832 | high card | 1,020 | 1.64% | 1 : 59.8 | 67.38% |
| 97 | A7 | A9732 | high card | 1,020 | 1.64% | 1 : 59.8 | 65.74% |
| 98 | A6 | A9632 | high card | 1,020 | 1.64% | 1 : 59.8 | 64.10% |
| 99 | A5 | A9532 | high card | 1,020 | 1.64% | 1 : 59.8 | 62.45% |
| 100 | A4 | A9432 | high card | 1,020 | 1.64% | 1 : 59.8 | 60.81% |
| 101 | KQ | KQ932 | high card | 1,020 | 1.64% | 1 : 59.8 | 59.16% |
| 102 | KJ | KJ932 | high card | 1,020 | 1.64% | 1 : 59.8 | 57.52% |
| 103 | KT | KT932 | high card | 1,020 | 1.64% | 1 : 59.8 | 55.88% |
| 104 | K8 | K9832 | high card | 1,020 | 1.64% | 1 : 59.8 | 54.23% |
| 105 | K7 | K9732 | high card | 1,020 | 1.64% | 1 : 59.8 | 52.59% |
| 106 | K6 | K9632 | high card | 1,020 | 1.64% | 1 : 59.8 | 50.95% |
| 107 | K5 | K9532 | high card | 1,020 | 1.64% | 1 : 59.8 | 49.30% |
| 108 | K4 | K9432 | high card | 1,020 | 1.64% | 1 : 59.8 | 47.66% |
| 109 | QJ | QJ932 | high card | 1,020 | 1.64% | 1 : 59.8 | 46.02% |
| 110 | QT | QT932 | high card | 1,020 | 1.64% | 1 : 59.8 | 44.37% |
| 111 | Q8 | Q9832 | high card | 1,020 | 1.64% | 1 : 59.8 | 42.73% |
| 112 | Q7 | Q9732 | high card | 1,020 | 1.64% | 1 : 59.8 | 41.09% |
| 113 | Q6 | Q9632 | high card | 1,020 | 1.64% | 1 : 59.8 | 39.44% |
| 114 | Q5 | Q9532 | high card | 1,020 | 1.64% | 1 : 59.8 | 37.80% |
| 115 | Q4 | Q9432 | high card | 1,020 | 1.64% | 1 : 59.8 | 36.16% |
| 116 | JT | JT932 | high card | 1,020 | 1.64% | 1 : 59.8 | 34.51% |
| 117 | J8 | J9832 | high card | 1,020 | 1.64% | 1 : 59.8 | 32.87% |
| 118 | J7 | J9732 | high card | 1,020 | 1.64% | 1 : 59.8 | 31.23% |
| 119 | J6 | J9632 | high card | 1,020 | 1.64% | 1 : 59.8 | 29.58% |
| 120 | J5 | J9532 | high card | 1,020 | 1.64% | 1 : 59.8 | 27.94% |
| 121 | J4 | J9432 | high card | 1,020 | 1.64% | 1 : 59.8 | 26.30% |
| 122 | T8 | T9832 | high card | 1,020 | 1.64% | 1 : 59.8 | 24.65% |
| 123 | T7 | T9732 | high card | 1,020 | 1.64% | 1 : 59.8 | 23.01% |
| 124 | T6 | T9632 | high card | 1,020 | 1.64% | 1 : 59.8 | 21.37% |
| 125 | T5 | T9532 | high card | 1,020 | 1.64% | 1 : 59.8 | 19.72% |
| 126 | T4 | T9432 | high card | 1,020 | 1.64% | 1 : 59.8 | 18.08% |
| 127 | 87 | 98732 | high card | 1,020 | 1.64% | 1 : 59.8 | 16.43% |
| 128 | 86 | 98632 | high card | 1,020 | 1.64% | 1 : 59.8 | 14.79% |
| 129 | 85 | 98532 | high card | 1,020 | 1.64% | 1 : 59.8 | 13.15% |
| 130 | 84 | 98432 | high card | 1,020 | 1.64% | 1 : 59.8 | 11.50% |
| 131 | 76 | 97632 | high card | 1,020 | 1.64% | 1 : 59.8 | 9.86% |
| 132 | 75 | 97532 | high card | 1,020 | 1.64% | 1 : 59.8 | 8.22% |
| 133 | 74 | 97432 | high card | 1,020 | 1.64% | 1 : 59.8 | 6.57% |
| 134 | 65 | 96532 | high card | 1,020 | 1.64% | 1 : 59.8 | 4.93% |
| 135 | 64 | 96432 | high card | 1,020 | 1.64% | 1 : 59.8 | 3.29% |
| 136 | 54 | 95432 | high card | 1,020 | 1.64% | 1 : 59.8 | 1.64% |