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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 | AK742 | flush | 4 | 0.01% | 1 : 15515 | 100.00% |
| 2 | AQs | AQ742 | flush | 4 | 0.01% | 1 : 15515 | 99.99% |
| 3 | AJs | AJ742 | flush | 4 | 0.01% | 1 : 15515 | 99.99% |
| 4 | ATs | AT742 | flush | 4 | 0.01% | 1 : 15515 | 99.98% |
| 5 | A9s | A9742 | flush | 4 | 0.01% | 1 : 15515 | 99.97% |
| 6 | A8s | A8742 | flush | 4 | 0.01% | 1 : 15515 | 99.97% |
| 7 | A6s | A7642 | flush | 4 | 0.01% | 1 : 15515 | 99.96% |
| 8 | A5s | A7542 | flush | 4 | 0.01% | 1 : 15515 | 99.95% |
| 9 | A3s | A7432 | flush | 4 | 0.01% | 1 : 15515 | 99.95% |
| 10 | KQs | KQ742 | flush | 4 | 0.01% | 1 : 15515 | 99.94% |
| 11 | KJs | KJ742 | flush | 4 | 0.01% | 1 : 15515 | 99.94% |
| 12 | KTs | KT742 | flush | 4 | 0.01% | 1 : 15515 | 99.93% |
| 13 | K9s | K9742 | flush | 4 | 0.01% | 1 : 15515 | 99.92% |
| 14 | K8s | K8742 | flush | 4 | 0.01% | 1 : 15515 | 99.92% |
| 15 | K6s | K7642 | flush | 4 | 0.01% | 1 : 15515 | 99.91% |
| 16 | K5s | K7542 | flush | 4 | 0.01% | 1 : 15515 | 99.90% |
| 17 | K3s | K7432 | flush | 4 | 0.01% | 1 : 15515 | 99.90% |
| 18 | QJs | QJ742 | flush | 4 | 0.01% | 1 : 15515 | 99.89% |
| 19 | QTs | QT742 | flush | 4 | 0.01% | 1 : 15515 | 99.88% |
| 20 | Q9s | Q9742 | flush | 4 | 0.01% | 1 : 15515 | 99.88% |
| 21 | Q8s | Q8742 | flush | 4 | 0.01% | 1 : 15515 | 99.87% |
| 22 | Q6s | Q7642 | flush | 4 | 0.01% | 1 : 15515 | 99.86% |
| 23 | Q5s | Q7542 | flush | 4 | 0.01% | 1 : 15515 | 99.86% |
| 24 | Q3s | Q7432 | flush | 4 | 0.01% | 1 : 15515 | 99.85% |
| 25 | JTs | JT742 | flush | 4 | 0.01% | 1 : 15515 | 99.85% |
| 26 | J9s | J9742 | flush | 4 | 0.01% | 1 : 15515 | 99.84% |
| 27 | J8s | J8742 | flush | 4 | 0.01% | 1 : 15515 | 99.83% |
| 28 | J6s | J7642 | flush | 4 | 0.01% | 1 : 15515 | 99.83% |
| 29 | J5s | J7542 | flush | 4 | 0.01% | 1 : 15515 | 99.82% |
| 30 | J3s | J7432 | flush | 4 | 0.01% | 1 : 15515 | 99.81% |
| 31 | T9s | T9742 | flush | 4 | 0.01% | 1 : 15515 | 99.81% |
| 32 | T8s | T8742 | flush | 4 | 0.01% | 1 : 15515 | 99.80% |
| 33 | T6s | T7642 | flush | 4 | 0.01% | 1 : 15515 | 99.79% |
| 34 | T5s | T7542 | flush | 4 | 0.01% | 1 : 15515 | 99.79% |
| 35 | T3s | T7432 | flush | 4 | 0.01% | 1 : 15515 | 99.78% |
| 36 | 98s | 98742 | flush | 4 | 0.01% | 1 : 15515 | 99.77% |
| 37 | 96s | 97642 | flush | 4 | 0.01% | 1 : 15515 | 99.77% |
| 38 | 95s | 97542 | flush | 4 | 0.01% | 1 : 15515 | 99.76% |
| 39 | 93s | 97432 | flush | 4 | 0.01% | 1 : 15515 | 99.76% |
| 40 | 86s | 87642 | flush | 4 | 0.01% | 1 : 15515 | 99.75% |
| 41 | 85s | 87542 | flush | 4 | 0.01% | 1 : 15515 | 99.74% |
| 42 | 83s | 87432 | flush | 4 | 0.01% | 1 : 15515 | 99.74% |
| 43 | 65s | 76542 | flush | 4 | 0.01% | 1 : 15515 | 99.73% |
| 44 | 63s | 76432 | flush | 4 | 0.01% | 1 : 15515 | 99.72% |
| 45 | 53s | 75432 | flush | 4 | 0.01% | 1 : 15515 | 99.72% |
| 46 | 77 | 77742 | three of a kind | 64 | 0.10% | 1 : 969 | 99.71% |
| 47 | 44 | 74442 | three of a kind | 64 | 0.10% | 1 : 969 | 99.61% |
| 48 | 22 | 74222 | three of a kind | 64 | 0.10% | 1 : 969 | 99.50% |
| 49 | 74 | 77442 | two pairs | 144 | 0.23% | 1 : 430 | 99.40% |
| 50 | 72 | 77422 | two pairs | 144 | 0.23% | 1 : 430 | 99.17% |
| 51 | 42 | 74422 | two pairs | 144 | 0.23% | 1 : 430 | 98.94% |
| 52 | AA | AA742 | one pair | 384 | 0.62% | 1 : 161 | 98.70% |
| 53 | KK | KK742 | one pair | 384 | 0.62% | 1 : 161 | 98.09% |
| 54 | QQ742 | one pair | 384 | 0.62% | 1 : 161 | 97.47% | |
| 55 | JJ | JJ742 | one pair | 384 | 0.62% | 1 : 161 | 96.85% |
| 56 | TT | TT742 | one pair | 384 | 0.62% | 1 : 161 | 96.23% |
| 57 | 99 | 99742 | one pair | 384 | 0.62% | 1 : 161 | 95.61% |
| 58 | 88 | 88742 | one pair | 384 | 0.62% | 1 : 161 | 94.99% |
| 59 | A7 | A7742 | one pair | 384 | 0.62% | 1 : 161 | 94.37% |
| 60 | K7 | K7742 | one pair | 384 | 0.62% | 1 : 161 | 93.75% |
| 61 | Q7 | Q7742 | one pair | 384 | 0.62% | 1 : 161 | 93.14% |
| 62 | J7 | J7742 | one pair | 384 | 0.62% | 1 : 161 | 92.52% |
| 63 | T7 | T7742 | one pair | 384 | 0.62% | 1 : 161 | 91.90% |
| 64 | 97 | 97742 | one pair | 384 | 0.62% | 1 : 161 | 91.28% |
| 65 | 87 | 87742 | one pair | 384 | 0.62% | 1 : 161 | 90.66% |
| 66 | 76 | 77642 | one pair | 384 | 0.62% | 1 : 161 | 90.04% |
| 67 | 75 | 77542 | one pair | 384 | 0.62% | 1 : 161 | 89.42% |
| 68 | 73 | 77432 | one pair | 384 | 0.62% | 1 : 161 | 88.81% |
| 69 | 66 | 76642 | one pair | 384 | 0.62% | 1 : 161 | 88.19% |
| 70 | 55 | 75542 | one pair | 384 | 0.62% | 1 : 161 | 87.57% |
| 71 | A4 | A7442 | one pair | 384 | 0.62% | 1 : 161 | 86.95% |
| 72 | K4 | K7442 | one pair | 384 | 0.62% | 1 : 161 | 86.33% |
| 73 | Q4 | Q7442 | one pair | 384 | 0.62% | 1 : 161 | 85.71% |
| 74 | J4 | J7442 | one pair | 384 | 0.62% | 1 : 161 | 85.09% |
| 75 | T4 | T7442 | one pair | 384 | 0.62% | 1 : 161 | 84.47% |
| 76 | 94 | 97442 | one pair | 384 | 0.62% | 1 : 161 | 83.86% |
| 77 | 84 | 87442 | one pair | 384 | 0.62% | 1 : 161 | 83.24% |
| 78 | 64 | 76442 | one pair | 384 | 0.62% | 1 : 161 | 82.62% |
| 79 | 54 | 75442 | one pair | 384 | 0.62% | 1 : 161 | 82.00% |
| 80 | 43 | 74432 | one pair | 384 | 0.62% | 1 : 161 | 81.38% |
| 81 | 33 | 74332 | one pair | 384 | 0.62% | 1 : 161 | 80.76% |
| 82 | A2 | A7422 | one pair | 384 | 0.62% | 1 : 161 | 80.14% |
| 83 | K2 | K7422 | one pair | 384 | 0.62% | 1 : 161 | 79.52% |
| 84 | Q2 | Q7422 | one pair | 384 | 0.62% | 1 : 161 | 78.91% |
| 85 | J2 | J7422 | one pair | 384 | 0.62% | 1 : 161 | 78.29% |
| 86 | T2 | T7422 | one pair | 384 | 0.62% | 1 : 161 | 77.67% |
| 87 | 92 | 97422 | one pair | 384 | 0.62% | 1 : 161 | 77.05% |
| 88 | 82 | 87422 | one pair | 384 | 0.62% | 1 : 161 | 76.43% |
| 89 | 62 | 76422 | one pair | 384 | 0.62% | 1 : 161 | 75.81% |
| 90 | 52 | 75422 | one pair | 384 | 0.62% | 1 : 161 | 75.19% |
| 91 | 32 | 74322 | one pair | 384 | 0.62% | 1 : 161 | 74.57% |
| 92 | AK | AK742 | high card | 1,020 | 1.64% | 1 : 59.8 | 73.96% |
| 93 | AQ | AQ742 | high card | 1,020 | 1.64% | 1 : 59.8 | 72.31% |
| 94 | AJ | AJ742 | high card | 1,020 | 1.64% | 1 : 59.8 | 70.67% |
| 95 | AT | AT742 | high card | 1,020 | 1.64% | 1 : 59.8 | 69.03% |
| 96 | A9 | A9742 | high card | 1,020 | 1.64% | 1 : 59.8 | 67.38% |
| 97 | A8 | A8742 | high card | 1,020 | 1.64% | 1 : 59.8 | 65.74% |
| 98 | A6 | A7642 | high card | 1,020 | 1.64% | 1 : 59.8 | 64.10% |
| 99 | A5 | A7542 | high card | 1,020 | 1.64% | 1 : 59.8 | 62.45% |
| 100 | A3 | A7432 | high card | 1,020 | 1.64% | 1 : 59.8 | 60.81% |
| 101 | KQ | KQ742 | high card | 1,020 | 1.64% | 1 : 59.8 | 59.16% |
| 102 | KJ | KJ742 | high card | 1,020 | 1.64% | 1 : 59.8 | 57.52% |
| 103 | KT | KT742 | high card | 1,020 | 1.64% | 1 : 59.8 | 55.88% |
| 104 | K9 | K9742 | high card | 1,020 | 1.64% | 1 : 59.8 | 54.23% |
| 105 | K8 | K8742 | high card | 1,020 | 1.64% | 1 : 59.8 | 52.59% |
| 106 | K6 | K7642 | high card | 1,020 | 1.64% | 1 : 59.8 | 50.95% |
| 107 | K5 | K7542 | high card | 1,020 | 1.64% | 1 : 59.8 | 49.30% |
| 108 | K3 | K7432 | high card | 1,020 | 1.64% | 1 : 59.8 | 47.66% |
| 109 | QJ | QJ742 | high card | 1,020 | 1.64% | 1 : 59.8 | 46.02% |
| 110 | QT | QT742 | high card | 1,020 | 1.64% | 1 : 59.8 | 44.37% |
| 111 | Q9 | Q9742 | high card | 1,020 | 1.64% | 1 : 59.8 | 42.73% |
| 112 | Q8 | Q8742 | high card | 1,020 | 1.64% | 1 : 59.8 | 41.09% |
| 113 | Q6 | Q7642 | high card | 1,020 | 1.64% | 1 : 59.8 | 39.44% |
| 114 | Q5 | Q7542 | high card | 1,020 | 1.64% | 1 : 59.8 | 37.80% |
| 115 | Q3 | Q7432 | high card | 1,020 | 1.64% | 1 : 59.8 | 36.16% |
| 116 | JT | JT742 | high card | 1,020 | 1.64% | 1 : 59.8 | 34.51% |
| 117 | J9 | J9742 | high card | 1,020 | 1.64% | 1 : 59.8 | 32.87% |
| 118 | J8 | J8742 | high card | 1,020 | 1.64% | 1 : 59.8 | 31.23% |
| 119 | J6 | J7642 | high card | 1,020 | 1.64% | 1 : 59.8 | 29.58% |
| 120 | J5 | J7542 | high card | 1,020 | 1.64% | 1 : 59.8 | 27.94% |
| 121 | J3 | J7432 | high card | 1,020 | 1.64% | 1 : 59.8 | 26.30% |
| 122 | T9 | T9742 | high card | 1,020 | 1.64% | 1 : 59.8 | 24.65% |
| 123 | T8 | T8742 | high card | 1,020 | 1.64% | 1 : 59.8 | 23.01% |
| 124 | T6 | T7642 | high card | 1,020 | 1.64% | 1 : 59.8 | 21.37% |
| 125 | T5 | T7542 | high card | 1,020 | 1.64% | 1 : 59.8 | 19.72% |
| 126 | T3 | T7432 | high card | 1,020 | 1.64% | 1 : 59.8 | 18.08% |
| 127 | 98 | 98742 | high card | 1,020 | 1.64% | 1 : 59.8 | 16.43% |
| 128 | 96 | 97642 | high card | 1,020 | 1.64% | 1 : 59.8 | 14.79% |
| 129 | 95 | 97542 | high card | 1,020 | 1.64% | 1 : 59.8 | 13.15% |
| 130 | 93 | 97432 | high card | 1,020 | 1.64% | 1 : 59.8 | 11.50% |
| 131 | 86 | 87642 | high card | 1,020 | 1.64% | 1 : 59.8 | 9.86% |
| 132 | 85 | 87542 | high card | 1,020 | 1.64% | 1 : 59.8 | 8.22% |
| 133 | 83 | 87432 | high card | 1,020 | 1.64% | 1 : 59.8 | 6.57% |
| 134 | 65 | 76542 | high card | 1,020 | 1.64% | 1 : 59.8 | 4.93% |
| 135 | 63 | 76432 | high card | 1,020 | 1.64% | 1 : 59.8 | 3.29% |
| 136 | 53 | 75432 | high card | 1,020 | 1.64% | 1 : 59.8 | 1.64% |