Introduction
The following table ranks the top hands in a 3-player game. This table assumes that all players stay in until the end.
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Explanation of column headings:- Cards: Initial two-card hand.
- Probability of win: Probability that this hand will win, or tie for the win.
- Average win: This is how much the player will win on average, including his own bets, if the player does win. This is less than 3 because sometimes the player will have to split the pot.
- Expected value: This is how many units the player can expected to win (positive) or lose (negative) with this hand. For example if the player had a pair of aces and contibuted $1 to the pot then the player could expect to have a net win of $1.20.
- Probability: Probability of getting this hand to begin with.
- Additive probability: Probability of getting this hand or any stronger hand to begin with.
Initial Hold'em Hands in Rank Order for 3-Player Game
| Cards | Probability of Win | Average Win | Expected Value | Probability | Additive Probability |
| Pair of A's | 73.78% | 2.99 | 1.2034 | 0.45% | 0.45% |
| Pair of K's | 69.21% | 2.99 | 1.066 | 0.45% | 0.9% |
| Pair of Q's | 65.29% | 2.98 | 0.9475 | 0.45% | 1.36% |
| Pair of J's | 61.57% | 2.98 | 0.835 | 0.45% | 1.81% |
| Pair of T's | 58.02% | 2.98 | 0.7272 | 0.45% | 2.26% |
| Pair of 9's | 54.08% | 2.97 | 0.6084 | 0.45% | 2.71% |
| A/K suited | 51.77% | 2.94 | 0.5221 | 0.3% | 3.02% |
| Pair of 8's | 50.46% | 2.97 | 0.4986 | 0.45% | 3.47% |
| A/Q suited | 50.56% | 2.93 | 0.4824 | 0.3% | 3.77% |
| A/K unsuited | 49.28% | 2.93 | 0.4462 | 0.9% | 4.68% |
| A/J suited | 49.49% | 2.92 | 0.4461 | 0.3% | 4.98% |
| K/Q suited | 48.28% | 2.93 | 0.4128 | 0.3% | 5.28% |
| A/T suited | 48.5% | 2.91 | 0.4121 | 0.3% | 5.58% |
| A/Q unsuited | 48.01% | 2.93 | 0.4045 | 0.9% | 6.49% |
| Pair of 7's | 47.02% | 2.97 | 0.3945 | 0.45% | 6.94% |
| K/J suited | 47.22% | 2.92 | 0.3772 | 0.3% | 7.24% |
| A/J unsuited | 46.84% | 2.91 | 0.3652 | 0.9% | 8.14% |
| K/T suited | 46.24% | 2.91 | 0.3436 | 0.3% | 8.45% |
| A/9 suited | 46.16% | 2.9 | 0.3366 | 0.3% | 8.75% |
| K/Q unsuited | 45.61% | 2.92 | 0.3318 | 0.9% | 9.65% |
| A/T unsuited | 45.79% | 2.9 | 0.3289 | 0.9% | 10.56% |
| Q/J suited | 45.55% | 2.91 | 0.3256 | 0.3% | 10.86% |
| A/8 suited | 45.31% | 2.88 | 0.3058 | 0.3% | 11.16% |
| Pair of 6's | 43.77% | 2.96 | 0.2958 | 0.45% | 11.61% |
| Q/T suited | 44.59% | 2.9 | 0.2932 | 0.3% | 11.92% |
| K/J unsuited | 44.46% | 2.91 | 0.293 | 0.9% | 12.82% |
| A/7 suited | 44.32% | 2.87 | 0.2719 | 0.3% | 13.12% |
| K/9 suited | 43.88% | 2.89 | 0.2689 | 0.3% | 13.42% |
| J/T suited | 43.44% | 2.9 | 0.2582 | 0.3% | 13.73% |
| K/T unsuited | 43.42% | 2.9 | 0.2576 | 0.9% | 14.63% |
| A/9 unsuited | 43.25% | 2.88 | 0.2473 | 0.9% | 15.54% |
| A/5 suited | 43.59% | 2.85 | 0.2431 | 0.3% | 15.84% |
| Q/J unsuited | 42.76% | 2.9 | 0.2406 | 0.9% | 16.74% |
| A/6 suited | 43.19% | 2.86 | 0.2348 | 0.3% | 17.04% |
| Q/9 suited | 42.25% | 2.89 | 0.2193 | 0.3% | 17.35% |
| A/4 suited | 42.7% | 2.85 | 0.2161 | 0.3% | 17.65% |
| A/8 unsuited | 42.31% | 2.87 | 0.2136 | 0.9% | 18.55% |
| Q/T unsuited | 41.73% | 2.89 | 0.206 | 0.9% | 19.46% |
| K/8 suited | 41.91% | 2.88 | 0.2048 | 0.3% | 19.76% |
| Pair of 5's | 40.7% | 2.95 | 0.2017 | 0.45% | 20.21% |
| A/3 suited | 41.8% | 2.85 | 0.1901 | 0.3% | 20.51% |
| J/9 suited | 41.11% | 2.88 | 0.1844 | 0.3% | 20.81% |
| K/7 suited | 41.19% | 2.86 | 0.1786 | 0.3% | 21.12% |
| A/7 unsuited | 41.25% | 2.85 | 0.177 | 0.9% | 22.02% |
| K/9 unsuited | 40.88% | 2.88 | 0.1769 | 0.9% | 22.93% |
| J/T unsuited | 40.58% | 2.89 | 0.171 | 0.9% | 23.83% |
| A/2 suited | 40.86% | 2.85 | 0.163 | 0.3% | 24.13% |
| T/9 suited | 40.38% | 2.88 | 0.1617 | 0.3% | 24.43% |
| Q/8 suited | 40.28% | 2.87 | 0.1564 | 0.3% | 24.74% |
| K/6 suited | 40.29% | 2.85 | 0.1483 | 0.3% | 25.04% |
| A/5 unsuited | 40.46% | 2.83 | 0.1458 | 0.9% | 25.94% |
| A/6 unsuited | 40.04% | 2.84 | 0.1374 | 0.9% | 26.85% |
| Q/9 unsuited | 39.2% | 2.87 | 0.1262 | 0.9% | 27.75% |
| K/5 suited | 39.51% | 2.84 | 0.122 | 0.3% | 28.05% |
| J/8 suited | 39.14% | 2.87 | 0.1219 | 0.3% | 28.36% |
| A/4 unsuited | 39.45% | 2.83 | 0.1155 | 0.9% | 29.26% |
| K/8 unsuited | 38.75% | 2.86 | 0.1079 | 0.9% | 30.17% |
| Pair of 4's | 37.42% | 2.95 | 0.1026 | 0.45% | 30.62% |
| T/8 suited | 38.46% | 2.86 | 0.1004 | 0.3% | 30.92% |
| K/4 suited | 38.63% | 2.84 | 0.0956 | 0.3% | 31.22% |
| Q/7 suited | 38.33% | 2.85 | 0.0937 | 0.3% | 31.52% |
| J/9 unsuited | 38.05% | 2.87 | 0.0908 | 0.9% | 32.43% |
| A/3 unsuited | 38.5% | 2.83 | 0.0879 | 0.9% | 33.33% |
| K/7 unsuited | 37.96% | 2.84 | 0.0792 | 0.9% | 34.24% |
| 9/8 suited | 37.74% | 2.86 | 0.079 | 0.3% | 34.54% |
| Q/6 suited | 37.7% | 2.84 | 0.0712 | 0.3% | 34.84% |
| K/3 suited | 37.78% | 2.84 | 0.0712 | 0.3% | 35.14% |
| T/9 unsuited | 37.36% | 2.86 | 0.0692 | 0.9% | 36.05% |
| J/7 suited | 37.21% | 2.85 | 0.0605 | 0.3% | 36.35% |
| Q/8 unsuited | 37.09% | 2.85 | 0.0585 | 0.9% | 37.25% |
| A/2 unsuited | 37.47% | 2.82 | 0.0579 | 0.9% | 38.16% |
| K/6 unsuited | 37% | 2.83 | 0.0469 | 0.9% | 39.06% |
| K/2 suited | 36.91% | 2.83 | 0.0464 | 0.3% | 39.37% |
| Q/5 suited | 36.93% | 2.83 | 0.0455 | 0.3% | 39.67% |
| T/7 suited | 36.51% | 2.85 | 0.0394 | 0.3% | 39.97% |
| J/8 unsuited | 35.94% | 2.85 | 0.0237 | 0.9% | 40.87% |
| 9/7 suited | 35.95% | 2.84 | 0.0223 | 0.3% | 41.18% |
| Q/4 suited | 36.08% | 2.83 | 0.0203 | 0.3% | 41.48% |
| K/5 unsuited | 36.15% | 2.82 | 0.0183 | 0.9% | 42.38% |
| 8/7 suited | 35.65% | 2.84 | 0.0134 | 0.3% | 42.68% |
| Pair of 3's | 34.33% | 2.94 | 0.0087 | 0.45% | 43.14% |
| T/8 unsuited | 35.26% | 2.84 | 0.0026 | 0.9% | 44.04% |
| J/6 suited | 35.33% | 2.83 | 0.0009 | 0.3% | 44.34% |
| Q/3 suited | 35.22% | 2.83 | -0.0042 | 0.3% | 44.65% |
| Q/7 unsuited | 35.01% | 2.83 | -0.0082 | 0.9% | 45.55% |
| K/4 unsuited | 35.19% | 2.81 | -0.0104 | 0.9% | 46.46% |
| J/5 suited | 34.79% | 2.82 | -0.0182 | 0.3% | 46.76% |
| 9/8 unsuited | 34.55% | 2.84 | -0.0185 | 0.9% | 47.66% |
| T/6 suited | 34.64% | 2.83 | -0.0194 | 0.3% | 47.96% |
| Q/2 suited | 34.4% | 2.83 | -0.0279 | 0.3% | 48.27% |
| Q/6 unsuited | 34.33% | 2.82 | -0.0326 | 0.9% | 49.17% |
| 9/6 suited | 34.08% | 2.83 | -0.0357 | 0.3% | 49.47% |
| K/3 unsuited | 34.26% | 2.81 | -0.0374 | 0.9% | 50.38% |
| 8/6 suited | 33.88% | 2.83 | -0.0416 | 0.3% | 50.68% |
| J/7 unsuited | 33.86% | 2.83 | -0.0422 | 0.9% | 51.58% |
| 7/6 suited | 33.85% | 2.83 | -0.0424 | 0.3% | 51.89% |
| J/4 suited | 33.95% | 2.82 | -0.043 | 0.3% | 52.19% |
| Q/5 unsuited | 33.48% | 2.81 | -0.0607 | 0.9% | 53.09% |
| T/7 unsuited | 33.19% | 2.82 | -0.0626 | 0.9% | 54% |
| K/2 unsuited | 33.34% | 2.81 | -0.0642 | 0.9% | 54.9% |
| J/3 suited | 33.14% | 2.82 | -0.0659 | 0.3% | 55.2% |
| T/5 suited | 32.81% | 2.81 | -0.0768 | 0.3% | 55.51% |
| 9/7 unsuited | 32.6% | 2.82 | -0.0799 | 0.9% | 56.41% |
| Pair of 2's | 31.4% | 2.93 | -0.0804 | 0.45% | 56.86% |
| 8/7 unsuited | 32.33% | 2.82 | -0.0881 | 0.9% | 57.77% |
| Q/4 unsuited | 32.55% | 2.8 | -0.0886 | 0.9% | 58.67% |
| J/2 suited | 32.33% | 2.82 | -0.0891 | 0.3% | 58.97% |
| 6/5 suited | 32.21% | 2.82 | -0.0923 | 0.3% | 59.28% |
| 9/5 suited | 32.24% | 2.81 | -0.0927 | 0.3% | 59.58% |
| T/4 suited | 32.22% | 2.81 | -0.0945 | 0.3% | 59.88% |
| 7/5 suited | 32.1% | 2.82 | -0.0962 | 0.3% | 60.18% |
| 8/5 suited | 32.06% | 2.81 | -0.0979 | 0.3% | 60.48% |
| J/6 unsuited | 31.85% | 2.81 | -0.106 | 0.9% | 61.39% |
| Q/3 unsuited | 31.63% | 2.8 | -0.115 | 0.9% | 62.29% |
| T/3 suited | 31.42% | 2.81 | -0.1172 | 0.3% | 62.59% |
| T/6 unsuited | 31.16% | 2.8 | -0.1262 | 0.9% | 63.5% |
| J/5 unsuited | 31.26% | 2.79 | -0.1268 | 0.9% | 64.4% |
| 5/4 suited | 30.98% | 2.81 | -0.1295 | 0.3% | 64.71% |
| T/2 suited | 30.6% | 2.81 | -0.1405 | 0.3% | 65.01% |
| Q/2 unsuited | 30.72% | 2.8 | -0.1413 | 0.9% | 65.91% |
| 9/6 unsuited | 30.61% | 2.8 | -0.1421 | 0.9% | 66.82% |
| 6/4 suited | 30.42% | 2.81 | -0.1453 | 0.3% | 67.12% |
| 8/6 unsuited | 30.43% | 2.8 | -0.1473 | 0.9% | 68.02% |
| 7/6 unsuited | 30.41% | 2.8 | -0.1477 | 0.9% | 68.93% |
| 9/4 suited | 30.35% | 2.8 | -0.1492 | 0.3% | 69.23% |
| 7/4 suited | 30.21% | 2.81 | -0.1522 | 0.3% | 69.53% |
| J/4 unsuited | 30.35% | 2.79 | -0.1538 | 0.9% | 70.44% |
| 8/4 suited | 30.16% | 2.8 | -0.1542 | 0.3% | 70.74% |
| 9/3 suited | 29.78% | 2.8 | -0.1654 | 0.3% | 71.04% |
| J/3 unsuited | 29.44% | 2.79 | -0.1798 | 0.9% | 71.95% |
| 5/3 suited | 29.18% | 2.8 | -0.1821 | 0.3% | 72.25% |
| T/5 unsuited | 29.21% | 2.78 | -0.1872 | 0.9% | 73.15% |
| 9/2 suited | 28.98% | 2.8 | -0.1883 | 0.3% | 73.45% |
| 6/5 unsuited | 28.7% | 2.79 | -0.1998 | 0.9% | 74.36% |
| 6/3 suited | 28.55% | 2.8 | -0.2002 | 0.3% | 74.66% |
| 9/5 unsuited | 28.63% | 2.78 | -0.2035 | 0.9% | 75.57% |
| J/2 unsuited | 28.56% | 2.78 | -0.2052 | 0.9% | 76.47% |
| 7/5 unsuited | 28.54% | 2.78 | -0.2053 | 0.9% | 77.38% |
| T/4 unsuited | 28.55% | 2.78 | -0.2072 | 0.9% | 78.28% |
| 4/3 suited | 28.28% | 2.8 | -0.2074 | 0.3% | 78.58% |
| 8/5 unsuited | 28.47% | 2.78 | -0.2078 | 0.9% | 79.49% |
| 7/3 suited | 28.3% | 2.8 | -0.2082 | 0.3% | 79.79% |
| 8/3 suited | 28.28% | 2.8 | -0.2093 | 0.3% | 80.09% |
| 8/2 suited | 27.73% | 2.79 | -0.2253 | 0.3% | 80.39% |
| T/3 unsuited | 27.68% | 2.77 | -0.2324 | 0.9% | 81.3% |
| 5/2 suited | 27.3% | 2.79 | -0.2371 | 0.3% | 81.6% |
| 5/4 unsuited | 27.37% | 2.78 | -0.2401 | 0.9% | 82.5% |
| 6/2 suited | 26.65% | 2.79 | -0.2559 | 0.3% | 82.81% |
| 6/4 unsuited | 26.76% | 2.77 | -0.2576 | 0.9% | 83.71% |
| T/2 unsuited | 26.79% | 2.77 | -0.2578 | 0.9% | 84.62% |
| 4/2 suited | 26.49% | 2.79 | -0.2599 | 0.3% | 84.92% |
| 7/2 suited | 26.44% | 2.79 | -0.2628 | 0.3% | 85.22% |
| 9/4 unsuited | 26.59% | 2.77 | -0.2644 | 0.9% | 86.12% |
| 7/4 unsuited | 26.51% | 2.77 | -0.2657 | 0.9% | 87.03% |
| 8/4 unsuited | 26.42% | 2.77 | -0.2687 | 0.9% | 87.93% |
| 9/3 unsuited | 25.97% | 2.76 | -0.2825 | 0.9% | 88.84% |
| 3/2 suited | 25.61% | 2.79 | -0.285 | 0.3% | 89.14% |
| 5/3 unsuited | 25.46% | 2.76 | -0.2961 | 0.9% | 90.05% |
| 9/2 unsuited | 25.1% | 2.76 | -0.3073 | 0.9% | 90.95% |
| 6/3 unsuited | 24.74% | 2.76 | -0.3168 | 0.9% | 91.86% |
| 4/3 unsuited | 24.49% | 2.76 | -0.3238 | 0.9% | 92.76% |
| 7/3 unsuited | 24.47% | 2.76 | -0.3256 | 0.9% | 93.67% |
| 8/3 unsuited | 24.4% | 2.75 | -0.3285 | 0.9% | 94.57% |
| 8/2 unsuited | 23.79% | 2.75 | -0.3462 | 0.9% | 95.48% |
| 5/2 unsuited | 23.43% | 2.75 | -0.3558 | 0.9% | 96.38% |
| 6/2 unsuited | 22.69% | 2.75 | -0.3769 | 0.9% | 97.29% |
| 4/2 unsuited | 22.56% | 2.75 | -0.3801 | 0.9% | 98.19% |
| 7/2 unsuited | 22.44% | 2.74 | -0.3854 | 0.9% | 99.1% |
| 3/2 unsuited | 21.61% | 2.74 | -0.4072 | 0.9% | 100% |
| Total | 2.84 | 100% |
Methodology:
This table is the result of a random simulation of 68,612,544,000 games and assumes all players stay in until the end of the hand.
The following table shows my power rating for each initial 2-card hand in a 3-player game. The numbers are on a 0 to 40 scale. Use the top table if you have a pair, the middle table if your cards are suited, and the bottom table if your cards are unsuited. Except for a pair,look up your high card along the left and your low card along the top.
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Written by: Michael Shackleford