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Power Rankings for Three-Player Texas Hold ’Em Games

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Introduction

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The table below lists the strongest hands in a game featuring three players. It is assumed that all players will remain in until the hand concludes.

Explanation of column headings:
  • Cards: Initial two-card hand.
  • Win Probability: This indicates the likelihood that this specific hand will either win outright or tie.
  • Average Payout: This identifies the typical earnings a player can expect when they win, factoring in their own stakes. It will often be below 3 because players may need to divide the winnings with others.
  • Expected Value: This measures the anticipated gains (positive) or losses (negative) a player might encounter with a given hand. For instance, if a player holds a pair of aces and bets $1 into the pot, their expected net gain would be around $1.20.
  • Hand Probability: This refers to the chance of being dealt this particular hand initially.
  • Cumulative Probability: This represents the likelihood of being dealt either this hand or any stronger ones from the start.

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Ranking of Initial Hold'em Hands for a Game with Three Players

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%
30.41% 2.8 T/7 unsuited 0.9% 68.93%
-0.0626 30.35% 2.8 K/2 unsuited 0.3% 69.23%
-0.0642 30.21% 2.81 J/3 suited 0.3% 69.53%
-0.0659 30.35% 2.79 T/5 suited 0.9% 70.44%
-0.0768 30.16% 2.8 9/7 unsuited 0.3% 70.74%
-0.0799 29.78% 2.8 Pair of 2's 0.3% 71.04%
-0.0804 29.44% 2.79 8/7 unsuited 0.9% 71.95%
-0.0881 29.18% 2.8 Q/4 unsuited 0.3% 72.25%
-0.0886 29.21% 2.78 J/2 suited 0.9% 73.15%
-0.0891 28.98% 2.8 6/5 suited 0.3% 73.45%
-0.0923 28.7% 2.79 9/5 suited 0.9% 74.36%
-0.0927 28.55% 2.8 T/4 suited 0.3% 74.66%
-0.0945 28.63% 2.78 7/5 suited 0.9% 75.57%
-0.0962 28.56% 2.78 8/5 suited 0.9% 76.47%
-0.0979 28.54% 2.78 J/6 unsuited 0.9% 77.38%
-0.106 28.55% 2.78 Q/3 unsuited 0.9% 78.28%
-0.115 28.28% 2.8 T/3 suited 0.3% 78.58%
-0.1172 28.47% 2.78 T/6 unsuited 0.9% 79.49%
-0.1262 28.3% 2.8 J/5 unsuited 0.3% 79.79%
-0.1268 28.28% 2.8 5/4 suited 0.3% 80.09%
-0.1295 27.73% 2.79 T/2 suited 0.3% 80.39%
-0.1405 27.68% 2.77 Q/2 unsuited 0.9% 81.3%
-0.1413 27.3% 2.79 9/6 unsuited 0.3% 81.6%
-0.1421 27.37% 2.78 6/4 suited 0.9% 82.5%
-0.1453 26.65% 2.79 8/6 unsuited 0.3% 82.81%
-0.1473 26.76% 2.77 0.9% 83.71%
T/7 unsuited 26.79% 2.77 -0.0626 0.9% 84.62%
K/2 unsuited 26.49% 2.79 -0.0642 0.3% 84.92%
J/3 suited 26.44% 2.79 -0.0659 0.3% 85.22%
T/5 suited 26.59% 2.77 -0.0768 0.9% 86.12%
9/7 unsuited 26.51% 2.77 -0.0799 0.9% 87.03%
Pair of 2's 26.42% 2.77 -0.0804 0.9% 87.93%
8/7 unsuited 25.97% 2.76 -0.0881 0.9% 88.84%
Q/4 unsuited 25.61% 2.79 -0.0886 0.3% 89.14%
J/2 suited 25.46% 2.76 -0.0891 0.9% 90.05%
6/5 suited 25.1% 2.76 -0.0923 0.9% 90.95%
9/5 suited 24.74% 2.76 -0.0927 0.9% 91.86%
T/4 suited 24.49% 2.76 -0.0945 0.9% 92.76%
7/5 suited 24.47% 2.76 -0.0962 0.9% 93.67%
8/5 suited 24.4% 2.75 -0.0979 0.9% 94.57%
J/6 unsuited 23.79% 2.75 -0.106 0.9% 95.48%
Q/3 unsuited 23.43% 2.75 -0.115 0.9% 96.38%
T/3 suited 22.69% 2.75 -0.1172 0.9% 97.29%
T/6 unsuited 22.56% 2.75 -0.1262 0.9% 98.19%
J/5 unsuited 22.44% 2.74 -0.1268 0.9% 99.1%
5/4 suited 21.61% 2.74 -0.1295 0.9% 100%
T/2 suited   2.84   100%  

-0.1405

This table is derived from a simulated run of a staggering 68,612,544,000 games, assuming all participants play until the hand concludes.

The following table represents my power assessment of each combination of two initial cards in a three-player setting. The ratings are on a scale from 0 to 40. Use the upper table for a pair, the middle one for suited cards, and the lower one for unsuited cards. If you have high cards instead of a pair, match your high card with those on the left and your low card with those on the top.

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