Texas Holdem Ladder
The second most popular form of Texas Hold'em is Limit Holdem.Whereas No-Limit is a game of brute force where players play big stacks and run up huge bluffs, Fixed Limit Hold'em is a more subtle, gentleman's game where players look to exploit small edges: a game of finesse and well-timed aggression. In high games, like Texas hold 'em and seven-card stud, the highest-ranking hands win. In low games, like razz, the lowest-ranking hands win. In high-low split games, both the highest-ranking and lowest-ranking hands win, though different rules are used to rank the high and low hands.
Introduction
The following table ranks the top hands in an 8-player game. This table assumes that all players stay in until the end.
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 8 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 $2.09.
- 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 8-Player Game
| Cards | Probability of Win | Average Win | Expected Value | Probability | Additive Probability |
| Pair of A's | 39.05% | 7.94 | 2.099 | 0.45% | 0.45% |
| Pair of K's | 33.26% | 7.92 | 1.6328 | 0.45% | 0.9% |
| Pair of Q's | 28.71% | 7.88 | 1.2628 | 0.45% | 1.36% |
| A/K suited | 26% | 7.67 | 0.9953 | 0.3% | 1.66% |
| Pair of J's | 25.13% | 7.84 | 0.9705 | 0.45% | 2.11% |
| A/Q suited | 24.51% | 7.6 | 0.8628 | 0.3% | 2.41% |
| K/Q suited | 23.72% | 7.61 | 0.8043 | 0.3% | 2.71% |
| A/J suited | 23.41% | 7.53 | 0.7616 | 0.3% | 3.02% |
| Pair of T's | 22.32% | 7.79 | 0.7395 | 0.45% | 3.47% |
| A/K unsuited | 22.68% | 7.61 | 0.7264 | 0.9% | 4.37% |
| K/J suited | 22.66% | 7.53 | 0.7073 | 0.3% | 4.68% |
| A/T suited | 22.55% | 7.45 | 0.6803 | 0.3% | 4.98% |
| Q/J suited | 22.1% | 7.52 | 0.6622 | 0.3% | 5.28% |
| K/T suited | 21.87% | 7.47 | 0.633 | 0.3% | 5.58% |
| Q/T suited | 21.38% | 7.45 | 0.5936 | 0.3% | 5.88% |
| J/T suited | 21.26% | 7.44 | 0.5813 | 0.3% | 6.18% |
| A/Q unsuited | 20.98% | 7.51 | 0.5765 | 0.9% | 7.09% |
| Pair of 9's | 19.89% | 7.81 | 0.5527 | 0.45% | 7.54% |
| K/Q unsuited | 20.31% | 7.52 | 0.5281 | 0.9% | 8.45% |
| A/9 suited | 20.28% | 7.39 | 0.4981 | 0.3% | 8.75% |
| A/J unsuited | 19.7% | 7.41 | 0.4607 | 0.9% | 9.65% |
| K/9 suited | 19.5% | 7.42 | 0.4466 | 0.3% | 9.95% |
| A/8 suited | 19.66% | 7.32 | 0.4386 | 0.3% | 10.26% |
| K/J unsuited | 19.1% | 7.43 | 0.4183 | 0.9% | 11.16% |
| Pair of 8's | 18.19% | 7.79 | 0.4164 | 0.45% | 11.61% |
| T/9 suited | 19.18% | 7.38 | 0.4162 | 0.3% | 11.92% |
| Q/9 suited | 19.03% | 7.41 | 0.4107 | 0.3% | 12.22% |
| J/9 suited | 18.96% | 7.4 | 0.4032 | 0.3% | 12.52% |
| A/5 suited | 19.29% | 7.21 | 0.3914 | 0.3% | 12.82% |
| A/7 suited | 19.12% | 7.26 | 0.3883 | 0.3% | 13.12% |
| Q/J unsuited | 18.67% | 7.41 | 0.3832 | 0.9% | 14.03% |
| A/T unsuited | 18.74% | 7.31 | 0.3705 | 0.9% | 14.93% |
| A/4 suited | 18.86% | 7.23 | 0.3638 | 0.3% | 15.23% |
| A/6 suited | 18.62% | 7.22 | 0.3448 | 0.3% | 15.54% |
| A/3 suited | 18.41% | 7.26 | 0.336 | 0.3% | 15.84% |
| K/T unsuited | 18.18% | 7.33 | 0.3328 | 0.9% | 16.74% |
| K/8 suited | 18.05% | 7.33 | 0.3234 | 0.3% | 17.04% |
| Pair of 7's | 16.85% | 7.77 | 0.309 | 0.45% | 17.5% |
| Q/T unsuited | 17.83% | 7.32 | 0.3044 | 0.9% | 18.4% |
| J/T unsuited | 17.86% | 7.3 | 0.3041 | 0.9% | 19.31% |
| A/2 suited | 17.86% | 7.28 | 0.2997 | 0.3% | 19.61% |
| T/8 suited | 17.68% | 7.32 | 0.2949 | 0.3% | 19.91% |
| Q/8 suited | 17.51% | 7.34 | 0.285 | 0.3% | 20.21% |
| J/8 suited | 17.44% | 7.33 | 0.2792 | 0.3% | 20.51% |
| K/7 suited | 17.57% | 7.27 | 0.2777 | 0.3% | 20.81% |
| 9/8 suited | 17.31% | 7.38 | 0.2768 | 0.3% | 21.12% |
| K/6 suited | 17.17% | 7.23 | 0.2413 | 0.3% | 21.42% |
| Pair of 6's | 15.84% | 7.75 | 0.2282 | 0.45% | 21.87% |
| K/5 suited | 16.83% | 7.2 | 0.2117 | 0.3% | 22.17% |
| 8/7 suited | 16.38% | 7.35 | 0.2033 | 0.3% | 22.47% |
| K/4 suited | 16.44% | 7.22 | 0.1869 | 0.3% | 22.78% |
| 9/7 suited | 16.2% | 7.33 | 0.1868 | 0.3% | 23.08% |
| T/7 suited | 16.3% | 7.26 | 0.1827 | 0.3% | 23.38% |
| Q/7 suited | 16.22% | 7.25 | 0.1756 | 0.3% | 23.68% |
| A/9 unsuited | 16.27% | 7.2 | 0.1711 | 0.9% | 24.59% |
| J/7 suited | 16.07% | 7.26 | 0.1662 | 0.3% | 24.89% |
| K/3 suited | 16.06% | 7.26 | 0.1653 | 0.3% | 25.19% |
| Pair of 5's | 14.93% | 7.73 | 0.1542 | 0.45% | 25.64% |
| 7/6 suited | 15.66% | 7.33 | 0.1481 | 0.3% | 25.94% |
| K/2 suited | 15.7% | 7.29 | 0.1446 | 0.3% | 26.24% |
| Q/6 suited | 15.85% | 7.2 | 0.1417 | 0.3% | 26.55% |
| T/9 unsuited | 15.71% | 7.21 | 0.1332 | 0.9% | 27.45% |
| K/9 unsuited | 15.62% | 7.24 | 0.1308 | 0.9% | 28.36% |
| 8/6 suited | 15.37% | 7.3 | 0.1223 | 0.3% | 28.66% |
| Q/5 suited | 15.56% | 7.17 | 0.1158 | 0.3% | 28.96% |
| Pair of 4's | 14.31% | 7.76 | 0.1103 | 0.45% | 29.41% |
| J/9 unsuited | 15.34% | 7.22 | 0.1081 | 0.9% | 30.32% |
| 6/5 suited | 15.12% | 7.32 | 0.1067 | 0.3% | 30.62% |
| Q/9 unsuited | 15.27% | 7.23 | 0.1044 | 0.9% | 31.52% |
| A/8 unsuited | 15.55% | 7.1 | 0.1037 | 0.9% | 32.43% |
| Q/4 suited | 15.16% | 7.2 | 0.0916 | 0.3% | 32.73% |
| 9/6 suited | 14.99% | 7.26 | 0.0891 | 0.3% | 33.03% |
| 5/4 suited | 14.74% | 7.32 | 0.0789 | 0.3% | 33.33% |
| T/6 suited | 15.03% | 7.18 | 0.0785 | 0.3% | 33.63% |
| Pair of 3's | 13.83% | 7.8 | 0.0782 | 0.45% | 34.09% |
| 7/5 suited | 14.74% | 7.29 | 0.0741 | 0.3% | 34.39% |
| Q/3 suited | 14.81% | 7.24 | 0.0721 | 0.3% | 34.69% |
| J/6 suited | 14.92% | 7.17 | 0.0691 | 0.3% | 34.99% |
| Pair of 2's | 13.49% | 7.83 | 0.057 | 0.45% | 35.44% |
| Q/2 suited | 14.46% | 7.28 | 0.0524 | 0.3% | 35.75% |
| A/5 unsuited | 15.1% | 6.95 | 0.0489 | 0.9% | 36.65% |
| A/7 unsuited | 14.94% | 7.01 | 0.0473 | 0.9% | 37.56% |
| J/5 suited | 14.66% | 7.13 | 0.0454 | 0.3% | 37.86% |
| 6/4 suited | 14.07% | 7.33 | 0.0306 | 0.3% | 38.16% |
| 8/5 suited | 14.22% | 7.24 | 0.0303 | 0.3% | 38.46% |
| J/4 suited | 14.28% | 7.16 | 0.0222 | 0.3% | 38.76% |
| A/4 unsuited | 14.63% | 6.96 | 0.0184 | 0.9% | 39.67% |
| 5/3 suited | 13.71% | 7.33 | 0.0049 | 0.3% | 39.97% |
| J/3 suited | 13.92% | 7.2 | 0.0023 | 0.3% | 40.27% |
| A/6 unsuited | 14.39% | 6.95 | 0 | 0.9% | 41.18% |
| T/8 unsuited | 14.07% | 7.11 | -0.0002 | 0.9% | 42.08% |
| K/8 unsuited | 14.01% | 7.09 | -0.0059 | 0.9% | 42.99% |
| 9/5 suited | 13.81% | 7.19 | -0.0066 | 0.3% | 43.29% |
| T/5 suited | 13.98% | 7.09 | -0.0092 | 0.3% | 43.59% |
| A/3 unsuited | 14.15% | 6.99 | -0.0111 | 0.9% | 44.49% |
| 9/8 unsuited | 13.73% | 7.18 | -0.0137 | 0.9% | 45.4% |
| J/2 suited | 13.59% | 7.24 | -0.0154 | 0.3% | 45.7% |
| 7/4 suited | 13.48% | 7.28 | -0.0187 | 0.3% | 46% |
| J/8 unsuited | 13.68% | 7.11 | -0.0278 | 0.9% | 46.91% |
| T/4 suited | 13.64% | 7.11 | -0.0304 | 0.3% | 47.21% |
| Q/8 unsuited | 13.6% | 7.11 | -0.0331 | 0.9% | 48.11% |
| 4/3 suited | 13.09% | 7.37 | -0.0351 | 0.3% | 48.42% |
| T/3 suited | 13.3% | 7.15 | -0.049 | 0.3% | 48.72% |
| A/2 unsuited | 13.54% | 7.01 | -0.0507 | 0.9% | 49.62% |
| K/7 unsuited | 13.48% | 7 | -0.0557 | 0.9% | 50.53% |
| 6/3 suited | 12.85% | 7.33 | -0.0587 | 0.3% | 50.83% |
| 8/4 suited | 12.98% | 7.22 | -0.0626 | 0.3% | 51.13% |
| T/2 suited | 12.95% | 7.19 | -0.0682 | 0.3% | 51.43% |
| 5/2 suited | 12.5% | 7.33 | -0.0839 | 0.3% | 51.73% |
| 8/7 unsuited | 12.79% | 7.13 | -0.0877 | 0.9% | 52.64% |
| 9/4 suited | 12.71% | 7.16 | -0.0908 | 0.3% | 52.94% |
| K/6 unsuited | 13.02% | 6.94 | -0.0972 | 0.9% | 53.85% |
| 4/2 suited | 12.08% | 7.38 | -0.1079 | 0.3% | 54.15% |
| 7/3 suited | 12.25% | 7.27 | -0.1101 | 0.3% | 54.45% |
| 9/3 suited | 12.37% | 7.19 | -0.1108 | 0.3% | 54.75% |
| 9/7 unsuited | 12.54% | 7.09 | -0.1114 | 0.9% | 55.66% |
| T/7 unsuited | 12.55% | 6.98 | -0.1238 | 0.9% | 56.56% |
| 9/2 suited | 12.03% | 7.24 | -0.1287 | 0.3% | 56.86% |
| K/5 unsuited | 12.65% | 6.88 | -0.1298 | 0.9% | 57.77% |
| 7/6 unsuited | 12.08% | 7.09 | -0.1433 | 0.9% | 58.67% |
| 8/3 suited | 11.88% | 7.19 | -0.1452 | 0.3% | 58.97% |
| 3/2 suited | 11.49% | 7.43 | -0.1454 | 0.3% | 59.28% |
| 6/2 suited | 11.62% | 7.32 | -0.1492 | 0.3% | 59.58% |
| Q/7 unsuited | 12.22% | 6.95 | -0.1511 | 0.9% | 60.48% |
| J/7 unsuited | 12.18% | 6.97 | -0.1514 | 0.9% | 61.39% |
| K/4 unsuited | 12.21% | 6.9 | -0.1579 | 0.9% | 62.29% |
| 8/2 suited | 11.57% | 7.23 | -0.163 | 0.3% | 62.59% |
| 8/6 unsuited | 11.7% | 7.04 | -0.1767 | 0.9% | 63.5% |
| K/3 unsuited | 11.79% | 6.94 | -0.1818 | 0.9% | 64.4% |
| 6/5 unsuited | 11.51% | 7.07 | -0.1865 | 0.9% | 65.31% |
| Q/6 unsuited | 11.81% | 6.87 | -0.189 | 0.9% | 66.21% |
| 7/2 suited | 11.19% | 7.24 | -0.1897 | 0.3% | 66.52% |
| K/2 unsuited | 11.41% | 6.98 | -0.2035 | 0.9% | 67.42% |
| 5/4 unsuited | 11.12% | 7.06 | -0.2149 | 0.9% | 68.33% |
| 9/6 unsuited | 11.22% | 6.97 | -0.2182 | 0.9% | 69.23% |
| Q/5 unsuited | 11.46% | 6.82 | -0.2191 | 0.9% | 70.14% |
| 7/5 unsuited | 11.07% | 7 | -0.2249 | 0.9% | 71.04% |
| T/6 unsuited | 11.18% | 6.83 | -0.2361 | 0.9% | 71.95% |
| Q/4 unsuited | 11.03% | 6.84 | -0.2454 | 0.9% | 72.85% |
| J/6 unsuited | 10.94% | 6.8 | -0.2562 | 0.9% | 73.76% |
| 6/4 unsuited | 10.39% | 7.05 | -0.2677 | 0.9% | 74.66% |
| Q/3 unsuited | 10.63% | 6.88 | -0.2679 | 0.9% | 75.57% |
| 8/5 unsuited | 10.47% | 6.92 | -0.2757 | 0.9% | 76.47% |
| J/5 unsuited | 10.64% | 6.73 | -0.2837 | 0.9% | 77.38% |
| Q/2 unsuited | 10.26% | 6.93 | -0.289 | 0.9% | 78.28% |
| 5/3 unsuited | 10.04% | 7.04 | -0.2936 | 0.9% | 79.19% |
| J/4 unsuited | 10.22% | 6.76 | -0.3091 | 0.9% | 80.09% |
| 9/5 unsuited | 9.97% | 6.82 | -0.3206 | 0.9% | 81% |
| 7/4 unsuited | 9.73% | 6.95 | -0.3238 | 0.9% | 81.9% |
| T/5 unsuited | 10.06% | 6.65 | -0.3308 | 0.9% | 82.81% |
| J/3 unsuited | 9.83% | 6.81 | -0.3312 | 0.9% | 83.71% |
| 4/3 unsuited | 9.38% | 7.08 | -0.336 | 0.9% | 84.62% |
| J/2 unsuited | 9.46% | 6.86 | -0.3512 | 0.9% | 85.52% |
| T/4 unsuited | 9.66% | 6.67 | -0.3554 | 0.9% | 86.43% |
| 6/3 unsuited | 9.08% | 7 | -0.3642 | 0.9% | 87.33% |
| 8/4 unsuited | 9.12% | 6.84 | -0.3766 | 0.9% | 88.24% |
| T/3 unsuited | 9.28% | 6.72 | -0.3767 | 0.9% | 89.14% |
| 5/2 unsuited | 8.73% | 7 | -0.3892 | 0.9% | 90.05% |
| T/2 unsuited | 8.93% | 6.76 | -0.3962 | 0.9% | 90.95% |
| 9/4 unsuited | 8.76% | 6.71 | -0.4126 | 0.9% | 91.86% |
| 4/2 unsuited | 8.3% | 7.06 | -0.4138 | 0.9% | 92.76% |
| 7/3 unsuited | 8.41% | 6.88 | -0.4219 | 0.9% | 93.67% |
| 9/3 unsuited | 8.4% | 6.74 | -0.4338 | 0.9% | 94.57% |
| 9/2 unsuited | 8.04% | 6.8 | -0.4531 | 0.9% | 95.48% |
| 3/2 unsuited | 7.67% | 7.12 | -0.4543 | 0.9% | 96.38% |
| 6/2 unsuited | 7.79% | 6.94 | -0.46 | 0.9% | 97.29% |
| 8/3 unsuited | 7.96% | 6.73 | -0.4646 | 0.9% | 98.19% |
| 8/2 unsuited | 7.61% | 6.77 | -0.4844 | 0.9% | 99.1% |
| 7/2 unsuited | 7.28% | 6.77 | -0.5073 | 0.9% | 100% |
| Total | 7.2 | 0 | 100% |
Methodology
This table is the result of a random simulation of 25,729,704,000 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 8-player game. The numbers are on a 0 to 40 scale. Basically, you should only play hands that are dark green, blue, or purple. Of course you should be more be more liberal in late position and picky in early position.
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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