Introduction
In Texas Hold 'Em a hand is said to be dominated if another player has a similar, and better, hand. To be more specific, a dominated hand is said to rely on three or fewer outs (cards) to beat the hand dominating it, not counting difficult multiple-card draws. There are four types of domination, as follows.
Texas Hold'em Cheat SheetOdds Based on Outs after the Flop. If after the flop, you have: Two outs: Your odds are 11 to 1 (about 8.5 percent) A common scenario would be when you have a pair and you are hoping your pair becomes a three-of-a-kind (a set). Texas Hold'em Poker probabilities. When calculating probabilities for a card game such as Texas Hold'em, there are two basic approaches. The first approach is to determine the number of outcomes that satisfy the condition being evaluated and divide this by the total number of possible outcomes. Rough Odds for Texas Hold'em. Playing poker is about playing the odds. The following list gives the odds for outcomes in Texas Hold'em hands. When you realize how heavily the odds are stacked against you, you may want to rethink going all-in before the flop with two suited cards. Use the odds to your advantage. Using a Poker odds Calculator. Want to know how far ahead or behind you are in a Texas Hold'em hand against one, two or more opponents? Our poker calculator is the perfect medium for finding out the odds in any given situation.
- A pair is dominated by a higher pair. For example J-J is dominated by Q-Q. Only two cards help the J-J, the other two jacks.
- A non-pair is dominated by a pair of either card. For example, Q-5 is dominated by Q-Q or 5-5. In the case of 5-5, three cards only will help the Q-5, the other three queens.
- A non-pair is dominated by a pair greater than the lower card. For example, Q-5 is dominated by 8-8. Only three cards will help the Q-5, the other three queens.
- A non-pair is dominated by another non-pair if there if there is a shared card, and the rank of the opponent's non-shared card is greater the dominated non-shared card. For example Q-5 is dominated by K-5 or Q-7. In the former case (K-5 over Q-5) only three cards can help Q-5, the other three queens.
That said, the following tables present the probability of every two-card hand being dominated, according to the total number of players.
Texas Hold Em Odds Tables
Probability of Domination — PairsExpand
| Cards | 2 Players | 3 Players | 4 Players | 5 Players | 6 Players | 7 Players | 8 Players | 9 Players | 10 Players |
|---|---|---|---|---|---|---|---|---|---|
| 2,2 | 0.0588 | 0.1142 | 0.1659 | 0.2150 | 0.2609 | 0.3044 | 0.3449 | 0.3835 | 0.4195 |
| 3,3 | 0.0540 | 0.1049 | 0.1532 | 0.1983 | 0.2419 | 0.2826 | 0.3212 | 0.3576 | 0.3922 |
| 4,4 | 0.0489 | 0.0956 | 0.1400 | 0.1820 | 0.2220 | 0.2602 | 0.2966 | 0.3313 | 0.3640 |
| 5,5 | 0.0441 | 0.0862 | 0.1265 | 0.1653 | 0.2021 | 0.2376 | 0.2710 | 0.3031 | 0.3345 |
| 6,6 | 0.0392 | 0.0767 | 0.1133 | 0.1481 | 0.1816 | 0.2136 | 0.2448 | 0.2745 | 0.3036 |
| 7,7 | 0.0344 | 0.0675 | 0.0996 | 0.1306 | 0.1605 | 0.1895 | 0.2177 | 0.2447 | 0.2709 |
| 8,8 | 0.0295 | 0.0581 | 0.0858 | 0.1129 | 0.1391 | 0.1648 | 0.1894 | 0.2138 | 0.2369 |
| 9,9 | 0.0246 | 0.0485 | 0.0720 | 0.0947 | 0.1173 | 0.1391 | 0.1604 | 0.1813 | 0.2017 |
| T,T | 0.0196 | 0.0389 | 0.0578 | 0.0765 | 0.0947 | 0.1126 | 0.1300 | 0.1478 | 0.1649 |
| J,J | 0.0147 | 0.0293 | 0.0435 | 0.0577 | 0.0719 | 0.0856 | 0.0992 | 0.1132 | 0.1262 |
| Q,Q | 0.0098 | 0.0195 | 0.0292 | 0.0389 | 0.0483 | 0.0579 | 0.0674 | 0.0766 | 0.0861 |
| K,K | 0.0049 | 0.0098 | 0.0147 | 0.0196 | 0.0245 | 0.0294 | 0.0341 | 0.0391 | 0.0439 |
| A,A | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Probability of Domination — Non-PairsExpand
| Cards | 2 Players | 3 Players | 4 Players | 5 Players | 6 Players | 7 Players | 8 Players | 9 Players | 10 Players |
|---|---|---|---|---|---|---|---|---|---|
| 3,2 | 0.2742 | 0.4785 | 0.6289 | 0.7389 | 0.8187 | 0.8753 | 0.9156 | 0.9438 | 0.9629 |
| 4,2 | 0.2645 | 0.4634 | 0.6124 | 0.7227 | 0.8036 | 0.8626 | 0.9049 | 0.9350 | 0.9562 |
| 4,3 | 0.2496 | 0.4417 | 0.5877 | 0.6986 | 0.7815 | 0.8433 | 0.8888 | 0.9220 | 0.9459 |
| 5,2 | 0.2546 | 0.4487 | 0.5956 | 0.7060 | 0.7881 | 0.8489 | 0.8934 | 0.9255 | 0.9486 |
| 5,3 | 0.2399 | 0.4263 | 0.5701 | 0.6805 | 0.7645 | 0.8279 | 0.8754 | 0.9108 | 0.9367 |
| 5,4 | 0.2253 | 0.4036 | 0.5439 | 0.6539 | 0.7393 | 0.8050 | 0.8556 | 0.8937 | 0.9227 |
| 6,2 | 0.2450 | 0.4338 | 0.5786 | 0.6885 | 0.7718 | 0.8344 | 0.8809 | 0.9152 | 0.9403 |
| 6,3 | 0.2302 | 0.4110 | 0.5525 | 0.6620 | 0.7470 | 0.8118 | 0.8614 | 0.8986 | 0.9266 |
| 6,4 | 0.2154 | 0.3881 | 0.5254 | 0.6344 | 0.7199 | 0.7869 | 0.8394 | 0.8796 | 0.9105 |
| 6,5 | 0.2008 | 0.3647 | 0.4975 | 0.6047 | 0.6911 | 0.7599 | 0.8146 | 0.8581 | 0.8919 |
| 7,2 | 0.2350 | 0.4186 | 0.5611 | 0.6709 | 0.7550 | 0.8191 | 0.8676 | 0.9042 | 0.9311 |
| 7,3 | 0.2204 | 0.3955 | 0.5340 | 0.6430 | 0.7285 | 0.7948 | 0.8461 | 0.8854 | 0.9155 |
| 7,4 | 0.2057 | 0.3724 | 0.5065 | 0.6138 | 0.7000 | 0.7681 | 0.8220 | 0.8642 | 0.8971 |
| 7,5 | 0.1910 | 0.3484 | 0.4776 | 0.5833 | 0.6693 | 0.7388 | 0.7951 | 0.8402 | 0.8761 |
| 7,6 | 0.1763 | 0.3244 | 0.4478 | 0.5510 | 0.6365 | 0.7071 | 0.7651 | 0.8128 | 0.8514 |
| 8,2 | 0.2255 | 0.4034 | 0.5434 | 0.6526 | 0.7375 | 0.8032 | 0.8536 | 0.8923 | 0.9213 |
| 8,3 | 0.2105 | 0.3800 | 0.5157 | 0.6237 | 0.7095 | 0.7771 | 0.8300 | 0.8714 | 0.9034 |
| 8,4 | 0.1959 | 0.3563 | 0.4870 | 0.5932 | 0.6791 | 0.7481 | 0.8037 | 0.8478 | 0.8828 |
| 8,5 | 0.1812 | 0.3323 | 0.4574 | 0.5614 | 0.6467 | 0.7168 | 0.7743 | 0.8208 | 0.8586 |
| 8,6 | 0.1666 | 0.3078 | 0.4272 | 0.5277 | 0.6122 | 0.6829 | 0.7416 | 0.7904 | 0.8311 |
| 8,7 | 0.1518 | 0.2829 | 0.3952 | 0.4922 | 0.5750 | 0.6453 | 0.7056 | 0.7563 | 0.7992 |
| 9,2 | 0.2156 | 0.3878 | 0.5250 | 0.6338 | 0.7194 | 0.7862 | 0.8388 | 0.8793 | 0.9104 |
| 9,3 | 0.2010 | 0.3643 | 0.4968 | 0.6039 | 0.6895 | 0.7583 | 0.8130 | 0.8564 | 0.8904 |
| 9,4 | 0.1862 | 0.3402 | 0.4674 | 0.5720 | 0.6577 | 0.7274 | 0.7843 | 0.8300 | 0.8668 |
| 9,5 | 0.1714 | 0.3157 | 0.4371 | 0.5388 | 0.6234 | 0.6937 | 0.7523 | 0.8003 | 0.8398 |
| 9,6 | 0.1569 | 0.2911 | 0.4061 | 0.5036 | 0.5868 | 0.6573 | 0.7167 | 0.7667 | 0.8088 |
| 9,7 | 0.1419 | 0.2658 | 0.3734 | 0.4669 | 0.5476 | 0.6174 | 0.6776 | 0.7289 | 0.7730 |
| 9,8 | 0.1274 | 0.2403 | 0.3400 | 0.4282 | 0.5061 | 0.5742 | 0.6342 | 0.6867 | 0.7320 |
| T,2 | 0.2057 | 0.3722 | 0.5066 | 0.6143 | 0.7005 | 0.7688 | 0.8229 | 0.8654 | 0.8987 |
| T,3 | 0.1910 | 0.3485 | 0.4772 | 0.5831 | 0.6691 | 0.7387 | 0.7950 | 0.8402 | 0.8762 |
| T,4 | 0.1764 | 0.3240 | 0.4474 | 0.5501 | 0.6352 | 0.7055 | 0.7638 | 0.8111 | 0.8499 |
| T,5 | 0.1617 | 0.2995 | 0.4163 | 0.5153 | 0.5991 | 0.6696 | 0.7286 | 0.7784 | 0.8196 |
| T,6 | 0.1470 | 0.2742 | 0.3843 | 0.4790 | 0.5606 | 0.6305 | 0.6904 | 0.7413 | 0.7847 |
| T,7 | 0.1323 | 0.2487 | 0.3512 | 0.4411 | 0.5196 | 0.5881 | 0.6478 | 0.6996 | 0.7448 |
| T,8 | 0.1176 | 0.2227 | 0.3169 | 0.4008 | 0.4754 | 0.5418 | 0.6009 | 0.6532 | 0.6993 |
| T,9 | 0.1030 | 0.1965 | 0.2817 | 0.3586 | 0.4286 | 0.4923 | 0.5492 | 0.6010 | 0.6473 |
| J,2 | 0.1960 | 0.3566 | 0.4877 | 0.5944 | 0.6808 | 0.7505 | 0.8063 | 0.8508 | 0.8862 |
| J,3 | 0.1813 | 0.3324 | 0.4578 | 0.5617 | 0.6476 | 0.7180 | 0.7757 | 0.8227 | 0.8610 |
| J,4 | 0.1665 | 0.3078 | 0.4271 | 0.5275 | 0.6120 | 0.6828 | 0.7419 | 0.7911 | 0.8317 |
| J,5 | 0.1519 | 0.2827 | 0.3954 | 0.4916 | 0.5741 | 0.6441 | 0.7042 | 0.7549 | 0.7976 |
| J,6 | 0.1371 | 0.2573 | 0.3621 | 0.4537 | 0.5336 | 0.6026 | 0.6625 | 0.7143 | 0.7590 |
| J,7 | 0.1223 | 0.2314 | 0.3284 | 0.4142 | 0.4901 | 0.5572 | 0.6164 | 0.6688 | 0.7145 |
| J,8 | 0.1077 | 0.2050 | 0.2931 | 0.3725 | 0.4442 | 0.5083 | 0.5658 | 0.6174 | 0.6638 |
| J,9 | 0.0931 | 0.1785 | 0.2571 | 0.3289 | 0.3948 | 0.4553 | 0.5100 | 0.5601 | 0.6061 |
| J,T | 0.0783 | 0.1515 | 0.2199 | 0.2837 | 0.3427 | 0.3979 | 0.4493 | 0.4967 | 0.5409 |
| Q,2 | 0.1862 | 0.3406 | 0.4685 | 0.5739 | 0.6604 | 0.7312 | 0.7886 | 0.8352 | 0.8727 |
| Q,3 | 0.1713 | 0.3161 | 0.4379 | 0.5402 | 0.6255 | 0.6968 | 0.7557 | 0.8044 | 0.8445 |
| Q,4 | 0.1568 | 0.2910 | 0.4062 | 0.5045 | 0.5880 | 0.6590 | 0.7189 | 0.7696 | 0.8119 |
| Q,5 | 0.1422 | 0.2658 | 0.3736 | 0.4671 | 0.5482 | 0.6180 | 0.6783 | 0.7299 | 0.7744 |
| Q,6 | 0.1273 | 0.2400 | 0.3400 | 0.4280 | 0.5055 | 0.5734 | 0.6333 | 0.6857 | 0.7312 |
| Q,7 | 0.1126 | 0.2139 | 0.3048 | 0.3868 | 0.4600 | 0.5254 | 0.5835 | 0.6357 | 0.6818 |
| Q,8 | 0.0979 | 0.1875 | 0.2691 | 0.3435 | 0.4113 | 0.4730 | 0.5289 | 0.5800 | 0.6257 |
| Q,9 | 0.0833 | 0.1606 | 0.2321 | 0.2983 | 0.3600 | 0.4166 | 0.4689 | 0.5173 | 0.5619 |
| Q,T | 0.0687 | 0.1332 | 0.1940 | 0.2516 | 0.3052 | 0.3557 | 0.4032 | 0.4480 | 0.4894 |
| Q,J | 0.0540 | 0.1055 | 0.1547 | 0.2020 | 0.2474 | 0.2902 | 0.3313 | 0.3707 | 0.4082 |
| K,2 | 0.1763 | 0.3246 | 0.4491 | 0.5532 | 0.6395 | 0.7111 | 0.7702 | 0.8185 | 0.8579 |
| K,3 | 0.1616 | 0.2998 | 0.4178 | 0.5178 | 0.6027 | 0.6740 | 0.7343 | 0.7848 | 0.8269 |
| K,4 | 0.1469 | 0.2745 | 0.3851 | 0.4808 | 0.5633 | 0.6343 | 0.6948 | 0.7466 | 0.7908 |
| K,5 | 0.1322 | 0.2491 | 0.3517 | 0.4422 | 0.5211 | 0.5904 | 0.6509 | 0.7037 | 0.7494 |
| K,6 | 0.1175 | 0.2230 | 0.3171 | 0.4013 | 0.4763 | 0.5431 | 0.6025 | 0.6550 | 0.7016 |
| K,7 | 0.1029 | 0.1964 | 0.2814 | 0.3586 | 0.4285 | 0.4918 | 0.5490 | 0.6007 | 0.6473 |
| K,8 | 0.0881 | 0.1697 | 0.2447 | 0.3139 | 0.3777 | 0.4367 | 0.4905 | 0.5397 | 0.5853 |
| K,9 | 0.0734 | 0.1423 | 0.2069 | 0.2675 | 0.3238 | 0.3765 | 0.4259 | 0.4720 | 0.5148 |
| K,T | 0.0588 | 0.1146 | 0.1678 | 0.2183 | 0.2665 | 0.3120 | 0.3555 | 0.3961 | 0.4350 |
| K,J | 0.0441 | 0.0866 | 0.1277 | 0.1671 | 0.2058 | 0.2426 | 0.2780 | 0.3125 | 0.3452 |
| K,Q | 0.0294 | 0.0582 | 0.0865 | 0.1141 | 0.1414 | 0.1679 | 0.1940 | 0.2195 | 0.2444 |
| A,2 | 0.1665 | 0.3086 | 0.4294 | 0.5316 | 0.6177 | 0.6901 | 0.7505 | 0.8009 | 0.8425 |
| A,3 | 0.1517 | 0.2835 | 0.3970 | 0.4949 | 0.5791 | 0.6509 | 0.7120 | 0.7641 | 0.8080 |
| A,4 | 0.1372 | 0.2578 | 0.3636 | 0.4565 | 0.5376 | 0.6082 | 0.6695 | 0.7227 | 0.7684 |
| A,5 | 0.1224 | 0.2318 | 0.3294 | 0.4164 | 0.4934 | 0.5618 | 0.6223 | 0.6754 | 0.7225 |
| A,6 | 0.1077 | 0.2054 | 0.2940 | 0.3741 | 0.4462 | 0.5115 | 0.5702 | 0.6228 | 0.6701 |
| A,7 | 0.0931 | 0.1787 | 0.2575 | 0.3300 | 0.3963 | 0.4572 | 0.5129 | 0.5638 | 0.6101 |
| A,8 | 0.0783 | 0.1516 | 0.2200 | 0.2837 | 0.3428 | 0.3983 | 0.4498 | 0.4976 | 0.5418 |
| A,9 | 0.0637 | 0.1241 | 0.1810 | 0.2352 | 0.2866 | 0.3347 | 0.3804 | 0.4237 | 0.4647 |
| A,T | 0.0490 | 0.0959 | 0.1411 | 0.1847 | 0.2264 | 0.2664 | 0.3049 | 0.3417 | 0.3770 |
| A,J | 0.0343 | 0.0677 | 0.1003 | 0.1320 | 0.1629 | 0.1931 | 0.2223 | 0.2507 | 0.2784 |
| A,Q | 0.0195 | 0.0389 | 0.0582 | 0.0769 | 0.0956 | 0.1140 | 0.1320 | 0.1500 | 0.1676 |
| A,K | 0.0049 | 0.0098 | 0.0147 | 0.0195 | 0.0243 | 0.0292 | 0.0340 | 0.0388 | 0.0436 |
Methodology: These tables were created by a random simulation. Each cell in the table above for pairs was based on 7.8 million hands, and 21.7 million for the non-pairs.
2-Player Formula
The probability of domination in a two player game is easy to calculate. For pairs it is 6×(number of higher ranks)/1225. For example, the probability a pair of eights is dominated is 6×6/1225 = 0.0294, because there are six ranks higher than 8 (9,T,J,Q,K,A).
For non-pairs the formula is (6+18×(L-1)+12×H)/1225, where
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L=Number of ranks higher than lower card
H=Number of ranks higher than higher card Best casino odds in lake charles.
For example, the probability that J-7 is dominated is (6+18×(7-1)+12×3)/1225 = 150/1225 = 0.1224.
That said, the following tables present the probability of every two-card hand being dominated, according to the total number of players.
Texas Hold Em Odds Tables
Probability of Domination — PairsExpand
| Cards | 2 Players | 3 Players | 4 Players | 5 Players | 6 Players | 7 Players | 8 Players | 9 Players | 10 Players |
|---|---|---|---|---|---|---|---|---|---|
| 2,2 | 0.0588 | 0.1142 | 0.1659 | 0.2150 | 0.2609 | 0.3044 | 0.3449 | 0.3835 | 0.4195 |
| 3,3 | 0.0540 | 0.1049 | 0.1532 | 0.1983 | 0.2419 | 0.2826 | 0.3212 | 0.3576 | 0.3922 |
| 4,4 | 0.0489 | 0.0956 | 0.1400 | 0.1820 | 0.2220 | 0.2602 | 0.2966 | 0.3313 | 0.3640 |
| 5,5 | 0.0441 | 0.0862 | 0.1265 | 0.1653 | 0.2021 | 0.2376 | 0.2710 | 0.3031 | 0.3345 |
| 6,6 | 0.0392 | 0.0767 | 0.1133 | 0.1481 | 0.1816 | 0.2136 | 0.2448 | 0.2745 | 0.3036 |
| 7,7 | 0.0344 | 0.0675 | 0.0996 | 0.1306 | 0.1605 | 0.1895 | 0.2177 | 0.2447 | 0.2709 |
| 8,8 | 0.0295 | 0.0581 | 0.0858 | 0.1129 | 0.1391 | 0.1648 | 0.1894 | 0.2138 | 0.2369 |
| 9,9 | 0.0246 | 0.0485 | 0.0720 | 0.0947 | 0.1173 | 0.1391 | 0.1604 | 0.1813 | 0.2017 |
| T,T | 0.0196 | 0.0389 | 0.0578 | 0.0765 | 0.0947 | 0.1126 | 0.1300 | 0.1478 | 0.1649 |
| J,J | 0.0147 | 0.0293 | 0.0435 | 0.0577 | 0.0719 | 0.0856 | 0.0992 | 0.1132 | 0.1262 |
| Q,Q | 0.0098 | 0.0195 | 0.0292 | 0.0389 | 0.0483 | 0.0579 | 0.0674 | 0.0766 | 0.0861 |
| K,K | 0.0049 | 0.0098 | 0.0147 | 0.0196 | 0.0245 | 0.0294 | 0.0341 | 0.0391 | 0.0439 |
| A,A | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Probability of Domination — Non-PairsExpand
| Cards | 2 Players | 3 Players | 4 Players | 5 Players | 6 Players | 7 Players | 8 Players | 9 Players | 10 Players |
|---|---|---|---|---|---|---|---|---|---|
| 3,2 | 0.2742 | 0.4785 | 0.6289 | 0.7389 | 0.8187 | 0.8753 | 0.9156 | 0.9438 | 0.9629 |
| 4,2 | 0.2645 | 0.4634 | 0.6124 | 0.7227 | 0.8036 | 0.8626 | 0.9049 | 0.9350 | 0.9562 |
| 4,3 | 0.2496 | 0.4417 | 0.5877 | 0.6986 | 0.7815 | 0.8433 | 0.8888 | 0.9220 | 0.9459 |
| 5,2 | 0.2546 | 0.4487 | 0.5956 | 0.7060 | 0.7881 | 0.8489 | 0.8934 | 0.9255 | 0.9486 |
| 5,3 | 0.2399 | 0.4263 | 0.5701 | 0.6805 | 0.7645 | 0.8279 | 0.8754 | 0.9108 | 0.9367 |
| 5,4 | 0.2253 | 0.4036 | 0.5439 | 0.6539 | 0.7393 | 0.8050 | 0.8556 | 0.8937 | 0.9227 |
| 6,2 | 0.2450 | 0.4338 | 0.5786 | 0.6885 | 0.7718 | 0.8344 | 0.8809 | 0.9152 | 0.9403 |
| 6,3 | 0.2302 | 0.4110 | 0.5525 | 0.6620 | 0.7470 | 0.8118 | 0.8614 | 0.8986 | 0.9266 |
| 6,4 | 0.2154 | 0.3881 | 0.5254 | 0.6344 | 0.7199 | 0.7869 | 0.8394 | 0.8796 | 0.9105 |
| 6,5 | 0.2008 | 0.3647 | 0.4975 | 0.6047 | 0.6911 | 0.7599 | 0.8146 | 0.8581 | 0.8919 |
| 7,2 | 0.2350 | 0.4186 | 0.5611 | 0.6709 | 0.7550 | 0.8191 | 0.8676 | 0.9042 | 0.9311 |
| 7,3 | 0.2204 | 0.3955 | 0.5340 | 0.6430 | 0.7285 | 0.7948 | 0.8461 | 0.8854 | 0.9155 |
| 7,4 | 0.2057 | 0.3724 | 0.5065 | 0.6138 | 0.7000 | 0.7681 | 0.8220 | 0.8642 | 0.8971 |
| 7,5 | 0.1910 | 0.3484 | 0.4776 | 0.5833 | 0.6693 | 0.7388 | 0.7951 | 0.8402 | 0.8761 |
| 7,6 | 0.1763 | 0.3244 | 0.4478 | 0.5510 | 0.6365 | 0.7071 | 0.7651 | 0.8128 | 0.8514 |
| 8,2 | 0.2255 | 0.4034 | 0.5434 | 0.6526 | 0.7375 | 0.8032 | 0.8536 | 0.8923 | 0.9213 |
| 8,3 | 0.2105 | 0.3800 | 0.5157 | 0.6237 | 0.7095 | 0.7771 | 0.8300 | 0.8714 | 0.9034 |
| 8,4 | 0.1959 | 0.3563 | 0.4870 | 0.5932 | 0.6791 | 0.7481 | 0.8037 | 0.8478 | 0.8828 |
| 8,5 | 0.1812 | 0.3323 | 0.4574 | 0.5614 | 0.6467 | 0.7168 | 0.7743 | 0.8208 | 0.8586 |
| 8,6 | 0.1666 | 0.3078 | 0.4272 | 0.5277 | 0.6122 | 0.6829 | 0.7416 | 0.7904 | 0.8311 |
| 8,7 | 0.1518 | 0.2829 | 0.3952 | 0.4922 | 0.5750 | 0.6453 | 0.7056 | 0.7563 | 0.7992 |
| 9,2 | 0.2156 | 0.3878 | 0.5250 | 0.6338 | 0.7194 | 0.7862 | 0.8388 | 0.8793 | 0.9104 |
| 9,3 | 0.2010 | 0.3643 | 0.4968 | 0.6039 | 0.6895 | 0.7583 | 0.8130 | 0.8564 | 0.8904 |
| 9,4 | 0.1862 | 0.3402 | 0.4674 | 0.5720 | 0.6577 | 0.7274 | 0.7843 | 0.8300 | 0.8668 |
| 9,5 | 0.1714 | 0.3157 | 0.4371 | 0.5388 | 0.6234 | 0.6937 | 0.7523 | 0.8003 | 0.8398 |
| 9,6 | 0.1569 | 0.2911 | 0.4061 | 0.5036 | 0.5868 | 0.6573 | 0.7167 | 0.7667 | 0.8088 |
| 9,7 | 0.1419 | 0.2658 | 0.3734 | 0.4669 | 0.5476 | 0.6174 | 0.6776 | 0.7289 | 0.7730 |
| 9,8 | 0.1274 | 0.2403 | 0.3400 | 0.4282 | 0.5061 | 0.5742 | 0.6342 | 0.6867 | 0.7320 |
| T,2 | 0.2057 | 0.3722 | 0.5066 | 0.6143 | 0.7005 | 0.7688 | 0.8229 | 0.8654 | 0.8987 |
| T,3 | 0.1910 | 0.3485 | 0.4772 | 0.5831 | 0.6691 | 0.7387 | 0.7950 | 0.8402 | 0.8762 |
| T,4 | 0.1764 | 0.3240 | 0.4474 | 0.5501 | 0.6352 | 0.7055 | 0.7638 | 0.8111 | 0.8499 |
| T,5 | 0.1617 | 0.2995 | 0.4163 | 0.5153 | 0.5991 | 0.6696 | 0.7286 | 0.7784 | 0.8196 |
| T,6 | 0.1470 | 0.2742 | 0.3843 | 0.4790 | 0.5606 | 0.6305 | 0.6904 | 0.7413 | 0.7847 |
| T,7 | 0.1323 | 0.2487 | 0.3512 | 0.4411 | 0.5196 | 0.5881 | 0.6478 | 0.6996 | 0.7448 |
| T,8 | 0.1176 | 0.2227 | 0.3169 | 0.4008 | 0.4754 | 0.5418 | 0.6009 | 0.6532 | 0.6993 |
| T,9 | 0.1030 | 0.1965 | 0.2817 | 0.3586 | 0.4286 | 0.4923 | 0.5492 | 0.6010 | 0.6473 |
| J,2 | 0.1960 | 0.3566 | 0.4877 | 0.5944 | 0.6808 | 0.7505 | 0.8063 | 0.8508 | 0.8862 |
| J,3 | 0.1813 | 0.3324 | 0.4578 | 0.5617 | 0.6476 | 0.7180 | 0.7757 | 0.8227 | 0.8610 |
| J,4 | 0.1665 | 0.3078 | 0.4271 | 0.5275 | 0.6120 | 0.6828 | 0.7419 | 0.7911 | 0.8317 |
| J,5 | 0.1519 | 0.2827 | 0.3954 | 0.4916 | 0.5741 | 0.6441 | 0.7042 | 0.7549 | 0.7976 |
| J,6 | 0.1371 | 0.2573 | 0.3621 | 0.4537 | 0.5336 | 0.6026 | 0.6625 | 0.7143 | 0.7590 |
| J,7 | 0.1223 | 0.2314 | 0.3284 | 0.4142 | 0.4901 | 0.5572 | 0.6164 | 0.6688 | 0.7145 |
| J,8 | 0.1077 | 0.2050 | 0.2931 | 0.3725 | 0.4442 | 0.5083 | 0.5658 | 0.6174 | 0.6638 |
| J,9 | 0.0931 | 0.1785 | 0.2571 | 0.3289 | 0.3948 | 0.4553 | 0.5100 | 0.5601 | 0.6061 |
| J,T | 0.0783 | 0.1515 | 0.2199 | 0.2837 | 0.3427 | 0.3979 | 0.4493 | 0.4967 | 0.5409 |
| Q,2 | 0.1862 | 0.3406 | 0.4685 | 0.5739 | 0.6604 | 0.7312 | 0.7886 | 0.8352 | 0.8727 |
| Q,3 | 0.1713 | 0.3161 | 0.4379 | 0.5402 | 0.6255 | 0.6968 | 0.7557 | 0.8044 | 0.8445 |
| Q,4 | 0.1568 | 0.2910 | 0.4062 | 0.5045 | 0.5880 | 0.6590 | 0.7189 | 0.7696 | 0.8119 |
| Q,5 | 0.1422 | 0.2658 | 0.3736 | 0.4671 | 0.5482 | 0.6180 | 0.6783 | 0.7299 | 0.7744 |
| Q,6 | 0.1273 | 0.2400 | 0.3400 | 0.4280 | 0.5055 | 0.5734 | 0.6333 | 0.6857 | 0.7312 |
| Q,7 | 0.1126 | 0.2139 | 0.3048 | 0.3868 | 0.4600 | 0.5254 | 0.5835 | 0.6357 | 0.6818 |
| Q,8 | 0.0979 | 0.1875 | 0.2691 | 0.3435 | 0.4113 | 0.4730 | 0.5289 | 0.5800 | 0.6257 |
| Q,9 | 0.0833 | 0.1606 | 0.2321 | 0.2983 | 0.3600 | 0.4166 | 0.4689 | 0.5173 | 0.5619 |
| Q,T | 0.0687 | 0.1332 | 0.1940 | 0.2516 | 0.3052 | 0.3557 | 0.4032 | 0.4480 | 0.4894 |
| Q,J | 0.0540 | 0.1055 | 0.1547 | 0.2020 | 0.2474 | 0.2902 | 0.3313 | 0.3707 | 0.4082 |
| K,2 | 0.1763 | 0.3246 | 0.4491 | 0.5532 | 0.6395 | 0.7111 | 0.7702 | 0.8185 | 0.8579 |
| K,3 | 0.1616 | 0.2998 | 0.4178 | 0.5178 | 0.6027 | 0.6740 | 0.7343 | 0.7848 | 0.8269 |
| K,4 | 0.1469 | 0.2745 | 0.3851 | 0.4808 | 0.5633 | 0.6343 | 0.6948 | 0.7466 | 0.7908 |
| K,5 | 0.1322 | 0.2491 | 0.3517 | 0.4422 | 0.5211 | 0.5904 | 0.6509 | 0.7037 | 0.7494 |
| K,6 | 0.1175 | 0.2230 | 0.3171 | 0.4013 | 0.4763 | 0.5431 | 0.6025 | 0.6550 | 0.7016 |
| K,7 | 0.1029 | 0.1964 | 0.2814 | 0.3586 | 0.4285 | 0.4918 | 0.5490 | 0.6007 | 0.6473 |
| K,8 | 0.0881 | 0.1697 | 0.2447 | 0.3139 | 0.3777 | 0.4367 | 0.4905 | 0.5397 | 0.5853 |
| K,9 | 0.0734 | 0.1423 | 0.2069 | 0.2675 | 0.3238 | 0.3765 | 0.4259 | 0.4720 | 0.5148 |
| K,T | 0.0588 | 0.1146 | 0.1678 | 0.2183 | 0.2665 | 0.3120 | 0.3555 | 0.3961 | 0.4350 |
| K,J | 0.0441 | 0.0866 | 0.1277 | 0.1671 | 0.2058 | 0.2426 | 0.2780 | 0.3125 | 0.3452 |
| K,Q | 0.0294 | 0.0582 | 0.0865 | 0.1141 | 0.1414 | 0.1679 | 0.1940 | 0.2195 | 0.2444 |
| A,2 | 0.1665 | 0.3086 | 0.4294 | 0.5316 | 0.6177 | 0.6901 | 0.7505 | 0.8009 | 0.8425 |
| A,3 | 0.1517 | 0.2835 | 0.3970 | 0.4949 | 0.5791 | 0.6509 | 0.7120 | 0.7641 | 0.8080 |
| A,4 | 0.1372 | 0.2578 | 0.3636 | 0.4565 | 0.5376 | 0.6082 | 0.6695 | 0.7227 | 0.7684 |
| A,5 | 0.1224 | 0.2318 | 0.3294 | 0.4164 | 0.4934 | 0.5618 | 0.6223 | 0.6754 | 0.7225 |
| A,6 | 0.1077 | 0.2054 | 0.2940 | 0.3741 | 0.4462 | 0.5115 | 0.5702 | 0.6228 | 0.6701 |
| A,7 | 0.0931 | 0.1787 | 0.2575 | 0.3300 | 0.3963 | 0.4572 | 0.5129 | 0.5638 | 0.6101 |
| A,8 | 0.0783 | 0.1516 | 0.2200 | 0.2837 | 0.3428 | 0.3983 | 0.4498 | 0.4976 | 0.5418 |
| A,9 | 0.0637 | 0.1241 | 0.1810 | 0.2352 | 0.2866 | 0.3347 | 0.3804 | 0.4237 | 0.4647 |
| A,T | 0.0490 | 0.0959 | 0.1411 | 0.1847 | 0.2264 | 0.2664 | 0.3049 | 0.3417 | 0.3770 |
| A,J | 0.0343 | 0.0677 | 0.1003 | 0.1320 | 0.1629 | 0.1931 | 0.2223 | 0.2507 | 0.2784 |
| A,Q | 0.0195 | 0.0389 | 0.0582 | 0.0769 | 0.0956 | 0.1140 | 0.1320 | 0.1500 | 0.1676 |
| A,K | 0.0049 | 0.0098 | 0.0147 | 0.0195 | 0.0243 | 0.0292 | 0.0340 | 0.0388 | 0.0436 |
Methodology: These tables were created by a random simulation. Each cell in the table above for pairs was based on 7.8 million hands, and 21.7 million for the non-pairs.
2-Player Formula
The probability of domination in a two player game is easy to calculate. For pairs it is 6×(number of higher ranks)/1225. For example, the probability a pair of eights is dominated is 6×6/1225 = 0.0294, because there are six ranks higher than 8 (9,T,J,Q,K,A).
For non-pairs the formula is (6+18×(L-1)+12×H)/1225, where
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L=Number of ranks higher than lower card
H=Number of ranks higher than higher card Best casino odds in lake charles.
For example, the probability that J-7 is dominated is (6+18×(7-1)+12×3)/1225 = 150/1225 = 0.1224.
Poker Hand Odds Calculator Texas Holdem
Written by: Michael Shackleford