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 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. For example: To calculate your hand odds in a Texas Hold'em game when you hold two hearts and there are two hearts on the flop, your hand odds for making a flush are about 2 to 1. This means that for approximately every 3 times you play this hand, you can expect to hit your flush one of those times. And the odds of making a royal flush is 649,739 to 1. This is correct assuming that every game plays to the river. In poker terms, the river is the name for the fifth card dealt, face-up on the board. In total, there are 2,598,960 possible poker hands with 52 cards. The odds of getting four of a kind in Texas Hold ‘Em.
The poker odds calculators on CardPlayer.com let you run any scenario that you see at the poker table, see your odds and outs, and cover the math of winning and losing poker hands. Texas Hold'em Omaha. The Texas Hold'em odds for each of the different situations have been given in both percentage and ratio odds, so use whichever format you feel comfortable with. Other poker odds charts. For more useful odds charts that you can use for when you are working out whether or not to call when on a drawing hand, use the following tables.
That said, the following tables present the probability of every two-card hand being dominated, according to the total number of players.
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 |
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.
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
L=Number of ranks higher than lower card
H=Number of ranks higher than higher card
For example, the probability that J-7 is dominated is (6+18×(7-1)+12×3)/1225 = 150/1225 = 0.1224.
The following Texas Holdem odds table highlights some common probabilities that you may encounter in Hold'em. It is not vital that you learn these probabilities, but it is useful to be aware of the chances of certain situations arising.
Situation | Percentage Odds | Ratio Odds |
---|---|---|
Preflop Probabilities: | ||
Dealt AA. | 0.45% | 220 to 1 |
Dealt AK. | 1.2% | 82 to 1 |
Dealt AKs. | 0.3% | 331 to 1 |
Dealt 72o. | 0.9% | 109 to 1 |
Being dealt AA vs. KK (heads up). | 0.004% | 22,559 to 1 |
Dealt a pocket pair. | 6% | 16 to 1 |
Dealt suited connectors. | 4% | 24 to 1 |
Flop Probabilities: | ||
Flopping a pair. | 32.4% | 2.2 to 1 |
Flopping a set (with pockets). | 11.8% | 7.5 to 1 |
Paired Board: | ||
2 players, probability of trips. | 17% | 4.8 to 1 |
3 players, probability of trips. | 26% | 3 to 1 |
4 players, probability of trips. | 34% | 2 to 1 |
5 players, probability of trips. | 43% | 1.4 to 1 |
The odds in this Texas Hold'em odds table are unlikely to directly help your overall strategy, but they are pretty interesting nonetheless. The Texas Hold'em odds for each of the different situations have been given in both percentage and ratio odds, so use whichever format you feel comfortable with.
For more useful odds charts that you can use for when you are working out whether or not to call when on a drawing hand, use the following tables:
Both of these tables give the odds for completing your draw depending on how many outs you have. You can find out more on how to work out odds and all that mathematical stuff in the article on pot odds.
Go back to the poker odds charts.
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