- A number of poker experts have written on the subject of good poker starting hands for Texas Holdem. Beginners should read the best poker writers to further their study of poker hand strength. David Sklansky and Mason Malmuth of 2+2 fame designed an influential set of Texas Holdem starting hand charts in 1999.
- It is sometimes useful to know the frequency of each of the different poker hands. In Texas Hold’em, each player is making a hand out of seven available cards. To determine the probability of each hand occuring we can count the number of distinct ways of obtaining each hand and divide by the total number of possible hands.
- Poker Odds Of Hitting A Hand On The Flop; Hand that you might flop Poker Odds,% One pair (hitting one of your hole cards) 32%: Set (hitting three of a kind with pocket pair) 11.8%: Two pair hand (both of your hole cards) 2%: Straight (with two connected cards like) 1.3%: A flush: 0.8%.
- The world's most trusted Texas hold'em poker odds calculator. Improve your poker or find out just how bad that bad beat was. And cover the math of winning and losing poker hands. Texas Hold'em.
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Calculating Texas Hold ‘em Odds. Also consider that there are four cards of any given value in each deck and there are 169 different hole card combinations. That being said, there’s a roughly one in 1326 chance that players will be dealt any specific hand, so it’s important to know what kind of odds you should keep in mind whenever you step to the poker table. Statistical knowledge of probabilities helps players make intelligent betting decisions by eliminating the random factors of the game. In Texas Hold'Em, there is no way to predict what the next card will be. There are, however, ways to factor the odds to make logical, and hopefully profitable, assumptions about the way a hand will play out.
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In other words, after one player bets, there can be a maximum of three raises, making it a total of 4 bets each player would need to put into the pot.A maximum of 4 bets on each of the four rounds of betting equals 12 big bets total. Secondly, you’ll want to have enough chips to go all the way to the river should the betting be capped. It’s pretty demoralizing having to reach into the wallet to pull out more money, time and time again – all in order to have a decent enough stack on the table. Let me explain.Most limit hold’em games are a 4 cap game, meaning there is a maximum of 4 bets allowed on each round. Crown poker minimum buy in.
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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.
- 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.
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
L=Number of ranks higher than lower card
H=Number of ranks higher than higher 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.