WOO logo
  • Home ›
  • Texas Hold'Em Dominated Hand Probabilities

On this page

Texas Hold'Em Dominated Hand Probabilities

On this page

Introduction

Texas Hold'Em Dominated Hand Probabilities

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.

  1. 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.
  2. 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.
  3. 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.
  4. 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.

Top 6 Online Poker Bonuses View All

888 Poker
Players rated 888 Poker 3.7 out of 5 Stars
Sign Up

Sign Up Bonus

$20

New customers only. T&C's apply. 18+.This offer is not available for players residing in Ontario. New Customer Offer. T&C’s Apply. 19+. Eligible members will be offered a Bonus Package equivalent to $20 FREE (based on their registration country & IP address). The FREE Bonus Package will be equal to $20 regardless of the currency exchange rate.
No Info
Claim
William Hill Poker
Players rated William Hill Poker 3.7 out of 5 Stars
Sign Up

Sign Up Bonus - United Kingdom

100% up to
£100

New Customer Offer. T&C's apply. 18+. #ad. Opt-in required. X1 per customer. Min first deposit/transfer £10 to a poker account. Game restrictions and Terms Apply. Twister Discovery Pack: 1x tournament tickets total value of €6. 3x €1 Age of the Gods Twister, 3x €1 Twister. £100 Bonus Money: WHPoints to redeem Bonus (two stage redemption rate), expires in 45 days. Bonus Spins: x40 wagering. Expires in 14 days, Max redemption £20.
No Info
Claim
Betsson Poker
Players rated Betsson Poker 3.8 out of 5 Stars
Sign Up

Sign Up Bonus

100% up to
€600

New customers only. T&C's apply. 18+. This offer is not available for players residing in Ontario. New Customer Offer. T&C’s Apply. 19+. The first €5 of the bonus is redeemable in €1 chunks by accumulating 25 Loyalty Points. The following €95 of the bonus is redeemable in €5 chunks by accumulating 250 Loyalty Points. Any remaining bonus over the first €100 is redeemable in €10 chunks for every 500 Loyalty Points accumulated.
No Info
Claim
Bodog Poker
Players rated Bodog Poker 3.5 out of 5 Stars
Sign Up

Sign Up Bonus - Canada

100% up to
C$1000

This offer is not available for players residing in Ontario. New Customer Offer. T&C’s Apply. 19+. Minimum deposit CA$10. Bonuses will be unlocked in $5 increments for every 150 Rewards Points earned in Poker. There is no rollover on bonuses unlocked from Rewards Points earned.
No Info
Claim
Juicy Stakes
Players rated Juicy Stakes 3.4 out of 5 Stars

Bonus Code

1000JUICY
Sign Up

Sign Up Bonus

200% up to
$1000

New customers only. T&C's apply. 18+. This offer is not available for players residing in Ontario. New Customer Offer. T&C’s Apply. 19+. Bonus funds are earned in $5 increments based on Frequently Player Points (FPPs) accumulated through real-money ring or tournament game-play. Players need to collect 83.335 FPP for every $5 increment. The minimum deposit required is $25 unless otherwise stated.
No Info
Claim
NetBet Poker
Players rated NetBet Poker 3.5 out of 5 Stars

Bonus Code

FREE20
Sign Up

Sign Up Bonus

€20

New customers only. T&C's apply. 18+. This offer is not available for players residing in Ontario. New Customer Offer. T&C’s Apply. 19+. Minimum deposit: €20. The bonus will be credited in 2 stages: Half will be credited immediately after your deposit, another half will be credited 7 days after your deposit
No Info
Claim

Probability of Domination — Pairs

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-Pairs

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

For example, the probability that J-7 is dominated is (6+18×(7-1)+12×3)/1225 = 150/1225 = 0.1224.

US-OH Ohio Recommended Online Poker Rooms

View All

200 % up to

1000$

+25 spins

Play

150 % up to

1500$

Play

100 % up to

1000$

Play

100 % up to

1000$

Play

Written by: Michael Shackleford