We have created a poker math and probability PDF chart (link opens in a new window) which lists a variety of probabilities and odds for many of the common events in Texas hold ‘em. This chart includes the two tables above in addition to various starting hand probabilities and common pre-flop match-ups. In Texas Hold’em a hand where aces, kings and queens pair up preflop is very rare. At a 9 player table this scenario unfolds roughly every 17,000 hands. The odds are 1:16,830 and the probability is 0.006%. Queens does happen every now and then, for example during this hand at the Bike. The Texas Hold’em odds of how likely hands are to unfold after the flop will help guide almost every action you make on the flop Odds On the Flop in Texas Hold’em. The flop is the turning point of a Hold’em hand. This is where you’re going to make your biggest and most expensive decisions. Using The 'Outs' To Calculate Texas Hold'em Poker Odds. We have already determined that you have nine 'outs'. Now there are 52 cards in a deck and two of those are in your hand, leaving 50.

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.

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.

Poker hands odds & outs: a crash course-guide on poker odds, pot odds, probabilities & odds charts so you can win at Texas Hold’em at the tables or online. One of the most important things that a poker player should know is what their poker odds are in a given situation.

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).

Texas Holdem Hand Odds Probabilities Chart

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.

Texas Holdem Hand Odds Probabilities Odds

Written by: Michael Shackleford