Probabilities in poker

Here are some important probabilities in Texas hold'em that is very good to be familiar with. Knowledge about probabilities helps you to correct evaluate situations in poker, so that you don't call when you shouldn't and fold when you have the odds in your favor.

Table 1. Pre-flop probabilities
Situation Odds Percent
Probability of being dealt a pocket pair 16-1 6%
Probability of being dealt A-A (or any specific pair) 220-1 0.5%
Probability of being dealt suited cards  3-1 24%
Probability of being dealt connectors   11-1 9%
Probability of being dealt suited connectors 46-1 2%
Probability of being dealt A-K suited (or any specific suited hand) 331-1 0.3%

Comments

The best hand in Texas hold'em, A-A, will in average be dealt 1 in 221 hands. It is also interested to know how often one of the highest pocket pairs: T-T to A-A will be dealt. The answer is 1 in 85 hands (1.2%).

Two suited cards will in average be dealt 1 in 4 hands. So, obviously a non-suited hand will be dealt 3 in 4 hands. There are four combinations of every suited hand and twelve combinations of every non-suited (pocket pairs excluded).

The best suited hand is A-Ks. As shown in the table, the chance for this is 1 in 332. A-K suited is more uncommon than A-A, which may seems strange, but there are only four possible combinations of A-Ks in comparison to six of A-A).

The best off suited connected hand is A-Ko. The chance for be dealt either A-Ks or A-Ko is 1 in 83 (1.2%).

Table 2. Flop probabilities
Situation Odds Percent
Probability of making a pair on the flop 2-1 32%
Probability of hitting a two pair on the flop 49-1 2%
Probability of hitting a set (or better) when holding a pocket pair 8-1 12%

Comments

You will make a pair on the flop little less than 1 in 3. That means that in most situations, you will hit nothing and only have a high card.

In cases there you have one low and one high card you would obviously prefer to hit the higher card. For this there are approximately 16% chance.

As can be seen in the table, a much less chance to hit a two pair with a non-pocket pair hand than hitting a set with a pocket pair.

Table 3. Draw probabilities
Situation Odds Percent
Probability of hitting a flush draw on the turn or river 2-1 35%
Probability of hitting an open-ended straight on the turn or river 2-1 32%
Probability of hitting an inside straight draw on the turn or river 5-1 17%

Comments

The odds and Percent are the chances on the turn and river together. I you instead which to know what it is for turn or river, just divide the odds or Percent with two. It will be a little more on the river if the draw wasn't hit, because the outs left in the deck are more in relation to the others when was the case before the turn.

Table 4. Starting hand versus average hand
Situation Percent
A-A to win against average hand 85%
K-K to win against average hand 83%
Q-Q to win against average hand 79%
J-J to win against average hand 78%
T-T to win against average hand 75%
9-9 to win against average hand 72%
8-8 to win against average hand 70%
7-7 to win against average hand 67%
6-6 to win against average hand 64%
5-5 to win against average hand 61%
4-4 to win against average hand 59%
3-3 to win against average hand 55%
2-2 to win against average hand 52%
A-Ks to win against average hand 68%
A-Ko to win against average hand 66%
A-Qs to win against average hand 67%
A-Qo to win against average hand 66%
A-Js to win against average hand 67%
A-Jo to win against average hand 65%
K-Qs to win against average hand 65%
K-Qo to win against average hand 63%
Q-Js to win against average hand 61%
Q-Jo to win against average hand 59%
J-Ts to win against average hand 60%
J-To to win against average hand 58%
7-2o to win against average hand 39%
3-2o to win against average hand 38%

No decimals are used. (Source: Pokerprobability.net odds calculator)

Comments

All the exemples in Table 4 are refering to when a starting hand meet one average hand in Texas Hold'em. If more hands are involved, the winning chance are obvioulsy reduced. The letters "s" and "o" stands for suited and off suited.

As you can see, two aces win a more than eight out of ten, but it's never a lock when you are going all in against a hand in poker, not even with aces.

Table 5. Starting hand versus specific hand
Situation % equity % equity
A-A vs. K-K 81.95% 18.05%
A-A vs. Q-Q 81.55% 18.45%
A-A vs. J-J 81.15% 18.85%
A-A vs. 7-7 80.48% 19.52%
A-A vs. 2-2 82.22% 17.78%
A-A vs. A-Ks 87.86% 12.14%
A-A vs. A-Ko 93.17% 6.83%
A-A vs. 7-2o 88.20% 11.80%
A-A vs 3-2 87.21% 12.79%

(Source: Propokertools.com Simulator 2.0)


See more examples

Comments

Notice that the results are based on equity and not plain winning percent. This means that there is no value for split hand, even than that would be possible. Equity are the value of the respective hands in the situation, and the split possibility is included.

The reason to aces as a slightly minor favorite against two jacks than against two kings are that the straight possibility for the jacks blocked with fewer cards.

Low pocket pairs such as duces has lower winning chances against aces since the player can lose when the board are paired by a lower two pair.

Written by Oscar Sand

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