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Probability

Texas Hold’em Probabilities

Preflop
Probability of being dealt a pocket pair 5.9%
Probability of being dealt suited cards 23.5%
Probability of being dealt AA .45%
Probability of being dealt connecting cards 15.7%
Flop
Probability of hitting a three of a kind or quads at the flop when you hold a pocket pair 11.8%
Probability you will make a pair at the flop, holding two unpaired cards in the hole 32.4%
Probability of flopping a flush, holding two suited cards .84%
Probability of flopping a flush draw, holding two suited cards 11%
Turn-River
Probability of hitting a flush draw (both turn/river, needing one card to hit) 35%
Probability of hitting an open-ended straight draw (i.e. 4 straight cards, need one on either end to hit on turn or river) 31.5%
Probability of hitting a gutshot draw (inside straight draw) on turn or river 16.5%
Probability of hitting a backdoor flush, holding two suited cards 4.2%
Probability of hitting a flush on the turn 19.1%
Probability of hitting a flush on the river 19.6%*
Probability of hitting a straight on the turn 17%
Probability of hitting a straight on the river 17.4%
Hand against Hand
Probability of a lower pocket pair beating a higher pocket pair 18.5%
Probability of non-suited overcards beating a lower pocket pair 45%
Probability of suited overcards beating a lower pocket pair 47.3%
Probability of a dominated hand winning (e.g. AJ vs. AK) 24%
Probability of a severely dominated hand winning that is suited (e.g. AA vs. ATs) 12.7%
Probability of an unsuited severely dominated hand winning (e.g. AA vs. ATo) 7.2%
Probability of two unsuited undercards beating two unsuited overcards (e.g. JT vs. AK) 36.7%
Probability of two suited undercards beating two unsuited overcards (e.g. JTs vs. AK) 41%
Probability of two, unsuited, non-connecting undercards beating two suited, connecting overcards (e.g. T4o vs. AKs) 32.4%


* You may realize that the probability of hitting a flush/straight on the turn or river is not equivalent to hitting a flush/straight on turn + hitting a flush/straight on the river.
The reason is to calculate whether or not you will hit a flush on both, the proper statistical method is to calculate 1 – (probability of not hitting a flush on turn or river).
To illustrate why this is the proper method, consider flipping a coin twice.
To find what is the chance of hitting tails at least once, you would not add 50% plus 50% because that would mean you are guaranteed to hit tails at least once every two tries.
The proper method would be 1 – (probability of heads both times)= 1 (.50 X .50)= .75.


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