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Understanding Probability In Texas Holdem Is An Essential Aspect Of Profitable Play
– Pre-Flop Probability Guide
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Ever wondered how often you will be dealt Aces? Or what the chances of facing an over-pair are when you hold Jack-Jack? This section of the site will give you the probability of certain hands before the flop (this page) and in later pages the chances of certain flops (for example one suit flop probability) and the chances of dominating hands being out there to your ace-x hand (where x is one of several small to medium cards).
We start by looking at how the cards in the deck can be dealt based on a random distribution of the 1326 ways of 2 cards falling and how often you’ll expect to be dealt certain hands. Then we take suitedness into account – since there are less ways of being dealt 2 suited cards. Later articles in this series will continue with the essential poker probability and card distribution stats you need.
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Firstly, where did the number 1326 come from? Well with 52 cards in the deck your first card is 1/52 this is then multiplied by 1/51 and the total divided by 2 (since it does not matter what order your cards are dealt in) giving 1326 combinations of all cards in any suit.
Of course suitedness is not often important, especially for low cards. The next question is then – what is the number of unique starting hands in Texas Holdem, not counting suits? The answer here is 169 unique hands.
Pre-Flop Poker Probability - 169 Distinct Starting Hands
Now we are getting somewhere. Next we can use the numbers above to work out what the probability of being dealt AA, KK (or in fact any pair) is. This is a case of taking the total number of possible hands and then seeing how many of these are your pair. We will take a pair of Kings as an example. Of the 1326 possible combinations there are 6 ways of being dealt this hand pre-flop. The 6 combinations possible are Kh-Kd, Kh-Kc, Kh-Ks, Kd-Kc, Kd-Ks and Kc-Ks.
6 / 1326 = 0.00435 or 221-to-1
So the chances of being dealt any specific pair are 221:1 against, in fact with 13 possible pairs the chances of being dealt any pair go up to 16-to-1 (there are 78 pair combinations from 1326 total).
Next we can look at unpaired hands, a specific example is the number of ways of being dealt Ace-king pre-flop. Here we have more possible combinations, since there are 8 cards that can be dealt first and then 3 remaining cards to make this hand (we will ignore suitedness for the moment). This gives 16 ways in which A-K can be dealt out of the 1326 combinations – a probability of 0.0121% or approximately 82-to-1. In fact this is the same for any unpaired hand when you ignore the suits.
Pre-Flop Poker Probability - Probability Of Hands Pre-Flop Chart
The reference table below gives probabilities of being dealt specific hands pre-flop: The next article in this series will look at the chances of being dealt hands at the same time as one or more opponent is dealt a higher hand – for example AA vs KK and AK vs QQ.
Pre-flop Hand | Odds | |
AA | 0.045 | Same for any pocket pair |
AK (any suits) | 0.012 | Any 2 cards not inc. suits |
AK (suited) | 0.003 | |
Pair 10-10 or better | 0.023 | 10-10, JJ, QQ, KK or AA |
AK, AQ or AJ | 0.036 | Suits not considered |
2 Suited Cards 10+ | 0.03 | |
Any Suited Connector | 0.039 | 23 suited or better |
2 Cards Jack + | 0.09 | Suits not considered |
Finally we can look at how combinations of pre-flop hands work, asking the question what is the probability of being dealt a playable hand for each position. We will use arbitary early, middle and late position combinations here to demonstrate – the actually hands you play is up to your personal style!
Position | Combinations | ||
Early Position | AA to JJ, AKo, AQs | 46 | 29:1 |
Early Mid Position | AA to 99, AQo+, AJs | 18:1 | |
Mid Position | 77+, A10o+ A8s+ KQ+ | 140 | 9,5:1 |
Late Position | 55+, A7+, QJo+, 78s+ | 5,5:1 |
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