Understanding Probability In Texas Holdem Is An Essential Aspect Of Profitable Play
– PreFlop Probability Guide
Ever wondered how often you will be dealt Aces? Or what the chances of facing an overpair are when you hold JackJack? 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 acex 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.
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PreFlop 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 preflop. The 6 combinations possible are KhKd, KhKc, KhKs, KdKc, KdKs and KcKs.
6 / 1326 = 0.00435 or 221to1
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 16to1 (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 Aceking preflop. 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 AK can be dealt out of the 1326 combinations – a probability of 0.0121% or approximately 82to1. In fact this is the same for any unpaired hand when you ignore the suits.
PreFlop Poker Probability  Probability Of Hands PreFlop Chart
The reference table below gives probabilities of being dealt specific hands preflop: 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.
Preflop Hand 
Probability

Odds

Notes

AA 
0.045

221:1

Same for any pocket pair 
AK (any suits) 
0.012

82:1

Any 2 cards not inc. suits 
AK (suited) 
0.003

330:1


Pair 1010 or better 
0.023

43:1

1010, JJ, QQ, KK or AA 
AK, AQ or AJ 
0.036

27:1

Suits not considered 
2 Suited Cards 10+ 
0.03

32:1


Any Suited Connector 
0.039

24:1

23 suited or better 
2 Cards Jack + 
0.09

10:1

Suits not considered 
Finally we can look at how combinations of preflop 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

Playable Hands

Combinations

Odds 
Early Position 
AA to JJ, AKo, AQs 
46

29:1 
Early Mid Position 
AA to 99, AQo+, AJs 
74

18:1 
Mid Position 
77+, A10o+ A8s+ KQ+ 
140

9,5:1 
Late Position 
55+, A7+, QJo+, 78s+ 
240

5,5:1 