Poker Basics - Combinatorics

For new players, knowing how many combinations there are of every possible hand makes other decisions much easier at the tables.

Card counting will get you thrown out of a casino if you are playing Blackjack but it is a vital skill in poker. One very useful skill to memorise in poker is combinatorics. 

That is the word to describe the number of combinations there are of a particular card type or hand. It sounds like a very basic thing to understand in a complex game, but when you understand combinatorics it makes other aspects of the game easier. 

This is what is known as a poker grid, it shows every possible hand in poker. 

The yellow half represents suited hands, the bottom half are offsuit hands, and the green light in the middle are pocket pairs. 

There are 78 combinations of pocket pairs, 312 combinations of suited cards and 936 combinations of offsuit cards. That is 1,326 total hand combinations. 

This is already useful information. Your opponent is four times less likely to be dealt a pair than an unpaired hands, and three times less likely to be dealt a suited hand than unsuited. The grid visually makes it look like suited hands are as frequent as unsuited, but that is obviously not the case. 

When you are aware of this, playing a range of pairs and mostly suited Aces is a good way to play a tight range while also achieving board coverage. 

Individual hand combinations

Drilling down into individual hands. There are six combinations of every pocket pair, so for example: A A, A A, A A, A A, A A A A.

There are four combinations of every suited hand: A K, A K, A K, A K.

And there are 12 combinations of every offsuit hand: A K, A K, A K, A K, A K A K, A K, A K, A K, A K, A K A K.

Putting that into practice, let's say a very tight player raises under the gun and you put them on a range of JJ+ and AK. You have T T and the flop is 2 2 7

How likely are you to be ahead? 

There are six combinations of each pair - JJ,QQ,KK,AA = 24 combinations in total. There are 16 combinations of AK. 

In this spot there are 40 combinations in total and 16 you beat, which is 40% of the time. 60% of the time you are dominated on this flop. 

Combinatorics is one of those skills in poker that you should practice early in your poker education and it will stick with you. It is also very useful for understanding how to play draws and use blockers. 

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