In Poker, It is Profitable To Know How Many Starting Hand Combinations There Are

I’ve been asked by a new player to explain how I got to 169 possibilities of starting hands from a previous page. Good question!

In Texas Hold’em poker there are 2,652 possible starting hands. The way that you first get all the possible starting hands is to take the number of cards (52) and multiply that by 51 times.

Remember that the first 2 cards that can be dealt can be anything from the deck. Out of these 2,652 combinations, there may not be different hands though, because the same two cards dealt in two different orders are still the same hand.  In the following two examples, you can see that the cards are equal and that there aren’t any differences.  Kind of reminds you of algebra in school, huh?

   is EQUAL to

is EQUAL to

That reduces the number of hands, 2,652 down by half or 2,652/2 = 1,326.

Still with me?  Good.

Now, out of the 1,326 hands, thinking of the samples above, there is a lot of duplication in VALUE of the hands. 

The following hands are all equal in VALUE:

is EQUAL to is EQUAL to  

 

Okay, have you digested that?  Good.  One last thing.  Because of the possibility of getting a flush, cards like the following are NOT equal:

  is NOT EQUAL 

This is because the first two cards have a chance at making a flush and the second two cards not do not have a chance for making a flush. 

We need to get the total number of possibly suited starting cards from this bunch so that would be 13 x 12  /2 for a total of 78.

Continuing on, there should be 78 possible suited starting cards and 78 possible non-suited starting cards and 13 possible pairs for a total of 169 cards.

So looking at it this way, there are 169 possible starting hands in this game.   Hopefully I answered the question without making it too confusing.

 Any questions?  Comments?  Please drop me a line and check out the other posts and blog on this site!

 

Kim Greenblatt

Thanks for taking the time to visit and for more information or to get back to the beginning of the blog, go here.

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