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How many possible starting hands are there in Texas Hold'em?

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3 Answers 3

up vote 12 down vote accepted

169

While Chris is technically correct, as far as strategy is concerned, there is no difference between having an Ace & King of spades vs. Ace & King of hearts. There is however a difference between having a suited Ace & King vs. a non-suited Ace & King. Looking at it that way, there are 169 possible starting hands.

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I was thinking of looking up that number. Guess it's farther down in the wiki article. –  Chris Persichetti Nov 15 '10 at 19:30
    
@Chris TL;DR? ;) –  Jon Hadley Nov 15 '10 at 21:05
    
@John Exactly :). –  Chris Persichetti Nov 15 '10 at 22:19
    
This is a very useful link. It shows the starting hands in a nice grid format: en.wikipedia.org/wiki/Texas_hold_'em_starting_hands –  Neal Tibrewala Oct 20 '11 at 16:02

It depends on how you define "starting hand."

There are 52*51=2652 permutations of any two cards.

There are (52*51)/2 combinations of two cards, if you treat (Card A, Card B) as being equal to (Card B, Card A), e.g. ace of spades, king of hearts as being equal to king of hearts, ace of spades). the total is 1326.

There are 169 different hands consisting of the following:

13 pairs (one for each of 13 denominations from A to 2. 78 combinations of (X, Y) of the same suit. That is (Ace of spades, king of spades) is considered equivalent to (ace of hearts, king of hearts). 78 combinations of (x,Y) of two different suits. That is (ace of spades, king of hearts) is considered equivalent to (ace of clubs, king of diamonds).

13+78+78=169 different two card hands.

Reconciling different hand combinations:

13 pairs times 6 combinations= 78 pair combinations. 78 suited combinations times 4 (suits)= 312 suited combinations. 78 unsuited combinations times 12 =936 unsuited combinations.

78+312+936= 1326 hand combinations.

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1326

According to Wikipedia, using the formula (52 * 51) / 2.

http://en.wikipedia.org/wiki/Poker_probability_%28Texas_hold_%27em%29

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