1,326 possible starting hand combinations.
My Poker Math
The probability of being dealt various starting hands can be explicitly calculated. In Texas Hold 'em, a player is dealt two down (or hole or pocket) cards. The first card can be any one of 52 playing cards in the deck and the second card can be any one of the 51 remaining cards. This gives 52 × 51 ÷ 2 = 1,326 possible starting hand combinations. (Since the order of the cards is not significant, the 2,652 permutations are divided by the 2 ways of ordering two cards.)
Of the 1,326 combinations, there are 169 distinct starting hands grouped into three shapes:
13 pocket pairs (paired hole cards), 13 × 12 ÷ 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 169.
The relative probability of being dealt a hand of each given shape is different.
The probability of being dealt various starting hands can be explicitly calculated. In Texas Hold 'em, a player is dealt two down (or hole or pocket) cards. The first card can be any one of 52 playing cards in the deck and the second card can be any one of the 51 remaining cards. This gives 52 × 51 ÷ 2 = 1,326 possible starting hand combinations. (Since the order of the cards is not significant, the 2,652 permutations are divided by the 2 ways of ordering two cards.)
Of the 1,326 combinations, there are 169 distinct starting hands grouped into three shapes:
13 pocket pairs (paired hole cards), 13 × 12 ÷ 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 169.
The relative probability of being dealt a hand of each given shape is different.
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