9/20/2014

Texas Hold'em Poker Probability - Starting Hand

Poker is an imperfect information game, and it's all about the theory of probability.  The key to win is based on how we can use the probability to gain an edge with some call/raise skills.

In Texas Hold'em, you get two cards first, then the flop, the turn, and the river card.  In such a process, we can find out the probability of the starting hand (2 cards), the flop(3/5 cards), the turn (4/6 cards), and the river (5/7 cards).

If we simplify it a little bit, we focus on the starting hand, the flop, and the river.  We would like to know the 2-card, 3-card, 5-card, and 7-card probability of the combination of the cards.

There are 52 cards.

For the starting hand, 
the number of the combination of the starting hand is 1,326 = 52*51/2.
pair - 78 = 52*3/2
suited - 312 = 52*12/2
others - 936 = 52*(51-3-12)/2

pair : suited : others = 1:4:12

You have about 30% probability to get a pair(6%) or suited(24%) starting hand.

How to VERIFY: You can go to play online poker and keep a record of your starting hands to verify the result.

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