The relative probability of being dealt a hand of each given shape is different. 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. The only factors determining the strength of a starting hand are the ranks of the cards and whether the cards share the same suit. The 1,326 starting hands can be reduced for purposes of determining the probability of starting hands for Hold'em. Which is the number of possible combinations of choosing 2 cards from a deck of 52 playing 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.) Alternatively, the number of possible starting hands is represented as the binomial coefficient 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.

In Texas Hold'em, a player is dealt two down card (or pocket cards). Often, the key to determining probability is selecting the best approach for a given problem. There are 4 ways to be dealt an ace out of 52 choices for the first card resulting in a probability of There are 3 ways of getting dealt an ace out of 51 choices on the second card after being dealt an ace on the first card for a probability of The conditional probability of being dealt two aces is the product of the two probabilities: The second approach is to use conditional probabilities, or in more complex situations, a decision tree.

This gives a probability of being dealt two aces of. There are 52 ways to pick the first card and 51 ways to pick the second card and two ways to order the two cards yielding (52×51)/2=1326 possible outcomes when being dealt two cards. The first approach is to determine the number of outcomes that satisfy the condition being evaluated and divide this by the total number of possible outcomes.įor example, there are six outcomes for being dealt a pair of aces in Hold' em.

When calculating probabilities for a card game such as Texas Hold'em, there are two basic approaches.

Worst starting hands in texas holdem