For example, with a pair of jacks in a 10 player game the probability of a higher pocket pair is 3*9/2 = 13.5%. That is the percentage probability that there will be at least one higher pair. Take the number of higher pairs, multiply by the number of other players, and divide by 2. After this column appeared one of my fans, Larry B., wrote a brute force combinatorial program to solve this problems. So my approximation of the probability of at least one higher pocket pair is 1-e -n*r*(6/1225). The table below shows those probabilities. For examle if you have pocket queens and there are 9 other players the expected number of players with a higher pocket pair is 0.0882, so the probability of at least one player having a higher pocket pair is 1-e -0.0882 = 8.44%. Given that assumption the probability that at least one player will beat you is 1-e -µ, where µ is the mean. The probability for a full house is given above as 0.001441.To get the probability that at least one player will beat you I will make the not entirely correct assumption that the number of players with a higher pocket pair is a Poisson random variable with a mean in the above table. (Excludes royal flush and straight flush)Įxample: 3, 6, 8, 9, K (at least two different For example, 3 aces and 2 kings is a fullįor example, 2, 4, 5, 9, J (all hearts) is a flush. Ranking, Frequency and Probability of Poker HandsĪn example of a straight flush is: 5, 6, 7, 8, 9, all spades. Possible ways that different types of hands can arise and their The probability of being dealt a straight flush is through to the one starting at 10) and there are 4 suits, so there are 40 possible straight flushes.

The next most valuable type of hand is a straight flush, which is 5 cards in order, all of the same suit.įor example, 2♣, 3♣, 4♣, 5♣, 6♣ is a straight flush.įor each suit there are 10 such straights (the one starting with Ace, the one starting with 2, the one starting with 3. Ways of getting such a hand (because there are 4 suits), so the probability of being dealt a That it will occur) is the royal flush, whichĬonsists of 10, J, Q, K, A of the same suit. The best hand (because of the low probability

Texas holdem hand probability