Poker Hand Probabilities

In poker there are probabilities that you can use to determine your chances of winning a hand. Learning the different poker hand probabilities can give you a tremendous advantage over many of the other players. We all know what the different types of 5 card poker hands are. The straight flush, four of a kind, full house, flush, straight, 3 of a kind, two pairs, pare, and high card. But now we are going to tell you what the probabilities are of getting these hands.

Based on a 5 card hand there are over 2,598,960 possible hands from a 52 card deck.

Straight Flush – The probabilities of the straight flush are determined by the smallest cards which make them up. There are forty cards that can make the smallest card in a straight flush, so there are forty straight flushes available.

Four of a kind – There are 13 different choices in the number rank for 4 of a kind and 48 different cards. This means that there are 624 4 of a kind hands. You get this by multiplying the 48 cards x the 13 different choices.

Full house – There are 13 ranks for the trips and 12 ranks for the pairs and there are four different ways of choosing the trips and 6 ways of choosing the pairs. When multiplied 13 x 12 x 6 x 4 = 3,744 chances of getting a full house.

The Flush – There are 1,287 different choices for the flush iof the saim suits, and 10 of these are straight flushes so when these are taken out, there are 1277 flushes for one suit and when you multiply that by for different suits you have a total of 5108 different flushes.

A straight – there are four choices for every ranking card and there are ten ranks. There are over 10,200 different straights when you take out the straight flushes.

3 of a kind – There are 13 ranking choices for the trip and there are 66 different choices for the other 2 cards. There are 54,912 different variations to the three of a kind hands including the two other cards in the five card hands.

Two Pairs – There are 78 different choices in the ranking pairs and 4 choices for the pairs, and forty four different options for the other card in the hand. This gives you 123,552 different choices with two hand pairs.

Pair – there are 13 different choices for each ranking card and 6 choices for the pair. Then there are 220 different ranks and choices for the other 3 cards with 4 choices in each of those three cars, so the formula would be 1,098,240 different pair hands.

Unless you are an avid mathematician all of these numbers can be difficult to remember but many players keep a probabilities chart readily available to help them determine the probabilities of other players holding a certain hand.