Poker Mathematics

Poker is one of the most famous casino games; one of the main reasons for this is because of the level of skill that can be incorporated into the game, which plays a significant part in determining total winnings. But as with any casino game, there is also the inherent element of chance to be dealt with.

The principles of the theory of probability are inherent in any form of poker played at any casino – whether online or land-based. At the crux of this, one needs to ask oneself the questions: What are the chances of being dealt hand x or hand y? Then, what are the chances of that hand being the winning hand in any given game, in relation to an opponent’s hand?

An attraction of poker is that it is mostly based on dependent events as opposed to independent events. This means that each time a card is drawn, it has an effect on the next card(s) that could possibly be drawn, since the number of cards available to be drawn from the deck decreases each time; therefore, the probability of drawing a certain card increases each time that that card is not drawn.

Using mathematics to win poker games

The most common situation in poker where mathematics can be used to some extent to determine a course of action is when a player is on a draw, and the opponent has made a bet, and the player needs to decide whether to call to complete the draw or fold and concede the pot. The player can use mathematics, such as the theory of probability, to work out the pot odds, where the size of the opponent’s bet is considered in relation to the size of the pot.

Possible ways to draw various poker hands:

Since there are a finite number of cards in a game of poker, it is possible to mathematically ascertain, using the useful Combin Function, how many ways exist to draw a particular hand:

Royal Flush: 4

Straight Flush: 36

Four of a Kind: 624

Full House: 3 744

Flush: 5 108

Straight: 10 200

Three of a Kind: 54 912

Two Pair: 123 552

One Pair: 1 098 240

Naturally, the lower the number of ways that exist for a specific hand to be drawn, the lower the probability of that hand being drawn and the higher winning potential it offers.

Read about the mathematics of other casino games, or have a look at our mathematics of gambling glossary.