Poker mathematics

If you want to not only play poker, but also win some cash, you need to study our high-quality training articles on online poker strategy. In this section of the site you will find articles on basic and advanced poker strategy (mainly for no limit Texas hold'em), the strategies of tournament poker, as well as articles on the psychology of poker and poker math from well-known professional players.

Poker Mathematics

Poker is a game of skill, that’s why your abilities to read situations and opponents will give you an advantage in each and every hand. Moreover, poker is a game based on mathematics, where you would need to be able to calculate your odds and probabilities of your hand, and the hand of your opponent in every specific situation. In this section of our site you’ll be able to find all the necessary information about the mathematics of poker.

Will poker math help you to win more money?

This is a fairly common question. You’ll be able to win money in poker even without a good grasp of mathematics of course, but the knowledge and understanding of its basics, such as pot odds, implied odds, probabilities of improving your hand and your opponent’s hand, equity, fold equity, expected value and many others, will help you to win even more money in poker and will significantly improve your game. Mathematics in poker will give you an advantage over those opponents who do not want to devote it their time.

Almost all players use mathematics during the game even without knowing that they do it.

Where mathematics is used in poker?

Math and draw hands

Mathematics in poker can be used in a wide variety of situations. The most common example of using math in poker is calculating your equity with draw hands (flush draw or straight draw). When your opponent makes a bet and you, having a draw hand, do not know if you should call his bet hoping to improve your hand or fold your cards and give away the pot to an opponent.

In such a situation the player who is familiar with mathematics of poker will always know what he should do. At the same time a player not familiar with the math of poker will make his decision based on his feelings and lose in the long run.

Expected value (EV)

There are other situations where mathematics of poker is used more widely, for example, to calculate your expected value (expected profit). Imagine that you have a lower pair on the river and your opponent bets $4 into $10 pot. What should you do? If you don’t have any weighty proofs that one or another action from your side will be better than the other, just stick to the poker math and you’ll find the correct answer.

An example of using poker math

You should assess the likelihood of your opponent bluffing or having the weaker hand for starters. Let’s assume:

  • Our opponent plays aggressively and likes to bluff. We will have better hand on showdown once in three times.
  • That means, that the chances of getting the strongest hand for us equal 1 to 4
  • Thus, our odds to losing are 3 to 4
  • That means that we will lose 3 times and win 1 time (3 to 1)

As a result we can calculate that if we will call and have the best hand, we will win $14 per hand, but if we will call and lose, then we will lose $4 three times. Thus, if we will call every time we will lose $12 every 4 hands (3 x $4) and win $14. Net income will be $2. That’s how with the use of simple poker mathematics we have determined the profitability of the action.

Few nuances about poker math

A key moment that you should remember when using mathematics in poker is that decisions you made on the poker table will have no impact on your winnings short term.

Just because you have correctly calculated your winning odds in one specific hand and made a correct call doesn’t mean that you will win that hand. It also does not mean that you have made wrong decision if you had lost. If you will continue to make correct decisions based on odds, you will surely make profits in the long run, so try not to let your short term results have an impact on your game.

Studying poker mathematics may seem difficult, but we strongly encourage you not to be discouraged, because it will help you to become a winning player in the long run.