The Importance of Probability and Math in Poker

Last Updated on December 12, 2019 Author:Adrian Sterne

poker mathsWho said that maths doesn’t have everyday applications?

One of the most entertaining and compelling examples is the connection between maths and poker. Did you know that maths plays a vital role during poker tournaments? Is it possible to be a great poker player without integrating maths into your game?

We’ll answer both of these questions and more as we go over the topics like:

Pay close attention as we discuss how significant probability and maths are for the game of poker.

The Maths Behind Poker

While knowing maths may not be sufficient to get you all the way to the finals of WSOP, it can certainly give you an edge over those who don’t use it.

In the long run, poker is not a game of chance. There’s more to it than Texas Hold’Em — one of the most played poker variants in the world. Poker involves making calculations and combinations, much like in a game of bridge.

Luck doesn’t prevail in poker, but rather a perfect mastery of your emotions, the richness of combinations employed, and a dash of well-placed opportunism.

So, could poker be considered one big maths puzzle? Can maths really help you win at poker?

Is It Vital to Learn Maths to Play Poker?

Poker doesn’t have to be a complete gamble. There are several maths lessons that you can apply to poker.

To begin with, it’s a question of calculating the probability of the pot and considering questions like “How likely is it that I win this poker hand?

You cannot escape from the aspect of probability, as it plays a crucial role in poker. Good knowledge of numbers provides an essential basis for being a good poker player. So, the feat of maths is illogical at the poker table.

There will always be those, especially older players, who will try to convince you that poker is, above all, a game of perception, and that intuition counts for everything.

While you don’t have to be Einstein to play poker, this is not a piece of advice to be followed blindly. Letting your gut feeling determine your chances of winning a big pot will not help you prevail. Why? Because, in poker, everything revolves around numbers — it’s a purely mathematical game.

This concept might seem a little odd to non-poker players, but the key lesson is this — in poker, the most important thing to know is the probability of a specific draw appearing based on the cards you’re holding.

You can start off implementing this lesson by playing poker online and see how you do.

Maths and Psychology in Poker

If poker is merely a game of chance, it wouldn’t be one of the most popular card games in the world.

The success in this game depends on two essential factors: maths and psychology.

It certainly is possible that all the great mathematicians in history have had a slight advantage over their opponents. Among the maths geniuses who played poker are players like Paul Magriel, Andy Block and Chris Ferguson.

John Forbes NashPoker professionals have all heard about John Forbes Nash (played by Russel Crowe in the movie “A Beautiful Mind”). He was a specialist in game theory and someone who solidified the connection between poker and maths.

Nash was awarded a Nobel Prize for Economics in 1994 for his brilliant work on the Mathematics on Game Theory.

A Game Theory is a field of applied mathematics that focuses on analysing situations in which players make interdependent decisions. Nash thought that through this interdependence, one player’s choice would have a knock-on effect on the next player in line. Once one player makes a move, the other one will then consider the opponent’s possible decisions when formulating his or her own steps.

Basic Maths Principles in Poker

The maths principles generally applied to poker are straightforward and accessible to most people. Here are the most important ones:

  • The main context of the poker game is that there are 52 cards in a pack, and 13 in a suit.
  • There are the probabilities and the odds — these are must-know concepts to know your way around poker. One simple rule of thumb can give you an idea of your draw’s chances: Multiply the “turn” and the “river” — the “outs” on the flop. By knowing your outs, you can calculate the chances of getting one in the cards still in play that will give you a strong hand and a winning combination.
  • Calculate predicted gain (life expectancy): This is the probability of a profit which a specific bet can bring you. It may be positive or negative. When you calculate this chance, you anticipate potential changes in the situation, and therefore determine your actions and style of play.

As an example: If you toss a coin, you may bet $1 on tails, and the same amount on heads. The odds are then 1:1.

The mathematically predicted income is then zero because it is unlikely that you will either be behind or ahead, regardless of how many times you toss the coin.

How can you calculate the predicted gain? By subtracting your bet in the pot from the probability of winning the pot. If the result is negative, you have a theoretical chance of winning, but those odds will decrease the more you play. If the result is positive, then you have a higher chance of winning in the long run.

Maths Is not Everything in Poker

Keep in mind that learning maths lessons won’t 100% guarantee your success in poker. You must be aware that poker is a game where you never have all the information necessary to be 100% certain that you’ll win the hand.

Maths can be counterproductive if you neglect things like experience and intuition. All it takes is one slight mistake, and no math knowledge can help you during the rest of the poker game or the tournament.

If there is one thing to realise here, that would be that maths doesn’t help with all the facets of the game. It can, however, help you anticipate the profitability of risk in your poker game over the long term.

Useful Maths Skills in Poker

Percentages and probabilities 

A good poker player knows that they have 3 to 1 odds of having a flush on the top, and 8 to 1 odds of having 3 of a kind.

Pot odds 

Every good poker player knows how to calculate pot odds, as this is an essential factor in making decisions in poker.

Pot odds are basically the link between the pot size and the size of the stake. For example, if there are $20 in the pot and you placed $5, the odds are 4:1.

If you placed a $30 bet in the $60 pot, then the pot is at 2:1.

All of this may sound daunting at the beginning, but it gets easier as you gain more experience. Nevertheless, calculating the pot odds is essential for being a successful poker player in the long term.

Regardless of the outcome, you should always be aware of the pot.

The importance of outs

An out is one of the cards that could potentially improve your hand. How to calculate it? By multiplying your hand by two, then adding two, and you get the chance of landing a fantastic poker hand.

Final Thoughts

Figuring out equity is very important, yet quite easy to master and should come fairly quickly and naturally once learned and put into practice. Knowing this stuff helps you make better decisions in poker because you’ll eventually be playing against players who know it inside out, and realise that you don’t stand a chance against them, at least not in the long term. You don’t want Norman Chad laughing at you on TV someday for not knowing your equity in a specific hand.

What do you think, does knowing maths and probability indeed help or not? Let us know what you think about all of this in the comment section below.

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Hi, I am the Chief Editor of, this site is dedicated to all thing poker. I have been working around the poker industry for the last 15 years, with different brands. The main purpose of this site is to keep you uptodate with the industry and offer you the best deals around.

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