The Mathematics of Poker

Poker is one of the few games of chance that is also a game of skill. Winning the game isn’t just based on which cards you get and how you play them, it’s also about how you read the other people at the table, how easily you can be read and how well you understand the game and the odds of any given move you might make. At an expert level, poker can get very complicated, but it’s possible to get close to expert without completely stretching your brain.

A lot of study has been done into the various mathematics of poker. What we are really talking about here are the odds. But this is not to say simply the odds of any given card coming up as you play. We are also referring to applying mathematic principles to the behaviour of your opponent, or the possible outcomes you may be able expect from the calculations.

Lets’ look at one example that explains the above idea. Imagine you are playing a game and you have worked out that your opponent bluffs 1 in 3 times he has the best hand on the river. Now imagine that this player has put a $4 bet into a $10 pot, and you aren’t sure whether to call or not.

This is the perfect time to look at the mathematics of it.

You already know that your opponent bluffs 1 in 3 times. This means that you know that you only have a 1 in 4 chance of actually holding a better hand. However, if you call and you win, you will win $14. On the other hand, if you call and you lose you could potentially lose $4 3 times (based on the ratio he bluffs). So over 4 games, even if he is only bluffing once, and you lose the other three games, you will still make a profit of $2. So you should definitely call.

Can you see the mathematics only make sense over the long term? You may not win on the first hand and losing definitely does not mean that you have made the wrong choice. It just means that in the long run, your time is still coming. It can take a while to get your head around but it’s well worth it, and if you want to learn more, you can read The Mathematics of Poker by Bill Chen, as this book is every serious player’s favourite.