Poker Mathematics

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Jeffrey | Poker Mathematics

This article is a part of the Poker Mathematics series.

Being a good enough poker player to generate money playing online is about mastering several aspects of the game. The rules of Texas Holdem (or even Omaha) are deceitfully simple. From learning how to play the game to becoming a pro there’s a lifetime’s learning of a distance though.

In order to master the game, a player needs to be in complete control of its mathematical aspect, as well as its psychology and strategy sides. Mathematics is a very important part of being successful in poker and it does give beginners a pretty good guidance regarding the quintessential question in poker: should I call, should I fold or should I raise?

As soon as you sit down to the table and you realize where you are in relation to the dealer button, mathematics floats into the picture.

The mathematical odds that you get for your starting hands are deeply influenced by your position at the table. If you are under the gun or in a different early position, you should tighten your starting hand selection because the odds that you get for a K, J for instance are not the same as the ones you get for the same hand on the button or in the cut-off.

Starting hand selection is about math as well. Not all starting hands were created equal as some stand a higher mathematical chance to win than others. Correct starting hand assessment takes position into account, but pot odds need to be considered too.

Aggressive preflop play is about mathematics as well. Its aim is to drive out as many players as possible or to make them call and fold on the flop, thus leaving dead money in the pot.

The fewer players there are in a hand (the more you manage to chase away through aggressive preflop betting), the better the odds will be for every single hand that remains in the game. Players who leave dead money in the pot alter the pot odds, and thus they act to increase the odds for those who remain in the game.

Making the correct call has a very clearly defined mathematical side to it. In order to find out whether or not one needs to call a raise, to fold a hand or even re-raise, all he/she needs to do is to compare the odds of making a potentially victorious hand, and the pot odds. The pot odds are easy to calculate.

All our player needs to do is to compare the number of chips in the pot with the number of chips it takes to make the call. If there are $50 in the pot and the bet he’s facing is a $10 one, the odds are 5-1.

He needs to calculate the odds of making his hand (let’s say he has a 4-card flush on the flop). Taking all the cards already on the table into account, as well as the remaining outs, the odds of hitting a flush on the turn are 4.22-1 against. Since this number is smaller than the pot odds themselves, it will make sense for our player to make this call, but not a re-raise, since that would ruin the pot odds for him.

Mathematics can give you a clue or two about what calls you need to make, however, a large part of poker is about psychology and about putting opponents on hand-ranges based on their behavior and betting patterns. That’s where the mathematical element blends into the inexact science of psychology and behavior assessment.

Another wonderful example of how mathematics works in poker is rakeback. In real money play, you pay a rake on every single hand to the poker room. That is how the latter makes its revenue.

Rakeback gives you a certain percentage of that rake back.

Using simple mathematics one can easily prove that sign-up and other such limited-validity bonuses are in fact the equivalent of a rakeback deal, only they carry the rather overwhelming disadvantage that they expire over time.

Post By Steve.

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2 Comments to Poker Mathematics

Mark
October 9, 2008

Hi Steve

Nice overview about the mathematics involved in poker!

Chetan
March 13, 2009

A very clear and concise article. Does mathematical probabilities really increase the chances of winning?

Regards,

Chetan

Chetan’s last blog post..Learn Poker Advanced Strategy | Internet Poker Guide | Tips

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