# The poker mathematics

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#### Jeffrey | Poker Articles, Poker Mathematics

In this article, Steve gives a general introduction to the poker mathematics.

Poker is a game of fine psychology-based decision, betting and bluffing. There’s no math involved in it whatsoever, is it? Wrong! While in high-level poker the above named elements do indeed substitute the poker mathematical aspect to a certain degree, every poker player knows that there is quite of bit of math involved in the game indeed. Even players who never stop to think about the mathematical odds involved use them all the time, when making decisions which ‘feel right’ to them. “The poker mathematics” may sound a little daunting, but once one gains a grasp on what these odds are about it becomes pretty simple.

The bottom line about the poker mathematics aspect of the game is the comparison between the pot odds and the hand equity which gives the player a mathematically correct way to proceed. Basically, what one does is that he/she calculates his/her pot odds and then compares it to his/her odds for making a potentially winning hand. The first stage of the move is to calculate your pot odds.

Suppose you’re playing for a \$40 pot and the player in front of you makes a \$10 bet. It now costs you \$10 to tag along for the ride, and to possibly take down a \$50 pot. It basically costs you \$10 to gain a shot at a \$50 pot, which means your pot odds are 50-10 = 5-1. In order to find out your pot odds, always divide the current size of the pot (make sure you take all bets and raises occurring in front of you into account) with the amount you’re required to call to stay in contention. The bigger the pot odds, the better off you are, because  the bigger these odds are, the weaker the hand you can afford to make the call on.

According to Sklansky, the pot odds can be exaggerated in such a way that it becomes a viable choice for players to make the call on just about any two cards. Obviously, this can actually be proven mathematically too.

The next step of your odds escapade is to find out your hand equity. Suppose you’re looking to make a flush, a hand which you’re pretty certain would win the pot for you. In order to find out your hand equity (or the odds against your draw filling up), you need to take your number of outs into account. I’ll give you a simple example to make things easier to understand: you have a 4-card flush on the flop. You have the above situation on your hand, with the 5-1 pot odds. You know that a flush would win you the pot, what do you do? First, you calculate your number of outs: there are 52 cards in the deck, of which 3 are on the board face-up and 2 are in your possession. That leaves 52-5=47 cards. There are 13 cards of the same suit as your 4-card flush, 4 of which are already revealed. That leaves you with 9 outs. Of the 47 remaining cards, 9 will help you hit your flush and 47-9=38 will not. That means the odds against your flush filling up are 38-9. That leaves you with 4.22-1 odds (remember that these odds are against your flush), which are smaller than the 5-1 pot odds, which means it is mathematically correct for you to make the call here.

When counting your outs, make sure you take ALL your outs into account (you may have cards which could hit you for a straight or maybe even a set in the above situation), and to disregard all your anti-outs (cards which would hit your opponent for a better hand than yours).

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