Poker Mathematics

Poker Mathematics


Poker is a game of skill so the player having the maximum skill clearly has an advantage over others. Knowing the game theory, good understanding of the mathematics involved in Poker and the ability to read situations as well as opponents gives you an upper hand. Poker mathematics is important because it helps you to calculate the odds of your winning or losing a game. It is also used when you need to hit a card in order to make your hand into a winning hand, and you have to decide whether carrying on will give you benefit or not.

To make this decision we need to know 2 things:

1) What are the “Outs” we have i.e. the cards that will make us a winning hand.

2) “Pot Odds” i.e. how much money will we win in return for our total bet made during the game.

We then compare the likelihood of us hitting one of our Outs against the Pot Odds we are getting for our bet and see if mathematically it is a good bet. Let us look at each element individually first, then we’ll look at it together.

Number of Outs – When we are counting the number of “Outs” we have, we are actually reflecting on the fact that how many cards still remain in the deck that could come on the turn or river that we think will make our hand the winning hand. For example, you have the 10J of spades and the flop comes 4-hearts, 5-spades & 6-spades. You need a spade to make your flush which figures to be the best hand most of the time. There are 52 cards and 13 of each suit. We have 2 spades and there are 2 spades on the flop so that leaves 9 (13-2-2) remaining spades in the deck. Therefore we have 9 outs. Now, let’s assume we have 10J spades and the flop comes: 2-diamonds, Q-clubs & K-hearts. Here we figure we need to make a straight to have the best hand. We would need a 9 or an Ace to complete our straight draw. Knowing that there are four of each card we need one of 4 nine's or one of the 4 Aces. This means we have 8 outs to complete our straight draw.

Pot odds - When we calculate the Pot Odds we simply want to know how much money we will win in return for the amount of our bet made in the pot. It’s a very simple calculation:

Pot Odds = Total Pot / the Bet you would have to call

Pot odds boil down to percentages. The pot must be large enough to pay enough extra on the times you do hit your hand to make up for the losses when you don't. The key is to get your money into the pot when you have the best hand. If you use pot odds correctly, you will be well on your way to becoming a consistent winner.

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