Poker Probabilities

Calculating Poker Probabilities

To calculate the probabilities for any poker game a player will only have to use simple calculations and two basic approaches to the subject.

The first approach is that of possible outcomes, which involves dividing the number of outcomes that satisfy a given condition by the total number of outcomes possible. In the case of Texas Hold'em for instance, six outcomes are possible for a player to be dealt a pair of aces. Players have 52 ways to pick the first card, 51 ways to pick the second card, and 2 ways in which to arrange the cards (A, A), which yields a total of 1,326 possible outcomes. So the probability in this case is 6 divided by 1,326 or 1 divided by 221.

The second approach is that of conditional probabilities. In complex poker situations, this approach is also referred to as a decision tree. Players can be dealt an ace in 4 ways. Since there are 52 ways to pick the first of these 4 aces, the probability is 4 divided by 52 or 1 divided by 13. For the remaining 3 aces, there are 51 ways of picking the second ace, which makes the probability equal 3 divided by 51 or 1 divided by 17. The product of 1 divided by 13 and 1 divided by 17 or 1 divided by 221 is the conditional probability of getting 2 aces in this case.

It is important that poker players are careful when deciding on the best approach for a particular problem they are facing with the cards they have been dealt. Estimating poker probabilities requires quick calculation right in the middle of a poker game and as a result many poker players only calculate the probability for particularly important hands. Other players opt to use poker probability software systems to help them make their decisions.

Knowing the Difference

Beginner poker players can get a bit confused by the terms "odds and probabilities", especially when they are used synonymously by poker professionals. However, once you know how to calculate the odds for yourself, it is almost impossible to not understand what is being referred to.

Odds and probabilities are very closely related. Odds are usually expressed as the relationship between an event occurring and its failure to occur. Probabilities, on the other hand, are usually expressed as the ratio of possible outcomes to the total number of outcomes. Probabilities are commonly expressed as percentages, decimals or fractions.

To best understand the difference between odds and probabilities, consider this example.

Imagine a box containing 4 red balls and 1 green ball from which you have to select one ball.

In this case, the probability of you selecting the green ball can be calculated by dividing the number of green balls in the box by the number of chances you have of selecting a ball. So, the probability of selecting the green ball is 1/5, or 0.20 or 20 percent.

The odds that the green ball will be selected can be calculated by creating a ratio of the number of chances that you will select the green ball with the number of chances that you will not pull out a green ball but a red one instead. Therefore, the odds of selecting the green ball are 1:4.

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