The importance of poker mathematics

New poker players think, that rules of poker is everything they need to start playing poker. Playing poker, but not winning money. Without a clear understanding - or at least a great natural instinct for odds, probabilities and the ratios of risk and reward - success at poker is unlikely.

However, with enough knowledge of these odds and ratios to recognize situations of positive expectation, and the discipline to operate only in an environment of positive expectation, long-term poker success is virtually assured.

To get the maximum possible value from every hand, a player need only have perfect knowledge of

• The cards yet to come
• The cards held by opponents
• The future actions and reactions of opponents.

While such perfect knowledge is never available, an understanding of odds, probabilities and basic game theory can go a long way toward telling:

• How likely it is that certain cards will appear or not appear in any given situation
• How probable it is that certain opponents might hold certain powerful hands
• How opponents are likely to act or react when examined through a Game Theory lens.

This is not perfect knowledge. It is, however, very powerful poker decision support information.

Traditionally, pot or implied odds have been compared to a player’s odds of improving his hand to calculate expectation. In the section mathematics of poker the concept of a player’s Total Odds of winning the pot is introduced. Total Odds includes not only the odds that his hand is or will improve to the best hand, but also the likelihood that the right move at the right time will cause his opponents to fold and give up the pot.

In any given poker situation, a player with a positive expectation may raise the action, and his opponent(s) will have only 2 choices:

• Continue to play at a disadvantage and for higher stakes
• Refuse the raise and forfeit the pot.

This section of the site has articles that present a practical way to combine the application of traditional poker odds and probabilities with basic game theory to give players at every level of skill and experience a crystal with prisms that will allow them to see the best and the worst of their possibilities, their opponents’ strengths and their own best courses of action.

Certain practitioners can predict, with perfect accuracy, such natural phenomena as the day, the night, the tides and even celestial events that will occur a thousand years from now.

In poker, any player can predict with that same astonishing accuracy the likelihood of any card appearing at any time. He can predict the likely holdings of his opponents and, based on his own hand, he can predict the long-term profitability of any call, bet or raise.

In astrophysics and the navigation of spacecraft, the requirement for accuracy is absolute. In poker a close approximation is all you need.

The outcome of any hand of poker is determined by either or both of the fall of the cards and the actions of the players. If the cards fall so that you have the best hand and you don’t fold, you will win the pot. If you employ a betting strategy that compels your opponent(s) to fold, your cards could be blank and you will still win the pot.

Knowledge of odds and probabilities can turn seemingly random events, such as the fall of the cards, into eminently predictable occurrences. An understanding of positive or negative expectation will tell the long-term profitability of any given play and a grasp of basic Game Theory can tell much about the likely responses of opponents.