Pot Odds and Hand Distributions

There are three books over the history of poker that have truly revolutionized the game. In the early stages of poker, there was "Super/System" by Doyle Brunson. Doyle's book was the first to show people that poker was really a game of skill, rather than entirely a luck game like craps or roulette. In the modern era, Dan Harrington's "Harrington on Holdem" gave millions of players tools for winning poker tournaments that they weren't aware existed before. In between came "The Theory of Poker" by David Sklansky. Sklansky was one of the first authors to really look at the game mathematically, and show how a mathematical approach could lead to successful poker consistently.

One of his most important mathematical concepts was the concept of pot odds. Pot odds determine whether it is mathematically correct to stay in a hand. If the pot is $45 and the bet is $15 to you, you are being offered a 45-to-15 or 3-to-1 proposition. If you think you have a better than 3-to-1 chance of winning the hand, you have an easy call.

However, it's not always easy to know your chance of winning a hand. You might know that you are 35% to make your flush after the flop. This calculation is done in the most basic poker variations even in video poker. But what if it's a low flush and you know your opponent likes to play draws? What if the flop is jack high and you hold an ace? Will you win if you hit that ace or does your opponent already have two pair or a set? This is where hand distribution comes into play.

Using pot odds with hand distributions means you are putting your opponent on a likely range of hands. For example, in one situation you might say: In this particular scenario, this opponent is likely to hold 88-AA, Ax of hearts, AK or AQ with one heart, or two small hearts. Against that range of hands, I am 25 percent to beat the pairs, 75 percent to beat the one heart hands, and drawing dead against the two heart hands. You would then combine your odds against each hand in the range to create a rough estimation of your likelihood of winning the hand. Compare these to the pot odds to know whether you have a call. While it is difficult to make exactly this calculation while in a game, making a rough guess with this goal in mind is likely to result in better decisions.