Calculating Expected Value

Introduction to Maths & Expected Value (EV)

Poker is a game of skill.  A number of poker players make great careers out of the game professionally.  If poker were just a game of luck, we would see a more extensive list of winners in major tournaments such as the WSOP and European Poker Tour. 

Pro poker player Phil Hellmuth has a record 11 WSOP bracelets, however if the tournments he played in were just a game of luck it would be literally impossible for him to have won this many titles.  Statistically he’d less than a 1/2,000 chance of winning each title – not to mention 11.  Thus, since we can conclude poker is not just a game of luck we can now look at one of the most important cocepts of winning  poker strategy – expected value.

What is Expected Value?

Expected value is a mathematical concept every professional poker player applies to his game to make profitable decisions.  When an opponent raises a pot in poker your decision whether to call or fold is more or less completely dependant on expected value.  This is the calculation of whether the probability of winning a pot will make a call profitable in the long-term.

Calculating Expected Value in Poker

To calculate the expected value of a hand in poker we need to take into account the price of entering a pot, the probability of winning it (for example hitting a draw) and the value of the pot overall. The formula for expected value in poker is:

EV = (Size of Pot x Probability of Winning) – Cost of Entering it.

Example Calculating EV in Poker: Let’s say we have a pot worth $50 and it’ll cost us $10 to enter it.  The chances of winning the pot are 25%.  That means using the formula above, the expected value of entering the pot will be 60*0.25 – 10 = $5.  Because the number is positive (5>0), we can say that it will be a profitable decision to make in the long term.

Most importantly, the use of expected value as a mathematical guide in poker requires more than just learning the formula.  For example,when you’re playing a No Limit Holdem cash game and have a drawing hand you’ll need to know precisely what your chances of completing your hand to win the pot are (aka counting your outs).  You’ll therefore need to learn how to calculate your pot odds and “outs” in poker.

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Related posts:

1. Calculating Pot Odds
2. Calculating Win-Rate in Cash Games
3. Mathematics & Poker