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Calculating Expected Value in Poker

Introduction to Maths & Expected Value (EV)

Poker is a game steeped in skill and strategy, and in order to be successful you need to be able to make profitable calculations when it comes to calling re-raises and betting into pots.  If poker were just a game of luck and chance, then without any strategy we would see a more extensive list of winners in major tournaments such as the WSOP and European Poker Tour.  Phil Hellmuth, for example, has a record 11 WSOP bracelets, but if the tournments he played in were just a game of luck then it would be quite frankly impossible for him to have won so many times in such large fields.  Statistically, he’d have 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, and is in fact riddled with mathematical calculations and decisions, we can now look at one of the most important cocepts that sets the foundations for profitable poker strategy – expected value.

What is Expected Value?

Expected value is a mathematical concept used to judge whether calling a raise in a game of poker will be profitable.  When an opponent raises a pot in poker, such as on the flop or river, 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.  For more information on making ev poker decisions, you can visit the

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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