# How to Calculate EV?

Expected value, known as “EV”, is the expected return based upon the average result of an infinite number of repetitions. The classic example used to explain this is a coin flip. With 2 possible outcomes the statistical probability is 1 to 1. An even money wage would give you a neutral expected value however, if you were given 4 to 5 odds or better it would be a positive expected value, EV+. Flipping a coin 10 times will not necessarily wind up with 5 instances of heads and 5 of tails. The mathematical theorem of the Law of Large Numbers, “LLN”, states that over a large enough sample the results should be closer to the average mean. In poker we call the times of variance either “running good” or “running bad”.

To calculate the EV of calling a bet or raise, with a drawing hand, you would use the following formula:

- Count your “Outs” to calculate the odds of making your hand, based upon the number of community cards left to be dealt. For example, you have a 4 flush on the flop. Since there are 13 cards of each suit in the deck and you know about 4 of them, there are 9 remaining “Outs” that will make your hand. With 2 cards yet to come there is a 35 % chance of hitting 1 of the 9 remaining outs and making a flush.
- Compare the amount of money that you are required to call to the size of the pot. If the pot has $200 in it and you need to call a $50 bet, then you are getting 4 to 1 on your money.
- Put the 2 calculations together. Statistically you will make your flush, a little more than, 1 out of 3 times. You are getting paid 4 to 1 on your money. If you ran the identical situation over a long enough period of time, you would wager $50 for 3 of the hands for a total of $150 and would win once bringing in $200. This situation is obviously a call with an expectation of a positive return so it would be a positive EV play.

The idea is to make decisions, at the poker table that will bring you the highest implied odds. There will not always be a decision that has a positive EV, in which cases you should make the decision with the lowest possible negative EV. When you calculate your EV make certain to consider any future wagers that you might have to make in the hand and any additional calls that you can get in the event that you do make the hand.

Expected value is also used in other types of situations that occur at the poker table. Bluffing is a good example of this. With the knowledge that you have of your opponent, you have determined that making a pot sized bluff of $300 will cause your opponent to fold 3 out of 4 times. Based upon an average return you would win 3 x $300 for a total of $900 and lose 1 bluff of $300 making the bluff a positive EV play.

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