How to Calculate the Expected Value in Poker?

Expected value (EV) in poker is the mathematical expectation, the possible benefit from the game. The EV value is directly proportional to the number of winnings that you can receive. This indicator is extremely important over long distances and is taken into account by most professional poker players.

How EV Is Calculated

To determine the expected value, it is necessary to multiply the result after the occurrence of a certain event by the probability of its occurrence and add up the obtained figures for all such events.

In other words, EV is the sum of the results of the probabilities of events and their outcomes. Let’s calculate the expected value of a coin toss and a \$1 bet between two participants.

The probability of getting both heads and tails is the same – 50 to 50. What is the possible benefit for each player with each coin toss? According to the definition of EV, we have the following numbers: (\$1 x 0.5) + (- \$1 x 0.5) = \$0.

Provided that the game is played fairly, and even if one side of the coin is accidentally dropped more than 10 times, the final result, in the long run, will still have zero mathematical expectation.

EV in Poker: Practical Case

Now let’s look at a situation that often occurs at the gaming table: is it worth making a flush draw and in what cases it is profitable. The initial conditions are as follows:

• We have an ace and 10 suited on the turn.
• There are two cards of our suit on the board (we have a flush draw that is one card short).
• The pot has \$100, and the opponent brings in another \$50, going all-in.

Should we call this bet? Since the probability of making a flush is about 4.1 to 1, we will take the figure in the form of 20% or 0.2. Accordingly, the chances of not collecting a flush will be 80% or 0.8.

So, EV = (+ \$ 150) * 0.2 + (- \$ 50) * 0.8 = (\$ 30) + (- \$ 40) = – \$ 10

The solution clearly demonstrates that the best option in the long run is to fold, otherwise, we will periodically lose our bankroll.

The whole point of poker is to maximize profit with good hands and minimize losses with bad hands. Armed with the calculation of expected value, you move to a new level. Many players cannot constantly make the most of the situation at the table, and, therefore, you have a chance to use this for your purposes. This will strengthen your strategic line of play, and also allow you to lose less in adverse situations.