Expected Value

  • Expected value (short EV) defines the amount of currency or big blinds won or lost when building the sum of all involved outcomes multiplied by their respective probability.
    EV, short for expected value is used to compare situational decisions to find out which decision actually results in the highest EV possible, which is called maxEV, short for maximum expected value.

    EV can be positive, zero(0EV) or negative in value.

    It is the goal in poker to always play your hands maxEV, meaning to achieve the highest possible expected value against your specific opponent, while also trying to reduce the EV of that opponent to the smallest value possible.

    While EV can be either calculated in blinds or currency, $EV is a strictly monetary statistic used to see the monetary value of a hand or hand sample based solely on equity value mulitplied with the potsize when all-in. Players like to call $EV also true winnings or variance free winnings, meaning the statistic's value reflects what the player is winning or losing if variance is no longer part of the equation for the hand or hand sample for allin-situations.

    To calculate EV, you need to sum up all possible results multiplied by their probability (P(result)) with the amount to be won in that possible result.

    EV = P(result1)* amount1 + P(result2) * amount2 + ... + P(resultx) * amountx

    A street hustler is hiding a small ball in his fists after shuffling the hands behind the back. The player has to bet $1 to play, if he chooses the right fist with the ball, the player wins $2, if he chooses the wrong fist he loses his wager.

    In order to determine the EV for the player, we need to know the probabilies and the amount to be won if that result happens.

    So it is easy to see that the player has a 50% probability to choose the right fist. If the player choose the right fist he gets $2 from the hustler, netting a $1 win. If he chooses the empty fist he loses $1.

    So EV= .5 * $1 + .5 * -$1 = 0

    In this case the players EV is exactly zero for playing this game.

    Interestingly the same is true for the hustler. So be suspicious about street hustlers! ;)

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