Expected value in a Poker Game

Expected value (EV) tells you, on average, how much you can make or lose.

Example with dice: You roll a six-figure dice. If the number 6 falls, you get 18 euros, if you fall another number you lose 3 euros. It’s a question: Is it profitable for you to play such a game?

Solution:

One out of six will fall 6, so the probability is 1/6

Five times out of six the next number will fall, so the probability is 5/6

You will earn on average: 1/6 * 18 euros = 3 euros and on average you will lose: 5/6 * 3 euros = 2.5 euros. On average, you earn 3 euros – 2.5 euros = 0.5 euros.

So, the answer is: EV = 0.5 Euro, in other words, every time you roll a dice you earn an average of 0.5 Euro and it is profitable for us to play such a game.

Example poker game

Let’s say you hold it:

Pot 500 Euro, Flop:

The opponent bets € 200 All – in on the € 500 pot. Total in the bank: 500 + 200 = 700 euros. And the question: is it profitable for you to answer and call 200 euros if you believe he has two boys?

Solution:

Here’s a look at the PokerStars Equilab program:

And we see that ~ 33% will win and ~ 67% will lose. If we win the bank we win a total of 700 euros and if we lose we lose 200 euros. That is 33% we will win 700 euros and 67% we will lose 200 euros. The formula is: 700 * 0.33 – 200 * 0.67 = 97 euros. Answer: EV = 97 Euros, in other words, if we play in this situation, make a call, we will earn on average 97 Euros.