Expected value ( EV ) tells you on average how much money you can make or lose.
Example with dice: You roll a six-number dice. If the number 6 comes up, you get €18, if another number comes up, you lose €3. The question is: Is it profitable for you to play this game ?
6 out of 6 will fall once, so the probability is 1/6
Five times out of six another number will come up, so the probability is 5/6
On average, you will earn 1/6 * €18 = €3 and lose 5/6 * €3 = €2.5. So on average you will earn €3 - €2.5 = €0.5.
So, the answer is: EV = €0.5, in other words: every time you roll the dice, you earn €0.5 on average, and it's profitable for us to play this game.
Example in poker:
Let's say you are holding it in your hands:
500 euros in the pot, flop:
Your opponent bets €200 all-in into a pot of €500. Total in the pot:500 + 200 = 700 euros. And the question: is it profitable for you to call and make a call of 200 euros if you believe he has two boys ?
Let's take a look at PokerStars Equilab how likely it is to win:
And we can see that about ~33% will win and ~67% will lose. If we win the pot we win a total of €700, and if we lose, we lose €200. So 33% will win 700 euros and 67% 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, making a call, we will earn 97 euros on average.