Can you give me an example of how to calculate expected value?

[Mike_25]

Say you call a $10 raise on the turn with 20 outs to make your flush. There is $50 in the pot. You need to calculate if calling $10 EV is sound.

Your outs are 50% to make the flush, so you have 20/50 = 40% equity. $50 pot + $10 call = $60 total pot.
40% of $60 is $24. So the $24 EV of winning the $60 pot outweighs the $10 you call.

However, the opponent also has outs, so the $24 EV is high. But with position, their outs are fewer. And if they don't call a large raise, it's unlikely they have a flush draw.

You calculate all this quickly at the table. The math shows $14-$20 EV to call here, so the $10 call maintains positive EV. Fewer outs or a larger pot size would make the call much stronger. Luck still plays a role, but positive EV is your guide.

 

[Baniro]

Sure! Let's say you are playing a simple dice game where you roll a fair six-sided die. If you roll a 1, 2, or 3, you lose $10, but if you roll a 4, 5, or 6, you win $20. To calculate the expected value of this game, you can use the following formula:

Expected Value = (Probability of Outcome 1 × Value of Outcome 1) + (Probability of Outcome 2 × Value of Outcome 2) + ...

Now, let's calculate the expected value step by step:

Determine the probabilities of each outcome:
The probability of rolling a 1, 2, or 3 is 3/6 or 1/2 (since there are three favorable outcomes out of six total possibilities).

The probability of rolling a 4, 5, or 6 is also 3/6 or 1/2.

Determine the value of each outcome:

If you lose, the value is -$10.

If you win, the value is +$20.

 

[Dallax]

Let's say you are playing Texas Hold'em and you are dealt pocket aces (AA). The flop comes 10-J-K, all of which are suited. You have the best possible hand and you are almost certain to win the pot. In this situation, the expected value of calling a bet is very high. The probability of winning the hand is very high, and the amount of money you will win if you win is also very high.