How do you calculate your expected value in a hand of poker, and why is it important to know this?

Expected value, or EV for short, is a mathematical calculation used in poker to determine the average amount of money a player can expect to win or lose on a particular hand. By calculating the expected value of a hand, a player can make more informed decisions about whether to continue playing or fold, and can ultimately improve their chances of winning in the long run.

To calculate the expected value of a hand, a player needs to consider several factors, including the strength of their hand, the amount of money in the pot, and the likelihood of winning the hand based on the cards they hold and the cards on the board. The basic formula for calculating expected value is:

EV = (Probability of Winning Amount Won) - (Probability of Losing Amount Lost)

For example, let's say you are playing a hand of Texas Hold'em and you have been dealt pocket aces. There are four players in the hand, and the pot currently contains $100. You decide to raise the bet to $20, and one player calls.

On the flop, the board comes up with a 7 of hearts, a 9 of diamonds, and a 2 of clubs. You decide to make a continuation bet of $50, and the other player calls.

On the turn, the board shows a 3 of spades. You decide to bet again, this time for $100, and the other player folds. You win the pot of $220.

To calculate your expected value in this hand, you would first need to determine the probability of winning. Assuming that the other player had a weaker hand than you did, and that there were no cards left in the deck that would give them a better hand, your chances of winning the hand would be approximately 85%.

Next, you would need to calculate the amount won and the amount lost. In this case, you won $220 and lost $20 (the amount of your initial bet). Plugging these values into the formula, you would get:

EV = (0.85 $220) - (0.15 $20) = $184

This means that, on average, you could expect to win $184 every time you played this particular hand. If your expected value is positive, it means that the hand is likely to be profitable in the long run, and you should consider playing it. If your expected value is negative, it means that the hand is likely to be a losing proposition, and you should consider folding.