# Beginners guide to Poker Expected Value

30 Aug 2022
• Find out about Expected Value in Poker
• Learn how to calculate EV) at the poker tables!
EV, or Expected Value, is a term used in poker to refer to the potential outcomes of a hand.

If you were to play a certain hand infinitely, what should you expect as the result? To help clarify this idea, and keep it easy to understand, consider flipping a coin.

When you flip a coin there is a 50% chance it will land on heads and a 50% chance it will land on tails.

If you and a friend decided to start betting on a coin flip, as a coin will land on each side half the time, you would both expect to win 50% of the time. As you both are going to win as often as you lose, the Expected Value (EV) of the bet is \$0.

The expectation is to simply break even if you kept flipping the coin infinitely.

EV becomes important in understanding if something is a good or bad bet. In the coin flip example above, if your friend had offered \$1 each time you win but you would lose \$2 every time you lost, EV can be used to show why this is a bad bet.

On average, every 2 flips will have 1 head (you win \$1) and 1 tail (you lose \$2) with the net result being you lose \$1 every 2 flips. From this you can find that your EV is -\$0.50, or a loss of \$0.50 per flip.

A negative EV is always a bad deal and not a bet anyone should ever accept.

The reason why this concept is important is in poker, as long as you only make plays that are positive EV, you will be able to make money in the long run. You will find the opposite results if you consistently make negative EV plays. This is the same as flipping a coin; however, unlike the coin flip which is completely random, you can avoid a lot of the plays that would lead to negative EV results.

Aces vs Kings

Obviously, having Aces or Kings will make you happy. Naturally you want to play a big pot and win as much as possible, but how should you play this hand? What should you do in this case? Betting your hand, raising when against a bet, or even going all in against re-raises is the generally accepted strategy as either hand is strong enough to go all in pre-flop.

If you do go all in pre-flop with AA and get a call from someone holding KK, how much money can you expect to make? What is your EV?

To keep things simple using the CardPlayer Odds Calculator, Aces should win 81% of the time compared to the Kings (19%) when we get it all in pre-flop.

Poker is a game of incomplete information and these percentages change as more cards are exposed. We know that we will win 81% of the time, but what does that mean for our bankroll?

As an example, lets say you and your opponent both have \$50 in your respective stacks and go all in pre-flop with the hands above. This creates a total pot of \$100. We know that our Aces will win 81% of the time and lose 19% of the time. This means our EV for this hand is \$81 – we win the \$100 pot 81% of the time. Remember that your expected value is simply your odds to win multiplied by the current pot.

If you and your opponent bet \$100 each for 100 hands, with you holding AA and your opponent having KK, your EV would be \$16,200 for a profit of \$6,200.

• Your Bet: \$100 x 100 hands = \$10,000 total wagered
• Your Opponent: \$100 x 100 hands = \$10,000 total wagered
• Pot Total: \$20,000