# What is Expected Value and How to Calculate It

Expected Value (EV) in Poker describes whether a bet, call or raise has a positive or negative monetary outcome over time. The use of randomly dealt cards in poker means chance has a big influence on any individual hand. EV calculations are thus performed over a large sample to balance out these chance factors. For example a pair of aces will win against a pair of kings all-in pre-flop approximately 80% of the time – the EV of your \$10 all-in bet with aces is thus \$8 regardless of whether a king comes on the flop to beat you this time.

Expected Value calculations can be used to assess whether a particular starting hand has a positive or negative dollar value on average when playing heads-up poker. Hands will rarely be all-in before the flop heads-up so these calculations are performed over a large samples – accounting for different levels and playing styles.

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The following hands have a positive expectation against an equally skilled opponent in heads-up poker:

* All Pairs AA-44
* Off Suit Hands Containing An Ace down to A-7 off.
* All Suited Hands Containing An Ace
* Kings down to K9 off-suit or K5 suited
* QJ, Q10 and J10 off-suit
* Suited Queens and Jacks down to Q5s and J7s

EV can also be used in conjunction with both pot-odds and implied-odds to work out whether a bet or call during a heads-up poker game has a positive or negative value over time. This can also be used to assess whether a bluff or semi-bluff when you hold a drawing hand (for example a flush draw) would be profitable. The examples below show how to calculate your EV in each of these situations.

Your opponent has bet \$5 into a pot of \$20 after the turn in a heads up match. You have 2 spades in your hand and there are 2 on the board. You expect that your opponent has a pair and that making your flush will win you the hand. What is the EV of making this call?

Here you are calling \$5 to win the \$25 in the pot – your pot-odds are exactly 5/1. The chance of making you flush is approximately 4/1. Taking 5/1 odds on a 4/1 chance has a positive expectation, that is it will show a profit over time. Here the EV is calculated as a fraction of your \$5 bet – 4 times you will lose \$5, once you will win \$25 for an average profit of \$1 per attempt. The expected value of this call is thus \$1.

Taking implied odds into account make this potentially even more profitable. This describes the future bets that you might win if you make your hand. In this example we might expect to make another \$10 on the river betting round – increasing our EV to \$3 per attempt.

Finally EV can be calculated when you are semi-bluffing with a flush draw. This calculation is slightly more complex as we need to factor 3 outcomes – that your opponent folds, that he calls and you win, and that he calls and you lose. You have a flush draw with 1 card to come, making your chances approximately 4/1 of hitting your hand. The current pot is \$100 and you bet \$50 as a semi-bluff. Here is how the EV calculation might look if you estimate that your opponent folds 50% of the time.

50% Fold – Your Expectation = +\$25 (half the time you win \$100 and half lose \$50)
12.5% Opponent Calls and you win - +\$200
37.5% Opponent Calls and you lose = -\$50
So (50*\$25)+(12.5*\$200)+(37.5*-\$50)/100 = +\$18.75

The combined chances of your opponent folding and you winning the hand make this a positive expected value play. Note that both the bluff alone and winning chances alone would have been unprofitable!