Poker Expected Value (EV)

The goal of is to help people make money. And while gambling is generally not the path to wealth, we can’t deny that certain forms of gambling — executed correctly — can be very lucrative. And with poker becoming so popular this past decade, I’d be remiss by not at least touching on the subject of how to make (more) money playing poker. If you’re not a gambler (and that’s a good thing) and if you don’t understand the basics of playing, you probably won’t find this article to be very useful or interesting.

Skilled poker players who have a solid grasp of the basics and also understand the mathematics of the game can earn large sums of money by playing against less-skilled opponents. And one of the key mathematical components of the game is called Expected Value (or EV). Understanding EV is one key to becoming a consistently successful poker player.

What is EV

EV stands for “Expected Value”, and is the amount of money you can expect to earn in the long run by making a specific decision in a specific circumstance.

Using a non-poker example, imagine flipping a coin with two betting scenarios:

  1. You bet on the outcome, and receive even-money (i.e., you bet $1, you will win $1) on your bet.In this case, if you flip the coin 100 times, you can expect to win 50 times, and expect to lose 50 times. Overall, you win $50, and lose $50, to break even. You have neither won nor lost any money (and in the long run you will not expect to win or lose any money), so your EV is 0.
  2. You bet on the outcome, and receive 2:1 odds (i.e., you bet $1, you will win $2) on your bet.In this case, if you flip the coin 100 times, you still expect to win 50 times, and expect to lose 50 times. But, the 50 times you win will earn you $100 (50 * $2), and the 50 times you lose you will still only lose $50. So, over 100 flips, your profit will be $50, or an average of $.50 ($50 / 100 flips). Your EV is the average win/loss per event, or $.50. For every time this event occurs, you can expect to make $.50.

But remember, EV is the expected value in the *long run*. EV doesn’t relate to short-term results. In the coin-flip example, even if you’re getting 2:1 odds, you still may lose money on just a couple flips (if you get unlucky). You may even lose money on 100 flips (if you get very unlucky). But, in the long run (i.e., over thousands or millions of trials), you can expect to earn $.50 (the EV for this situation) per flip.

How is EV used in Poker?

The most common use for EV (“Expected Value”) in poker is to determine the long-term value of making a specific decision at a specific point in a hand. Generally, it’s not important to know the exact EV of a situation (in fact, with all the variables and unknown in poker, it’s generally impossible), but it is important to know whether a situation is +EV (i.e., you’ll make money long-term) or –EV (i.e., you’ll lose money long-term). It’s also generally helpful to know if a +EV situation is very +EV (i.e., you’ll make a lot of money long-term) or marginally +EV (i.e., you’ll make a little money long-term).

Here’s a simple example of figuring out if you’re +EV or not…

You’re in a hand, and on the river, you have two pair. Your opponent bet $100 into a $100 pot, and it’s your turn to call or fold (let’s ignore the raising situation here).

You know that you are getting 2:1 odds on making a call (if you call $100, you can win $200), which means long-term if you call, you need to win more than 1 out of 3 times to be +EV (if you do the math in example #2 above where you’re getting 2:1 odds but you only win 1 out of three times instead of 1 out of 2 times, and you’ll see that in that case your EV is 0, so if you win more than 1 out of 3 times, it’s +EV).

So, you know you need to win more than 1/3 of the time to be +EV, so how do we calculate that? This is where poker skill at reading your opponents comes in. Let’s assume you believe your opponent has one of four possible hands (flush, straight, one pair, or a bluff), and you think the likelihood of each of these possible hands is as follows:

  • Flush: 35%
  • Straight: 25%
  • One Pair: 20%
  • Bluff: 20%

Based on those numbers, you know that if you call, you believe you have a 60% chance of losing the hand (to a straight or flush) and a 40% chance of winning the hand (over a pair or a bluff). You believe you will win the hand 4 out of 10 times (or about 1.2 out of 3 times). Since you previously determined that you needed at least a 1 out of 3 chance of winning the hand to be +EV, and you now believe you have a 1.2 out of 3 chance of winning the hand if you call, making the call is a +EV decision.

Keep in mind that doing this one time will likely result in losing money (you are not favored to win the hand), but doing this lots and lots of times will result in profit (the times that you do win, you will win more than enough money to offset the times that you don’t).

So, what if you wanted to figure out the exact EV of this situation, instead of just whether you were +EV or not (this can be important, because in some situations – like tournaments – you may want to pass up a marginal +EV situation if you think a bigger +EV situation will arise later)? Here you go…

You know that in the example above, over 100 iterations, you will win 40 times and lose 60 times. The 40 times you win, you will win a total of $8000 ($200 in the pot * 40), and the 60 times you lose, you will lose $6000 ($100 that you call and lose * 60). Total profit over these 100 trials is $2000, or $20 per trial.

Your EV is therefore $20 if you call.