Expected Value (EV) Explained

Paper Chase
You don't make this kind of money flipping coins. Unless you're a rare coin dealer.

Poker is all about making money. Unfortunately, making all the right decisions doesn't ensure you'll book a win.

You can play great poker and still lose, because poker is heavily influenced by luck in the short term.

However, understanding and using the concept of expected value (EV) can go a long way toward helping you hone your play.

Expected Value: What Is It?

Every decision you make at the table can be classified as +EV or -EV.

Simply put, +EV is a good choice - one that will make you money in the long term. Negative (-)EV is a bad move, or one that will lose you money in the long run.

Wikipedia has this to say about expected value:

"In probability theory the expected value of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff).

"Thus, it represents the average amount one 'expects' as the outcome of the random trial when identical odds are repeated many times."

What that means in English: expected value is the amount of money you would win or lose on average on your bet.

Alex Jacob
Yale grad Alex Jacob: Very familiar with both EV and V05.
 

If you and a friend were to bet on the outcome of a coin flip and agree that you would be paid $5 for every time it came heads and you would pay him $5 every time it came tails, you would win half the time and he would win the other half of the time.

That would make the bet a neutral EV bet.

Let's say, though, that your opponent decided he would pay you $10 for every heads but you would still only pay him $5 for every tails.

The wager now becomes a +EV bet.

You're still going to be winning 50% of all of the flips; however, when you win, you're getting paid double what you pay him when you lose.

Your expected value on every flip is now $2.50.

Let's look at the math. One outcome of the flip is it comes tails (-$5); the other outcome is heads (+$10).

So 50% of the time you'll win $10 and the other 50% of the time you'll lose $5. $10 (.5) - $5 (.5) = +$2.5.

In poker this means you only want to make bets that show a positive expectation and avoid ones with a negative expectation.

This is where your money comes from - making bets that only show a positive expectation.

An example from the felt:

You have 5 6 and the board is 7 8 A. Your opponent accidentally flips over his hand as he bets $10 into a $60 pot.

He has A K. He has top pair aces with the best kicker.

You have a straight draw and a flush draw. You can only win if a spade falls or if a 9 or a 4 comes.

There are nine spades left in the deck plus three non-spade fours and three non-spade nines.

That makes a total of 15 outs.

Sam Farha
Some live and die by EV. Others, not so much.
 

You have seen 7 of the 52 cards in the deck leaving 45 remaining, meaning 15/45 cards win it for you.

The odds against you hitting your hand are 2-1. The pot odds are laying you 7-1 as you have to call $10 to win a $70 pot.

This bet is extremely +EV. On average you will win double your investment.

Conclusion

Expected value is crucial in poker because the game will have fluctuations.

In the short term, whether you play good poker or bad poker, you will win and you will lose.

Good players, however, are going to make money in the long run. Bad players are not.

That's because good players discipline themselves to make only +EV wagers, whereas bad players play with reckless disregard.

Do yourself a favor and become a good player: look for bets that show a positive expectation.

More strategy articles by Dan Skolovy:

assets/photos/authors/_resampled/croppedimage6060-daniel-skolovy.jpg
About Daniel Skolovy

Daniel Skolovy started out in the gaming industry as a lowly dealer, spending countless graveyard shifts dealing blackjack, pai gow, carribean stud, baccarat, etc. He quickly became bored dealing games that were so obviously weighted in the house's favor.

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Doug 2014-03-10 05:04:51

Thank you, but how do you elect not to complete the computation on the example drawn from actual poker?! I mean, this is the Pokerlistings site, right?

ray 2013-01-20 19:29:48

Thanks fot the wisdom

IMissFullTilt 2012-10-03 21:37:01

Giancario,
Comments like yours truly make me miss being able to poker online.

LeLedg 2012-09-21 14:48:41

What about the BB and SB? It seems this is example is for a heads up game so both players have paid blinds. Also both players have betted on the preflop to make it 60$ but that investment is not factored in the example. What I don't quite grasp yet is calculating EV factoring in the blinds and the preflop bet. All documentation on EV I've found all over the web mentions examples of EV calculation from the flop to the river. Never from the preflop.

cousteer 2010-10-21 12:18:00

should be:
EV = ($70*0.333)-($10*0.667) = +16.64

right? Anyway positive EV....

Sean Lind 2010-01-28 20:00:07

Jablouski,

In the scenario in the article, the player has 15 outs to win. To calculate the EV in a $ amount, I believe the formula would be as follows:

(Money you win*percentage of it happening) - (money you lose*percentage)

($70*0.348)- ($10*0.651) = $17.85

So each time you make this call, you expect to make a profit of $17.85, or your EV = +17.85.

If you're talking 56s vs AKo preflop then 56s is a dog, 42% against AK off (assuming the 56 is suited with suits NOT included in the AK)

Jablouski 2010-01-28 01:34:45

I've calculated a +32.35 EV for player holding 56s vs AKo.

Is this correct?

Sean Lind 2010-01-05 19:28:33

Eduard,

Any cards burned are never counted as "seen cards" when dealing with odds. Since we don't know what the cards are, we can't count them for or against us.

But don't worry, I think everyone has that same thought when learning this part of the game.

Eduard 2010-01-05 00:39:08

Sean, I'm not well experienced in here yet, but perhaps he counted the 2 extra cards you take off the deck before flipping the flop? :)

Sean Lind 2009-11-13 04:46:00

Actually, you're both incorrect.

In the scenario the player with AK has accidentally flipped over his cards. This means we've seen 7 cards (I'm not sure where Dan got 9 from... I'm assuming he had a third hand in the pot while writing it at some point)

Anywahs, with 7 cards out you're looking at

15/45

or 30-15

or 2-1

-sean

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