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# Expected Value (EV) Explained

Learn why expected value is so important to poker professionals, how to calculate it quickly and to get ahead of the competition.

Last Updated on February 15, 2024
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Understanding and knowing how to calculate expected value is one of the key elements to becoming a competitive poker player.

This guide will explain the basics of expected value in poker and how to derive it using a simple formula while also providing a few examples of positive and negative EVs.

## What Is Expected Value in Poker

Expected value (EV) is a mathematical concept used in a game of poker that determines whether a given play will win or lose money in the long run. Thus, we can either have a positive or negative expected value, or +EV and -EV, for short.

The goal, of course, is to find plays with +EV consistently. The bigger the +EV value, the more profitable the play. Now, despite a play having a +EV, it doesn’t guarantee us a win. It instead tells us how profitable that play is on average in the long run. The longer we utilize the play, the closer we will get to the true expected value.

### How to Calculate EV in Poker

We can calculate the expected value in poker using a relatively simple formula:

EV = (%W x \$W) – (%L x \$L)

• %W/L — How often we’ll win/lose a given hand
• \$W/L — How much money we’ll win/lose on a given hand

The simplest way to explain how this formula tells us the expected value is to use a coin example. If we flip a fair coin, the chances of it falling on either heads or tails are 50%. Therefore, both the %W and the %L are 0.50.

If both heads and tails carry the same reward, we have an EV of zero. But let’s say that winning with heads earns us \$2, and losing with tails loses us \$1. From here, we can calculate the EV of betting on heads:

EV = (0.5 x \$2) – (0.5 x \$1) = \$1 – \$0.5 = \$0.50

So, on average, every bet we place on heads will win us 50 cents per coin flip. Of course, we can’t win that exact sum after a winning flip, and we might even lose, but the longer we play, the closer we will get to that average. After 100 flips, we should bank in around \$50.

## Poker EV Example

We simplified things a little bit with our example above, but how do we calculate EV in an actual game of poker, which is much more complex than a coin flip?

Since we can’t see the cards our opponents are holding, we first must estimate their hand range, meaning all the hands our opponents could possibly be holding.

We can estimate this well by looking at the opposing players’:

• Positions
• Stack sizes
• How they made previous plays

We will look at the situation differently depending on whether our non-aggressive opponent raises from the small blind position or if a player raises from the middle position after being aggressive in the past.

In any case, let’s say that we are the ones raising from the middle position with A♣, A♥. Both the button and the small blind call, with the pot now being 2,000.

The flop is J♦, 10♦, 5♣, after which the SB checks, we raise to 1,500, and the button reraises to 5,500. The SB folds.

Now comes the hard part: you must estimate the opponent’s hand based on their:
• Position
• Stack
• How they played earlier in the session

After accounting for all of that, we estimate that their range is 50% jacks and tens, 40% straight and flush draws, 10% JT, and 55.

You will beat your opponent’s range enough times here to justify a call. You don’t want to raise as you don’t want to scare your opponent and make him fold all those hands you’re beating.

The turn is a four of spades, so our board now looks like this: J♦, 10♦, 5♣, 4♠.

This is a great card, as it kills any of our opponent’s flush or straight draws. You proceed to bet 6,500, and the button calls. Since they just called, you can assume they’re not holding a pair of jacks or tens. Meanwhile, they would likely fold any weak draws, so you can now narrow their hand range even further.

From here, we can estimate that our opponent’s hands are 85% strong draws and 15% hands that are beating you. The river spices things up with a K♥.

Since you are committed to the pot at this moment (there’s 26,000 in the pot) and your hand is very strong, folding comes out of the question. At this moment, you estimate that your opponent’s range beats you 75% of the time while you have the stronger hand 25% of the time.

Meanwhile, you only have 6,000 left in your stack, so do you go all-in?

Let’s see what the EV formula tells us:

EV = 0.75 x -6,000 + 0.25 x 26,000 = -4,500 + 6,500 = 2,000

Going all-in here gives us a +EV of 2,000, meaning we should go for it.

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## Conclusion

While calculating expected value could seem like rocket science to beginners, it’s actually not all that complicated.

You first must think and assess your opponent’s hand ranges and style of play, after which you just apply the EV formula and land on the best move.

Of course, you’ll sometimes have more than one move. Shoving is not always the only possible option, so calculate the EV for check-calling as well.

## FAQs

### What does it mean to have a positive expected value in poker?

Positive expected value (+EV) tells us that a move we’re about to make will win us money on average in the long run.

### Is there a poker expected value calculator?

Yes, you can find plenty of free poker EV calculators online. However, we advise you to practice using the formula without the help of a calculator, as you won’t be allowed to use one when playing live.

### Does positive expected value mean I’ll win every time?

No, a positive expected value does not guarantee a win. +EV just means that you’ll win money more times than you’ll lose it in a given scenario.

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