Poker EV Calculator

Welcome to the poker EV calculator, the royal flush of online tools for calculating the expected value of a poker play. Use our poker EV calculator to determine what odds are worth taking on and which rounds are best folded early.

In this article, you will learn:

• What EV in poker is;
• Why the EV poker formula is so important; and
• How to calculate expected value for poker and other games of chance.

Expected value (EV) is the amount of money (the value) you expect to gain from a single play. A positive EV means you'll gain money, and a negative EV means you'll lose money. If you make the same play (or similar) multiple times, you'll earn/lose this EV for each of them.

To calculate the expected value in poker, follow these simple steps:

1. Determine your chances of winning or losing with a given hand.
2. Determine how much money you'll gain if you win and how much you'll lose if you lose.
3. Multiply the winning numbers (chance and value) together, multiply the losing numbers together, and subtract the second product from the first.
4. That's the EV of that play.

Not in the mood for math? The poker EV calculator does all the above for you. You could also look into our probability calculator to learn more about probability and chance.

Restated mathematically, the EV formula is:

where:

• ${\rm EV}$ is the expected value;
• $P_{\rm W}$ and $P_{\rm L}$ are respectively the chances to win and lose a play; and
• $V_{\rm W}$ and $V_{\rm L}$ are respectively the value you gain if you win and the value you lose if you lose.

Remember to divide the probabilities by $100$ if they're expressed as percentages!

Expected value is more than just poker jargon — it's a widely-used statistical concept. You can learn more about it with our expected value calculator. The formula above works for other games of chance besides poker, but it's widely used in this ubiquitous card game and is, therefore, a crucial concept to understand.

We now know what EV is in poker (and in other games and in math) — but how does it work in practice? Let's look at an example.

An example using dice

Let's consider a simple dice-rolling game between you and a friend. You repeatedly roll a single six-sided die. For each 5 or 6 rolled, your friend must pay you $5. Otherwise, you must pay them $2. What is the expected value?

Well, let's assign the values in the EV formula from above:

• $P_{\rm W} = 2/6 \approx 33.33\%$, because there are six outcomes, and only two outcomes are a win for you.
• $P_{\rm L} = 4/6 \approx 66.67\%$ for the same reasons.
• $V_{\rm W} = \$5$.
• $V_{\rm L} = \$2$.

Let's plug these into the EV formula:

So with ${\rm EV} = \$0.33$ and $N$ rounds of rolling dice, we know that, on average, you'll make $\$0.33\times N$.

It's important to note that the die's odds are not in your favor and that you'll lose more frequently, but the bigger payout for winning makes the game favorable for you in the long term. If the payouts for winning and losing were both $\$2$, or both $\$5$, or both the same amount in general, then this game would have a negative expected value for you: you'd still lose twice as often, and so you'd lose more money than you'd win back.

Try this example in our poker EV calculator, or experiment with this game using our dice roller instead.

Back to poker

While the probabilities of poker hands are more complex and keep changing, the underlying EV formula for poker stays the same.

• The profit for winning is the pot (minus your contribution).
• The loss for losing is your bid (what you've already contributed to the pot).
• The chances of winning and losing are based on your hand, the revealed cards, and the cards of your opponents.

If you consistently take on the odds, you will gain/lose the EV for this play and each similar play you make, which may add up significantly over time. Remember — folding is also an option!

Yes, expected value can be negative. A negative expected value means you'd lose money in the long run. You're best off not making too many plays with negative EVs — unless you feel like taking on the odds and that the singular loss won't cost you much. Always game responsibly!

While adjacent, the two terms of equity and EV (expected value) are not quite the same.

• Equity is the probability that your hand will win over all your opponents'. You do need some idea of your equity to calculate your EV.
• EV is the amount of money per play that you expect to win/lose over multiple plays with the same equity.