Although poker is affected by luck, it’s also largely mathematical. As a result, you can measure most variables and make intelligent decisions while accounting for the game’s randomness.
Expected Value (EV) is one of the ways you can quantify poker, and it refers to the result you can expect from a play if made several times. It’s a vital poker measurement, and learning to analyze your hand’s EV will drastically improve your gameplay.
In this blog, we’ll discuss the formula for EV in poker, why it’s essential, and how you can use it to help you in your decision-making process.
What is the EV formula
Here’s a simple formula to derive your hand’s EV:
EV = (%W * $W) – (%L * $L)
The variables on the formula are as follows:
%W: the likelihood of winning
$W: the money you’ll earn if you win the hand
%L: the possibility of losing
$L: the money you’ll lose by losing the hand
You can use a poker odds calculator to get the percentages of winning or losing your hand (%W or %L).
All hands have a chance of losing. So ideally, you would want to consistently make positive EV plays, which will result in a profitable playthrough in the long run.
Before we compute poker EV, we can use the same formula for a simpler game: a coin toss.
We’ll take a regular, two-sided coin and flip it. If it lands on heads, you’ll receive $3, but if it lands on tails you’ll have to pay $1.
We can use the above formula to determine the play’s EV. Since we’re using a regular coin, we know it has an equal chance of landing on either side. Thus, the equation will be:
(50% * $3) – (50% * $1) = $1
This shows that, on average, you can expect to win $1 from our game whenever we toss the coin.
Of course, if we only toss the coin two times, the only possible outcomes are $6, $2, or -$2, which is different from the $1 EV we’ve computed. However, the EV formula focuses on a play’s long (and not short) term value.
Thus, it makes sense to always find plays that produce +EV and avoid those that have -EV. This will result in a profitable game overall.
EV applied in poker
Imagine you’re in a $2/$4 full-ring game as a button with $200. You have J♦ 9♦. An opponent from EP bets $16, and the other players choose to fold. So the pot is at $38.
The flop is 5♦ 10♦ 2♣, and the opponent bets $30. You call to increase the pot to $98, which leaves you with $154.
The turn is revealed to be 7♠. Your opponent bets $50, increasing the pot to $148.
Although you can call, we can use the EV formula to determine if going all-in will be better.
Since you’ve been playing with your opponent for a while, you can say that they may fold two-thirds (66%) of the time if they’re holding marginal cards. Moreover, let’s assume that they are holding a suited T9.
Based on those factors, you’ll have a W% of 34.09% and an L% of 65.91%. These will be the EV computation if you called the earlier $50 bet:
(34.09% * $252) – (65.91% * -$154) = -$16.50
We can use the call’s EV to compare with the EV if you shove. Remember, your opponent folds 66% of the time, which gives you a 33% chance that they’ll call.
(66% * $148) – (33% * -$16.50) = $92.23
Using the expected value formula shows that it’ll be more profitable for you to go all-in than to call ($92.23 vs. -$16.50). Bluffing makes more sense than heading to a showdown, where your weaker hand has fewer chances of winning. If you shove, it’s more likely that your opponent will fold and you’ll win the pot.
Poker Expected Value (EV) Formula
The example above depends on you having a good read of your opponent. The EV will be inaccurate and useless if you’ve judged them wrong (say, they’re a nit instead of a loose player).
Although EV is a mathematical formula, it relies on expected variables. Remember, although poker is largely a game of skill, it also involves luck, which cannot be controlled. Still, you can expect a profitable run regardless of your luck if you consistently make positive EVs.
Nonetheless, you won’t be able to access poker equity calculators and use the expected value formula during real gameplays. That’s why you should practice EV calculations and know the equity of various hands to make better decisions at the table.
Use the EV calculation skills you’ve learned in this blog at Capitol Casino, Sacramento’s finest poker destination. We offer a large selection of tables for every type of casino player and host regular tournaments with the biggest prize pools in the region.
To learn more, call us at (916) 446-0700 or email us at [email protected]