Expected Value (EV) ExplainedUnderstanding 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?
We can estimate this well by looking at the opposing players’:
- 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.
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.
- 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.
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♥.
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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ConclusionWhile 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.