When you play poker online, or indeed in a physical card room, the decisions you make are either profitable or not. In theory, it’s possible to put a long-term value on every single play and assess whether each call, fold, and raise makes money. This is the concept of expected value, or EV. This useful concept is not unique to poker and can also be applied to online casino games and other forms of gambling.
Learn how to calculate expected value, as well as how to use it.
Expected Value Defined
In its simplest form, expected value is the average amount of money you’ll make from a single proposition. It could be positive, but of course, it may also be negative, meaning it’s a long-term losing decision.
The formula behind EV looks like this:
Expected Value = (Probability of winning × Amount you’ll win) + (Probability of losing × Amount you’ll lose.)
Why Is EV Useful?
Expected value in poker allows you to determine whether or not a bet would make money over an infinite number of hands. What’s more, it puts an exact dollar value on the profit or loss, quantifying exactly how good or bad of a play it is.
For instance, say you call an all-in bet during an online poker tournament and lose. You’re out of the tournament — there’s no arguing about that. But did you make the right play? The theory of expected value would be one way to answer the question definitively.
Similarly, you might have taken down a pot in a cash game. But that doesn’t necessarily mean your reckless triple barrel bluff was anything other than lucky. With EV, you can put a figure on exactly how good the play was.
How To Find Expected Value
As previously mentioned, EV is not unique to online poker and can be used to calculate the long-term value of any wager. The classic example is that of a coin flip.
Imagine your friend offers you the following proposition: every time the coin shows a head, you must pay him $1. But if it lands on tails, he’ll give you $2. You instinctively know this is a good deal. But why? Well, the question can easily be answered using the concept of EV.
Simple EV Example
If you toss the coin once, there are two possible outcomes. In other words, there is a one in two chance of making a head, the same probability as flipping a tail. Expressing that as a probability percentage looks like this:
(1 / 2) × 100 = 50%.
So, 50% of the time, you’re going to make $2, and for the remaining 50%, you’ll have to pay $1 (meaning your odds of winning are +100.) Here’s the math, according to the earlier formula:
Heads: 50% × -$1 = -$0.50.
Tails: 50% × $2 = $1.00.
EV = -$0.50 + $1.00 = $0.50.
That means the wager has a positive expected value of $0.50. Every time you play this game, you can expect to make a profit of 50 cents.
EV Is Theoretical
Now, in reality, you might flip that coin once, and it comes up heads. Your friend walks away with your dollar in his pocket, and you’ve lost money. But the math clearly shows that you made a great bet and just happened to be unlucky.
If you play that same game 100 times, you’ll still make $0.50 per flip for an expected profit of $50. The more you flip, the lower the variance and the closer the profit will be to the true expected value. Just because it didn’t work out once, it doesn’t mean it was a bad play, so you should keep making that same bet in the future. This is underpinned by solid math.
Applying EV in Poker
Here’s a practical example of how EV can be applied in online poker tournaments. Picture this: your opponent, who has you covered, has pushed all-in on the turn. You’re the only player left to act in the pot, and if you call, your tournament life is at stake. You have no real hand other than an open-ended straight draw.
It’s going to cost your remaining stack of 2,000 chips to call. There are 1,000 chips in the pot before your opponent’s bet. Should you make the play, or fold and live to fight another day? Here’s what EV has to say on the matter.
Without getting into the math here, the chance of hitting an open-ended straight draw with one card to come is 17.4% (odds of +475.) If you call 2,000 chips and hit the draw, you’ll win a total of 3,000 chips. If you call and miss, you’ll lose 2,000 chips.
Now, plug all of this into the earlier formula and discover the EV of calling:
Win: 17.4% × 3,000 = 522 chips.
Lose: 82.6% × 2,000 = 1,652 chips.
EV = -1652 + 522 = -1,130 chips.
On average, this play will cost you 1,130 tournament chips and is, therefore, a long-term loser.
Rule of 2 and 4
Working out percentages on the fly is important if you want to crunch the EV numbers in poker games. But it’s not always easy to do, given the variables in play.
Perhaps you’re multi-tabling, or you’ve selected a poker table that’s getting through lots of hands per hour. Luckily, the rule of 2 and 4 helps make your life a bit easier when it comes to calculating pot odds.
When you’re on the flop and waiting for a turn, or if you’re on the turn and waiting for the river, use the rule of 2. If you’re on the flop and thinking about going all-in, use the rule of 4.
The rule of 2 means multiplying your outs by 2 to find the approximate percentage chance of winning the pot. Similarly, the rule of 4 requires you to multiply by 4.
In the earlier example, you’re on the turn with an open ender. You have 8 outs to hit. Multiply by 2, which gives 16% (odds of +525.) That’s close enough to the real value of 17.4% (+475 odds) and allows you to easily make split-second decisions under pressure.
Improve as a Poker Player at BetMGM
There’s always something new to learn if you’re seeking to improve your game. Studying the theory of poker, including concepts like EV, is a great place to start. But there’s no substitute for practicing at the real-money tables.
Head over to BetMGM today and register a new account. You can enter a plethora of freeroll tournaments or try the micro-stakes cash tables to learn in a low-risk environment. Alternatively, try your hand at live dealer casino games like blackjack and baccarat.