## What is EV? How to calculate EV in poker?

### Why is EV important in poker? Why do poker players use EV? Find out here!

EV (short from Expected Value) is widely used by poker players. Even though we all talk and hear about the money you can earn at poker, the real value of a poker player can only be measured in the quality of his decisions.

A poker player's knowledge, mastery and quality of plays is indeed represented by his EV.

Expected value shows the average value of repetitive action.

What exactly does it mean? It means that if you are repeating one action over a long time, you will achieve a specific expected result.

### Real-world example

Let's start with an example from the everyday world. A ticket for a train costs 5 \$, but you decide not to buy it and risk paying a fine of \$50. If you travel to work and back home by train five days per week (5 days * 2 times a day * \$5 = \$50), you need to get caught without a ticket less often than once per week - then, it will be a +EV decision. If you meet the conductor at least once per week, then you will lose on not buying your ticket. This will result in a -EV decision.

Accurate calculations of EV will involve knowing how often you will get caught.

• If there is a 5% chance that there will be someone to check your missing ticket, then on one trip you will average \$5 - 5% * \$50 = +\$2.50  per trip.
• If there is a 10% chance that there will be someone to check your missing ticket, then on one trip you will average \$5 - 10% * \$50 = \$0 per trip.
• However, if there is a 20% chance that there will be someone to check your missing ticket, then on one trip you will average \$5 - 20% * \$50 = -\$5 per trip.

That's what expected value is showing you. Those final numbers are the average values per trip of you repetitively not buying the train ticket. So:

• If you get caught once per two weeks (5% chance), you will save \$2.50 on your ride.
• If you get caught once a week (10% chance), you will break even.
• However, if you get caught on every fifth ride, then you better buy that ticket because you will lose a lot of value on every trip.

Bad news? You can calculate it accurately only when you know exactly when your train is checked by conductors. The real world doesn't exactly work like that.

Let's say that everything is up to the chance and conductors do not have a fixed schedule. This situation may happen:

One week you will pay 50 \$ on Monday. And then on Tuesday. And then, again, on Thursday. You will think that you just made a horrible decision not buying your ticket. You lost 150 \$! It's three weeks worth of tickets. But if your calculations are correct and you know that a chance of meeting a conductor is lower than 10%, then you will make a +EV decision when not buying a ticket, and this small sample is a deviation from your expected value.

That happens a lot!

If you flip a coin, it doesn't mean that heads will always be followed by tails. In fact, if you flip a coin six times, there is only a 5 out of 16 chance that there will be three heads there. Why? Because there are 64 scenarios how this situation may end and just in 20 of those scenarios heads come up three times. 20/64 is 4/16 after dividing by four.

Subconsciously, we all know that the faith doesn't follow the numbers to a T, but a lot of the time we (poker players included) tend to forget about this little detail and get furious that our aces got cracked. Again! And AGAIN! We scream it's unbelievable and we blame it all on luck and RNG and rigged sites. We just forget that it's only an 80% chance that we will win with them preflop against other pocket pairs.

So, let's move on to the poker example of EV at the Spin & Go's tables!

### Spin & Go's example

Accordingly, let's think about EV at the Spin & Go's table.

In this example, we take two players who go all-in preflop in the first hand for 500 chips each. One of them has QJs, and the other one is holding 99. Pocket nines are 52%-favourite over those suited connectors. So, what's the expected value of them clashing against each other?

• EV of QJs: 48% * pot - starting stack = -20 chips per every such all-in
• EV of 99: 52% * pot - starting stack = +20 chips per every such all-in

Of course, as we discussed above, poker is similar to life as it doesn't work that way. You don't win or lose 20 chips in that particular hand. You are playing for your full stacks, so you either win 500 chips or lose 500 chips.

This hand can end two ways:

• QJs wins:
• QJs takes 1,000 chips and is 520 chips above EV,
• 99 takes nothing and is 520 chips below EV.
• 99 wins:
• QJs takes nothing and is 480 chips below EV,
• 99 takes 1,000 chips and is 480 chips above EV.

Sometimes, you can hear about different kinds of EV. We get a lot of questions such as:

• What is cEV? "cEV" is a short version of "chipEV". You use chips in your equation to find the answer about your EV.
• What is cEV/hand? It's exactly what we calculated in the example above. In the QJs vs 99 hand, nines have +20 cEV/hand and suited queen-jack has -20 cEV/hand.
• What is cEV/game? It's a sum of all hands and their chipEV's in one game. So, if you finished the game in two hands and one of them ended with +20 cEV and the second one had +30 cEV, then your cEV/game is equal to +50.

Thankfully, all-ins in poker are much more frequent than our train ride so we may find out the answer for profitablity of our action much sooner. At the same time, the chances of winning or losing are also more even, and sometimes we may be the ones who get all-in against pocket aces.

When there is so much luck involved in poker, what can every player do? Focus on making good decisions.

### Why is EV important?

At Spin & Go's, we can translate our chip EV winnings (+/-20 chips as displayed in the QJs vs 99 hand above) into \$EV.

\$EV shows us how much money we should win in every hand and at every tournament, regardless of its multiplier. The equation takes into account many factors, including your chip EV from the whole tournament, its buy-in and its rake.

Because there is so much luck involved, sometimes we may feel lost and without any information whether we play good or bad. After a bad run, should we change something? Do we start opening wider? Do we need to cut our range a little? Do we start limping more? Do we fold top pair to our opponents' all-ins?

EV gives us stability in the crazy fast world of Spin & Go's.

You can't pay your bills in EV nor buy stuff you've ever dreamed of. However, in the long term, your play will be rewarded, and you shouldn't change your approach after a month of a bad run.

Focus on EV as it describes your game perfectly and why we in Smart Spin care about EV, not real winnings!