In poker, you can always find out which is the 'right' action by determining the EV of all possible actions and choosing the one with the highest expected value. If you are confronted with the choice between calling or folding, for instance, you can compute the EV to know exactly which decision is the better one. What is Expected Value (EV) in Poker For those of you that are unfamiliar with expected value or EV for short, it is a positive or negative outcome of a play or strategy if used consistently over the long haul. Since poker is a life long session, this is a very important concept to understand and use while you are playing poker.

• Poker Ev Formula With Fold Equity
• Ev Formula Poker
• Ev Calculator Poker
• Ev Formula Poker Game
• Ev Formula Poker Rules
• Ev Formula Poker Calculator
• Ev Formula Poker Table

I assume that IV and EV calculation share the same formula. Also, state each formula from each generation, if they have different formulas per gen. Note: I don't want an IV calculator or anything like that. I want the actual formula/algorithm for how to calculate IVs and EVs. Thank you, Indigo. Concept – Expected Value (EV). Expected Value is the probability-weighted average of possible results. EV = Win%. WinAmt - Lose%. LoseAmt. For example, – If Win% = 25% and you are facing a $60 bet into a pot of $100 – EV = 25%. (100+60) - 75%. 30 = 17.5. In general, decision rules will be made based on Expected Value. But when betting or raising yourself, utilizing a complex EV formula is powerful. And let’s be honest, there are very few things in poker that are more fun than shoving. And if you are considering doing more 5bet bluff shoving preflop or semi-bluff jamming postflop, then understanding the math behind it is crucial.

As a poker player you will have experienced times when you made the correct decision only to have the results make you want to punch the wall. Poker is a game with variance, meaning that things are going to happen that go against the odds of them happening (sometimes seeming like they defy all possibility). However, as long as you are making decisions that have a positive expected value (+EV), you will be profitable in the long run.

What exactly does expected value mean? Basically, if you were to flip a coin and someone offered you $1 for every time you called heads or tails correctly and there were no penalty for guessing incorrectly, that would have a positive expected value. Since there is an even 50/50 chance of earning $1 each flip, you can say that the EV of each flip of the coin is + $0.50.

Now if you wagered $0.50 each flip, it would be an even money bet. Half of the time, you would lose $0.50 and you would profit $0.50 the other half ($1 of winnings minus the original $0.50 wager).

Now let’s say you are given $1 if you call a coin flip correctly, but you have to wager $0.55 each time you flip the coin. You would not want to make this bet because it has a negative expected value (-EV). Over time, you would lose an average of $0.05 on each flip.

Playing Poker for the “Long Term”

Using the same coin flip analogy, in a sample size of 10 trials there are going to be times when heads comes up all 10 times. You know each time you flip the coin the odds of it coming up heads are 50%, but over the course of this relatively small number of flips the results seem to defy the odds. However, if you extend the number of flips to 100 or 1000 you will get closer to an accurate result of 50/50.

So that is what the “long term” is in poker. If you make the same play over an infinite number of trials, the resulting amount of chips you earn over time is either going to be positive or negative. Because the distribution of cards is random, there is rarely a guarantee that you will have the winning hand until all the cards are dealt. So in any given hand there is always a probability that the best hand can end up losing and the actual results deviate from the way the odds say they should. In hold’em, a pair of Aces is about an 80% favourite versus a pair of Kings pre-flop. That still means that 20% of the time the pair of Kings will win. But in the long run the Aces have a positive expectation to win.

Getting the Most Value Out of Hands

Expected value is not just about a singular outcome (winning vs. losing), but it’s also about maximizing the value in every hand you play. This means squeezing the most value out of hands when you are ahead and losing the least when you are behind. It can also mean knowing how much to risk on a bluff where the percentage of times it will work and the value of the pot makes it profitable in the long run.

How to Squeeze Maximum Value

Let’s look at a hand example to illustrate…

• No Limit Hold’em Tournament Play
• Blinds: 25/50
• You and your main opponent both have 3,000 in chips.

Pre-Flop

The following hand example will demonstrate how to squeeze maximum value against a player on a suspected drawing hand. Importantly, you already know that this player likes to play suited cards and likes to chase draws. Before the flop, your opponent in middle position limps and you elect to call from the button with . The small blind completes and the big blind checks.

The Flop

The flop is dealt and everyone checks to you, as shown in figure 1 below:

Figure 1

Jackpot, a set! But wait – what if someone has a flush draw?! Should you be afraid of someone drawing to another heart and try and shut the hand down right now by putting in a big bet? No, you shouldn’t. This is a very common mistake. Many players see the potential flush draw and overbet the pot or push all-in to “protect their hand”. Protection is incorrect thinking because it doesn’t maximize your expected value. If you try to shut the hand down now with a big bet you will lose money in the long run. Does this mean you should slow play by only betting a small amount or even checking? No, it doesn’t. It means that you should bet the maximum amount that you think someone will call to draw to their hand and make an incorrect decision.

For someone to correctly draw to the flush with one card to come, they need 4-to-1 odds. So in this case, the pot is 200. If you bet 50 trying to slow play, the pot will now have 250 and it will cost them 50 to call giving them 5-to-1 odds (250/50 = 5/1). This would be a correct decision for them to call and would be –EV for you because they will hit their draw better than the 5-to-1 odds you are giving them. So, what is the correct amount to bet? This depends on your opponent. If you know someone likes to chase draws, you should consider betting around the size of the pot. If you know they will only call a reasonable sized bet, then you should bet enough to give them about 3-to-1 odds. This would be an incorrect call on their part.

There are additional factors of implied odds to consider here, but that is for another lesson. In this case, you know at least one of your three opponents likes to chase draws, but you can’t be sure he has one now. I would bet around 100. This will make the size of the pot 300 and will give someone 3-to-1 odds to call. The guy in middle position who likes to chase, calls.

The Turn

The turn is a ten of spades and our opponent checks:

Figure 2

How much should you bet here on the turn to maximize EV? Well, you can be pretty confident that your opponent doesn’t have a King because they would have likely bet the flop against three opponents. While they could have a straight draw if they had a hand like 45 or 34, the most likely hand your opponent has contains two hearts including AX and connectors such as or . If he does have , he now has a pretty big draw and is unlikely to consider folding. But we don’t know that for sure, so we have to bet an amount that maximizes our EV against a range of drawing hands. The pot is now 400 and our opponent has 2,850 left. Based on our opponents tendencies, I would bet around the size of the pot, so let’s make it 350. Our opponent calls.

The River

Poker Ev Formula With Fold Equity

The river is a beautiful . If our opponent was on the flush draw, he just hit, but it also gives us a full house. The size of the pot is 1,100 and our opponent bets out 600:

Figure 3

His bet lets us know that he likely has the flush. He could also have a King, but it’s not likely based on his previous actions. Either way, we’re in a great situation.

Now, how do we get the most out of this hand? After his bet of 600, there would be 1,700 in the pot and it leaves him with 1,900. Many beginning players will raise the minimum here because they are afraid of making their opponent fold. But that is leaving money on the table.

Players who often chase draws will not fold when they make their hand. They feel emotionally attached because they have already spent a lot of their stack to get there. Also, we have 1,900 left and if we just raise the minimum to 1,200 we are committing most of our stack which looks like we have a huge hand. I would think for a few seconds and then push all-in. Our hand is pretty concealed and it looks like we have a King, so it’s highly likely we’ll get called here. Our opponent calls showing and we rake in a monster pot.

Don’t be Results Focused

Since you cannot control the final outcome of any given hand, the goal in poker is not to win every hand, but to make decisions that have a profitable expected value. Sometimes luck is in your favour and sometimes it’s against you, but if you are making +EV decisions that is what makes you money in the long run. It is important not to let negative results get you down or hurt your confidence in your abilities. Just remind yourself that you wanted that donkey to call you down with bottom pair because even though he spiked two-pair on the river this time, he is your personal ATM if he keeps making that play.

A firm grasp of the concept of expected value will serve you well. In our next lesson, calculating EV, we’ll take things a step further and discuss the additional criteria that must be incorporated into your decisions. We’ll also look at some common EV spots in both cash games and tournament poker – all with the intention of positively affecting the long-term profitability of your decisions.

By Donovan Panone

Donovan started playing poker in 2004 and is an experienced tournament and cash game player who has a passion for teaching and helping others improve their game.

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:

Ev Formula Poker

• 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.

Ev Calculator Poker

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 Formula Poker Game

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

Ev Formula Poker Rules

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.

Ev Formula Poker Calculator

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

Ev Formula Poker Table

For more information about why we care about EV profit, we invite you to read this article.