Ev Formula Poker
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.
Let's look at our EV formula, and state that situation X is the one where we bet, he raises, and we fold. Situation Y is where we bet and he calls. Situation Z is where we bet and he folds. I've been trying to add more math into my hand reviews lately. I want to brush-up on all the basics because I feel like I don't have a good grasp on it all when I'm at the table. Today I came across a hand where it seems like my EV math is wrong but I can't figure out why. GTO+ has a different number and so does the redchip EV calculator.
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
- 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.
Ev Formula Poker
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
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
$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!
For more information about why we care about EV profit, we invite you to read this article.
Expected value, known as “EV”, is the expected return based upon the average result of an infinite number of repetitions. The classic example used to explain this is a coin flip. With 2 possible outcomes the statistical probability is 1 to 1. An even money wage would give you a neutral expected value however, if you were given 4 to 5 odds or better it would be a positive expected value, EV+. Flipping a coin 10 times will not necessarily wind up with 5 instances of heads and 5 of tails. The mathematical theorem of the Law of Large Numbers, “LLN”, states that over a large enough sample the results should be closer to the average mean. In poker we call the times of variance either “running good” or “running bad”.
To calculate the EV of calling a bet or raise, with a drawing hand, you would use the following formula:
- Count your “Outs” to calculate the odds of making your hand, based upon the number of community cards left to be dealt. For example, you have a 4 flush on the flop. Since there are 13 cards of each suit in the deck and you know about 4 of them, there are 9 remaining “Outs” that will make your hand. With 2 cards yet to come there is a 35 % chance of hitting 1 of the 9 remaining outs and making a flush.
- Compare the amount of money that you are required to call to the size of the pot. If the pot has $200 in it and you need to call a $50 bet, then you are getting 4 to 1 on your money.
- Put the 2 calculations together. Statistically you will make your flush, a little more than, 1 out of 3 times. You are getting paid 4 to 1 on your money. If you ran the identical situation over a long enough period of time, you would wager $50 for 3 of the hands for a total of $150 and would win once bringing in $200. This situation is obviously a call with an expectation of a positive return so it would be a positive EV play.
The idea is to make decisions, at the poker table that will bring you the highest implied odds. There will not always be a decision that has a positive EV, in which cases you should make the decision with the lowest possible negative EV. When you calculate your EV make certain to consider any future wagers that you might have to make in the hand and any additional calls that you can get in the event that you do make the hand.
Expected value is also used in other types of situations that occur at the poker table. Bluffing is a good example of this. With the knowledge that you have of your opponent, you have determined that making a pot sized bluff of $300 will cause your opponent to fold 3 out of 4 times. Based upon an average return you would win 3 x $300 for a total of $900 and lose 1 bluff of $300 making the bluff a positive EV play.
Ev Formula Poker Rules
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