EV, short for ‘expected value’ is the focus of every poker player. Our goal is to make as many +EV decisions as possible, and the more +EV the better. In short, a play that is +EV is expected to net us money over the long term while plays that are -EV are going to cost us money over the long term.
The basic formula is simple: EV = (W%*$W) – (L%*$L)
Put another way, multiply what a win is worth by how often you expect to win and the subtract the multiple of what a loss costs you and how often you expect to lose. And of course, W%+L% = 100%.
Here is a quick example of how you could use this calculator:
On the river the pot is $700. Your opponent shoves for $500 and you are deciding if you want to call. Let’s break it down:
- If you call and win, you make $1200 (the $700 pot + his $500 bet). So add 1200 to the first entry above
- If you call and lose, you are out $500. So add $500 to the second entry above
- You think villain is bluffing half the time and beats your hand half the time. So add 50 to the third entry above
Notice your call is expected to earn you $350 in the long run. Sounds like a great call to me!
You can use this calculator to solve the EV of calls, shoves, and more. We also have another tool called the Fold Equity Calculator which is useful when trying to figure out how often villain needs to fold for your shoves to be +EV.
If you find any inaccuracies or find any cool results, let me know in the comments below!
10/20 Live NLHE.
MP open limps
Hero (BTN) makes it $100 :Ad :Qh
SB calls and all else fold and we go to the flop HU.
Flop :8c :9h :Th ($240)
Vs a SB range of 22-JJ, Aqo+, AJs, KQs we have about 35% equity on the flop.
We Cbet $160. (pot $400)
The first line of The EV calculator is the “expected profit” Should I plug in $400? that’s the pot $240 + cbet of$160
or just $240 (the pot)
Second line of calculator – Is my expected loss $160 (the cbet)?
Third – I expect to win 35%
My EV is = +$36? (that’s using expected profit of $400)
All add up or am I going wrong somewhere? or is this calculator not the correct tool for this problem?
Thanks in advance,
@Eric- question 1) villain hasn’t put any money in so the profit would be $240. Question 2) I believe you’re asking the wrong question here. This calculator is used when determining whether to call a bet, assuming no further action. If you’re trying to determine if your cbet is profitable, you need to calculate how often your opponent is folding (50%?, 60%?). Then your calculation would be EV= (%fold x pot) + %call((equity*pot+opponent call)-(1-equity)*bet).
Assume villian folds 50% of the time. EV= .5*240+ .5*(.35*400-.65*160)= +$138
How do you calculate the probability of your opponent or multiple opponents having connected with the King on a King deuce deuce flop where you suspect neither of them have a deuce. In other words, what is the probability of at least One of Two average players having been dealt played a king in small preflop raised pot?
There’s no general solution since it depends, even in the restricted case of a single preflop raise and two calls, on the ranges played by your opponents. However, you can arrive at an estimate once you’ve assigned such ranges for this specific case. You also need to assign yourself a specific hand to properly account for card removal effects.
Let’s suppose you open from EP with AhQh and both CO and BTN call. For simplicity we’ll give them identical calling ranges. Those ranges are a bit of a mess because of your blockers and the fact the ranges are beheaded (premiums chopped off since your opponents called rather than 3-bet). So I played around in Equilab and got the following:
JJ-22, KJs-KTs, JTs, AdQd, AsQs, AcQc, KdQd, KsQs, KcQc, AdJd, AsJs, AcJc, QdJd, QsJs, QcJc, AdTd, AsTs, AcTc, QdTd, QsTs, QcTc, Ad9d, As9s, Ac9c, Ad8d, As8s, Ac8c, Ad7d, As7s, Ac7c, Ad6d, As6s, Ac6c, Ad5d, As5s, Ac5c, Ad4d, As4s, Ac4c, Ad3d, As3s, Ac3c, Ad2d, As2s, Ac2c, KJo, AdQs, AdQc, AsQd, AsQc, AcQd, AcQs, AdJh, AdJs, AdJc, AsJd, AsJh, AsJc, AcJd, AcJh, AcJs, KdQs, KdQc, KhQd, KhQs, KhQc, KsQd, KsQc, KcQd, KcQs, QdJh, QdJs, QdJc, QsJd, QsJh, QsJc, QcJd, QcJh, QcJs
Oh fun. If you plug that into Equilab, you’ll get the correct range with removal. Easier is to use JJ-22,AQs-A2s,KTs+,QTs+,JTs,AQo-AJo,KJo+,QJo and let Equilab handle the card removal.
This range has 159 combos. Of those combos, 32 include a K. So the probability the CO holds a K is 32/159 = 0.20.
We have to ignore a second order effect here which is that the specific combo that CO holds impacts the combos BTN can hold, but to a first order approximation it’s reasonable to also assign BTN a 0.20 probability of holding a K.
To find out if at least one of them holds a K, we calculate the probability that neither of them holds a K
This is given by (1 – 0.20)^2 = 0.64.
Thus the probability at least one of them holds a K is 0.36.
A more accurate result would require using the initial ranges and running a Monte Carlo simulation which assigns CO and BTN a specific hand drawn randomly from that range for 10,000 iterations or so.
2-5 no limit HE, live
Pot is $640 after two players are all-in on the turn.
Board is 2-5-8-10, rainbow.
Villain has JJ.
Hero has KK.
River is J.
So is hero’s EV 95% of $640, or $608?
Same session, hand #2:
Pot is $770 after two players are all-in on the turn.
Board is A-J-3-9, rainbow.
Villain has A9.
Hero has AJ.
River is 9.
So is hero’s EV 95% of $770, or $731?
These were the only two hands of significance for me during this session. So please help me continue this method of calculation, because the reason I’m particularly curious is when I got home and told my wife I was stuck my $600 buy-in, she was unhappy with me. I told her I had a 90.25% chance of being up $810 (two pots: $640+$770 subtract $600 buy-in), and a a 0.0025 chance of being stuck $600. Are my calculations correct? And would this session then calculate to being $1,273 (total pot value $1,410*90.25%) under EV? Am I calculating this properly?
Thanks for your help,
How do you estimate what your opponent will do? That is hard for me…
It’s hard for everybody! The simple answer is that the more experience you gain, the better you become at profiling opponents and predicting how they will respond to different actions. The main skill that supports this ability is hand reading, which is a something this course comes back to again and again.
when does Ev come into play. only after the flop is dealt right ?
also when should I apply EV formula when im drawing like open ender, flush draw with open ender etc.
In some sense every poker decision we make is based on EV. You can use this formula for draws, but be aware that when there is money left to play it may not apply. It can be used directly for all-in situations.