Do you mean All-in EV or just EV? The first is easy to calculate, the second includes lots of guessing and is nearly impossible to get any sort of exact number.
Here is one approach for a relatively short intro to the EV concept
EV, or expected value, is a statistical term used to represent a long-run average. If a poker decision has an EV of +10bb, that means that if the same situation came up a number of times and the same decision was made, then the average profit/loss over all the similar cases would be 10bb.
Before we get into the details, let’s make sure we understand what the +10bb means. For a poker bet decision, say calling an all-in bet, the EV is the average difference between your stack size after the decision has been made and hand played out and the stack size just prior to the decision. EV then is equivalent to the average profit or loss associated with the decision. In my opinion, and I believe that of many prominent poker theorists, it is the most important metric for proper poker decision making.
Let’s consider a simple example, namely calling an all-in bet after the turn. The pot is 100bb and villain puts you all-in with a 50bb turn. You have the nut flush draw and top pair (aces) and based on your assessment of the villain and previous betting in the hand, you estimate that you have a 30% chance of winning the hand. Suppose you faced this situation 100 times. Then you would expect to win 30 of those times and lose 70. For each of the wins, you win the pot of 150bb or a total win of 30*150 = 4500bb. For each of the 70 losses you lose the call amount of 50bb. Therefore your total loss is 4500 – 3500 = 1000bb. Since this was for 100 hands, the average profit/loss per hand , or EV, is 1000/100 = 10bb.
Let’s show how we get this in equation form:
EV for an all-in call = Pr(win hand)*Pot after villain bet – Pr(lose hand) * Amount of the bet
In general terms, the above is win probability * amount won – lose probability * amount lost
Then for our example:
EV = 0.30 * 150 – 0.70 * 50 = 4500 – 3500 = 1000
If you take the above equation and do a little algebra it turns out that for a break-even EV the following holds:
The call decision is +EV if
Amount to be win/ Call amount > Pr(lose)/Pr(win)
In words, this says,
A call decision is +EV if Pot odds > Bet Odds, where bet odds is the odds against winning. For the example the pot odds are 150 to 50 or 3 to 1 so bet odds cannot be greater than 3 to 1 for +EV. That means you cannot lose more than once out of 4 times or 25%. So the EV equation tells us the for this example,my win probability has to be at least 25% to insure a +EV call decision.
Now this example was the simplest case - calling an all-in bet. What are some other decisions? Well, there are two classes for a single decision situation (we normally do not do EV analysis for a sequence of decisions but in some cases it is doable):
Call vs Raise vs Fold: For this case, you should compare the EV of calling with the possibility of raising (if that is available to you) or compare to the folding EV (see below).
Lead Bet vs Check For this case, you have the opening or lead bet. You can make a bet or you can check – folding would not normally be done for that’s giving up without knowing if your opponents may also check
For each of the above cases, you want to compare the EV’s and choose that decision which is maximum. Note if the decision is to make a bet or raise, then the amount of bet or raise enters into picture.
Several more introductory points: EV of a fold: By defining EV to be the stack size difference before and after a betting decision, the EV of a fold is always zero for your stack size will not change. Any money you put into the pot on a previous betting round now belongs to the pot and not you.
EV of bet and raise decisions. Here the EV equation is more complex because you can also win the pot by villain folding. If the bet is not an all-in bet then additional betting may take place and the EV calculation can get quite complicated. In such cases, you sometimes are forced from a practical basis to use the showdown win probability with possibly additional betting accounted for through implied and reverse implied odds (how much you might win or lose on a future betting round if you hit your hand)
EV of a check – here a common procedure is to assume the hand will be checked down, so again showdown win probability is used with an EV = Pr(Win)* Current Pot, a result that is always +EV. This EV will then be compared to that of making a lead bet or raising your opponent.
Many of the common rules you see in books and on forums such as the bet odds vs pot odds we illustrated above, or the minimum fold equity you need for a pure bluff to work or the implied future winnings needed for a draw situation are based on EV analysis so this is a concept well worth understanding.
