Expected value—commonly referred to as EV—is the long-term result of your decisions in a particular poker hand. It is your way to cut through poker’s blend of luck and strategy so you are able to see how profitable your decisions are. EV (expected value) EV is an abbreviation for expected value. Regardless if you play poker, blackjack or on horses you will always have an expected value for the outcome of your play. Most people who play poker or doing others sorts of gambling usually don’t know the exact conditions of the game they play.
What is Expected Value in Poker?
Expected value in poker is the average return that you estimate an action will bring. Formally, the expected value corresponds to the weighted average of all possible outcomes according to the probability of every outcome occurring.
Calculating the expected value of various possible actions can guide you towards the best one!
A simple example, the Coin-Flipping
Let’s consider the simplest of examples, the coin-flipping. If someone proposed you to play a game of “heads or tails,” where you would win 1$ when the coin lands on heads, and lose 2$ when the coin lands on tails, would you accept? Your intuition says that no! Let’s calculate the expected value of taking that bet to see why.
EV = P(heads) * $(win)- P(tails) * $(lose) = 0.5*1$-0,5*2$ = -0.5$
So, on average, by accepting that bet, you lose half a dollar every time that you toss the coin. This doesn’t mean that you cannot get lucky and win, but it is an unfavorable bet, and if you repeat it many times, chances are that you will end up loosing!
How can we use Expected Value in poker?
In poker, we have to calculate the weighted outcomes of each possible action, to estimate their expected value. Then, we must compare the expected values of all possible actions (fold, call, raise?) to choose the best one!
To become a winning poker player, you have to choose the actions that have the best +EV. This does not guarantee that each particular hand will turn out favorably. However, in the long run, the chance factor will more or less even out. The player that makes the best +EV decisions ends up with the most money!
a simple example
We will demonstrate this concept with a relatively straightforward situation where your opponent is all-in, and your only options are to call or fold. So, there will be no further action later on the hand.
You are playing heads up with a tight opponent that rarely bets without a solid hand. You have K♥3♥ and on the turn, the board is A♥10♥8♣4♠, so you have the nut flush draw.
There are 100$ in the pot, and your opponent bets his last 50$. You give your opponent credit for at least top pair, so you are only drawing for the flush. What should you do?
Calculating the Expected Value for each option
Your first option is to fold. Your expected value is equal to zero !! Whatever amount you have contributed to the pot is no longer yours. Since you will invest no more money in the pot and expect to gain nothing, your expected value is ZERO.
Your second option is to call. Let’s first calculate the probability that you will win the hand. You need to hit your flush draw to win the pot. This means that out of the 46 cards that are unknown to you, you have 9 outs. The 9 remaining hearts (13 total minus 4 exposed). You have 9 out of 46 or approximately a 20% chance to win. When you win, you gain 150$, the 100$ that is already in the pot plus the 50$ your opponent bet. The remaining 80% of the time that you do not hit your draw, you lose 50$, the amount that you invest by calling your opponent’s bet.
calculating the expected value
Your expected value can be calculated as:
EV (Call)= P(win) * $(win)- P(lose) * $(lose) = 0.2*150$-0,8*50$ = -10$
So on average, if you make the call you will lose 10$. Therefore, the correct choice is to fold since a zero expected value is better than a negative one!
a more complicated scenario
Let’s consider a slightly more complicated case in the above example.
You have K♥3♥ playing against the same tight opponent and on the turn, the board is as before A♥10♥8♣4♠, so you have the nut flush draw. There are 100$ in the pot, and your opponent bets 50$, but this time, your opponent has 150$ more left and you have him covered.
The situation becomes slightly more complicated as you have more choices to consider, and potentially an additional betting round to take into account. You can either fold, call with another betting round to follow after the river, or raise. As we saw before, folding has zero EV. Let’s examine the EV for the other two possibilities.
When you call, you will win about 20% of the time and lose the remaining 80%. However, when you make your draw, you will be able to make one more value bet and potentially extract more value from your hand. Let’s say that you plan to bet 150$ more when you make your flush and estimate that your opponent will call at least 40% of the time. So, the expected value is:
EV (Call)= P(win) * $(win)- P(lose) * $(lose) = 0.2*(150$+0.4*150$)-0,8*50$ = 2$
So, now calling becomes a +EV move.
Ev Poker Chart
When raising, you plan to raise to 200$ to put your opponent all-in. You estimate that your opponent will call at about 50% of the time and fold the remaining 50%. So, your expected value is:
EV (Raise)= P(opp.fold)*pot+P(opp.call)*{P(win) * $(win)- P(lose) * $(lose)} = 0.5*150$+0.5(0.2*300$-0,8*200$) = 25$
In this example, raising all-in is the best case scenario!
Ev Poker
Note that in order to make exact calculations you would have to factor in the case that your opponent has a set of Aces or Tens and makes a full-house when you make your flush by hitting the 8♥, or 4♥. On the table, you do not have to make exact calculations. You can treat these cases by adjusting your outs (considering some outs as half for example), or adjusting the probability that you will win the hand.
So, when can Expected Value be employed?
Calculating the expected value has many applications in poker. It can be used on the table when you are facing a relatively simple decision, like to call, fold, or to bet all-in, with all the betting ending after the decision. If there are subsequent betting rounds, the calculations may become difficult, at least when you are on the table. It can also be very valuable to do some off-table calculations and study examples like the one above, to improve your intuition and also improve your capacity to calculate estimations of the expected value when you are on the tables.
Positive Ev Poker
In the next tutorial, we will present another tool called pot odds, which can sometimes be used as a shortcut to reduce the computations that are necessary to calculate the expected value.
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Ev Poker Term
This tutorial is part of the Advanced Poker Strategy Course. You can continue to the next tutorial on Implied Odds!