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What Is Expected Value in Poker?
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. It is not enough to only observe the result of a hand because of how variance skews your perception of how good your strategy really was.
- This inherent variance in poker can be incredibly frustrating, but it is necessary. If weak poker players lost their money too fast they would soon get bored and never return to play with you.
- The downside is that you must dig deeper with your strategical explorations to be able to work out the most profitable actions. EV calculations are a concrete way for you to check how well you are playing.
Why Is EV Useful in Poker?
EV decisions are your toolbox for honing your strategies to make the most of every situation. It is not enough for you to simply choose a profitable course of action—you must strive to make the most profitable course of action available to you. Consider that your overall profit (more than just the pure amount of money that is at stake) is the total sum of every decision that you make at the poker table.
If you are playing against any opponents that are better than you, then you can expect to have a negative expectation overall. Conversely, you will be winning chips against worse players. By fighting for every single chip, you will win the most against weak players and lose the least against better players.
How To Use Expected Value in Poker
The following is a common example where you can check on the profitability of your bet size. These calculations are for analysis away from the table to allow you to build up your intuition when a complex calculation is not practical.
The classic mathematical formula for calculating expected value is:
EV = [Probability of winning * What you win] + [Probability of losing * What you lose]
Choosing a river bet size with the nuts when the pot size is $200:
$200 and you get called 20%
$80 and you get called 50%
$20 and you get called 90%
- EV = [0.20 * $200] + [0.80 * $0] = $40 + $0 = $40
Note that the probability of winning and the probability of losing must add up to 1.00 to represent 100%. Also, be aware that this example is simpler because we never lose any amount because we have the nuts.
- EV = [0.60 * $80] + [0.40 * $0] = $48 + $0 = $48
- EV = [0.90 * $20] + [0.10 * $0] = $18 + $0 = $18
You can see for yourself that betting big can be better than betting small, even if you only get called a small percentage of the time. The trick here is to accurately estimate how often your opponent will really call you.
What Is the Rule of Two and Four?
Doing calculations at the table is too time-consuming, but fortunately, there are some shortcuts you can use to make life easier. The rule of two and four is simple enough to be used by all players and will help you to estimate what your equity share in the pot is and therefore also your expected value in some situations.
- In no-limit hold’em, on the flop you can estimate your equity with a draw by multiplying the number of outs you have by four, with two cards to come, or on the turn by two, with one card to come.
For example, if you hold two hearts and there are two on the flop then there are nine more in the deck that complete your draw. 9 * 4 = 36% on the flop, or 9 * 2 = 18% on the turn. This is close to 2-1 pot odds needed on the flop and 4-1 on the turn.
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