Definition of expected value
The expected value of a cash game poker hand is the amount of money we expect to win, on average, for a given line. All money previously invested into the pot, is treated as dead money.
- We do not have to deduct our previous investments into the pot, when calculating expected value.
- Expected value may also be referred to as expectation, or by the abbreviation EV.
- Expected Value in cash game poker is expressed as a $ (or £,€, or any other currency) amount.
- In tournament poker, you can also look at chipEV, i.e. the amount of chips we expect to win, on average, for a given line.
Let us start with an easy to follow example, where no further betting is possible. Let us imagine after all the betting is done on the turn, we and our only remaining opponent are all-in. There is $600 in the pot (we have put in $290 of this, our only remaining opponent has put in $290, and $20 has been put in by players who have folded). Let’s say in this all-in scenario both players have decided to show their cards, and you calculate your hand has 90% equity, versus your opponent’s hand. This means your expected value is $600 x 0.90 = $540. Notice, we do NOT deduct the $290 we have invested, from the expected value calculation as this is dead money (once we have put it into the pot, it is no longer ours). Of course our $290 we have put in (as well as all the other money any other opponent has put in) is considered in the pot size, in the expected value calculation.
The ONLY time expected value can be calculated as (total pot size x equity) is IF all players remaining in the hand cannot place any more money into the pot. If further money can be placed into the pot, the total pot size is not yet known so this is not the way to calculate expected value.
EV is different from equity
Whilst equity and expected value are correlated, they should never be treated as the same concept. The equity of hand are the odds (usually expressed as a %, or ratio) of a particular hand/range to be the best hand when the river card has been dealt. There is a full strategy post on the subject of Equity that you can read here at poker.betzoo.uk.
The expected value of folding is 0
Given the definition of expected value states that all money previously invested into the pot is dead money, it follows that if a players fold their hand at any point their expected value is zero. You do not have to put in any more money to fold, and anything previously invested (even on the same street) is not relevant.
Results & EV differ in the short term
In any given poker hand (except in the case of a tie) you will usually win the entire pot, or end up with absolutely nothing (and thus lose everything you have invested). Let’s say in a cooler situation, you and your opponent are all-in before the flop. There is $1,000 in the pot, consisting of the money you and your remaining opponent have put in, plus anything from any players that have folded. One of you has AA and one of has KK. AA has an EV of approximately $1,000 x 0.80 = $800, and KK has an EV of approximately $1,000 x 0.20 = $200. However, in this one hand one of you will win $1,000, and one of you will win $0. 20 times out of 100, it will be the AA who will win $0.
Expected value is a long term concept. It tells you how much you will win, on average, if this hand was played from this point a large number of times.
Max your EV = goal in cash games
Short terms results in poker will be affected by the variance that is built into the game. As a studied poker player (which we know you are as you reading this poker.betzoo.uk strategy article), variance is one of the things that is helping you take the money from the unstudied or weaker players, over the long term. If there was no variance in the game, the most skilled players would win the money of the less skilled players faster, and unskilled players would quit at a faster rate. Variance means unstudied players may be rewarded in the short term for what are long term poor strategies, which may mean taking the money from studied players playing better long term strategies. However this is exactly what you want, and what makes poker so profitable. As a studied player, your goal should always be to maximize your long term expected value.
Dynamic fold equity EV
One of the most complicated looking (but really not hard to follow, once you have understood it), EV calculations is when you are calculating Dynamic Fold Equity. This is when you are considering a semi-bluff, but are wondering if it is worthwhile. A semi-bluff is when you hope to win the pot in 2 ways (a) either your opponent folds and you win a smaller pot, or (b) your opponent doesn’t fold but you make a better hand than your opponent, and win a bigger pot. Of course, sometimes your opponent, won’t fold, but you also don’t make a better hand than your opponent, and this needs to be taken into account.
An example of a semi-bluff is if your suited connector after the flop has a flush draw (2 more cards of your suit arrive on the flop, which didn’t give you a pair or straight draw), and believe you are up against a weak top pair hand (i.e. top pair, weak kicker). You believe you will always win the hand if another club comes, but won’t otherwise win except for a small amount of backdoor equity. You were the preflop raiser, and your opponent (in the big blind) who called preflop checks to you. To decide whether to proceed you will have to calculate your EV.
You need to consider all of the following:
- A = If your opponent folds, how much will you win?
- (frequency you expect your opponent to fold x pot size without counting our uncalled semi-bluff)
- B = If your opponent calls, and you make your flush (or otherwise win the hand via backdoors), how much will you win?
- (frequency you expect your opponent to call) x (hero’s equity) x (pot size before our semi-bluff + the amount of our semi-bluff)
- C = If your opponent calls, and you don’t make your flush (or otherwise win the hand via backdoors), how much will you will lose?
- (frequency you expect your opponent to call) x (opponent’s equity) x (the amount of our semi-bluff)
- EV = A + B – C