Expected Value
In the early days of poker, when guys like Doyle Brunson were “dodging bullets” looking for good poker games wherever they could get them, no one ever thought about or discussed EV, or expected value. However, that doesn’t mean they weren’t using it. Every successful poker player considers EV in some way, shape or form, even if they aren’t making specific mathematical calculations to do it.
How Does EV Work?
The expected value of a situation refers to how much a particular play is worth to you. It is another way of thinking about the concept of pot equity. If there is a $100 pot and four hands of hole cards, each of those hands is worth $25 in equity. Without knowing what is underneath, there is no expected value in picking one over the other.
However, let us say that one of the hole cards is turned over, revealing an ace. Now we know that that hand is likely to have more value. If given a choice, we will select that hand. But what if we have to pay $30 for the privilege? If that hand will give us more than $30 in equity, meaning in this case that we have a greater than 30 percent chance to win the pot if we buy that hand, then buying that hand has positive expected value, or +EV. If not, buying the hand has –EV.
EV in Practice
The aforementioned situation will never actually occur in a poker game. However, there are many situations that do occur where we can calculate expected value. For example, if you have a nut flush draw with one card to come, you know that you are about 20 percent to win the hand. This means your equity in a $100 pot is $20, so if you have to call $15 to see the river, you are making a play that is +$5 in expected value.
Benefits of EV
If you make more and higher value +EV plays over your career than –EV plays, you will be a long term winner. Make an effort to identify and eliminate your most common –EV plays and increase your incidence of +EV plays and you will be a more successful player.
Fold Equity
Equity may seem to some to be a term more appropriate for discussions of money market accounts, but in fact, equity plays an important role in poker. You need to know your equity in order to know whether or not to continue with a hand. If you’re not getting the right equity in the hands you play, you are setting yourself up to be a losing player.
Understanding Equity
Equity is how much value your cards have based on the amount of money in the pot. It is the same idea that you use when calculating pot odds. If you play Texas Hold’em and are drawing at a winning flush with one card to come, you are 4-to-1 to win. If there is $100 in the pot and you are facing a $20 bet, you are getting 5-to-1 odds to draw, so you have a correct call. In terms of equity, you will win this pot 20 percent of the time and 20 percent of $100 is $20, so you have $20 of equity in this pot, meaning you will win $20 for each time you are in this situation in the long term if you always make this call.
Understanding Fold Equity
Fold equity is an amount of equity based not on your hand strength or the likelihood of drawing to the winner, but on the likelihood that your opponent will fold if you bet out on a bluff. If you think your opponent will fold 30 percent of the time in a given situation, then it is worth 30 percent of whatever the pot is to try to make that happen. This is the idea behind a semi-bluff. When you semi-bluff, you get additional equity: the likelihood that you will draw at your hand and win plus the likelihood that your opponent will fold outright.
Things to Remember about Fold Equity
Remember that to factor in fold equity, there must be a realistic chance that your opponent will fold. Keep an eye on when your opponent is ‘pot committed’, that is, when he has so little money left relative to the pot that he is obligated to call. In situations like this, there is no fold equity.
When you’re semi-bluffing all-in against one potential caller, the EV of your play is the following 3three things added up:
1. (% he folds) * (pot size before you bet)
2. (% he calls) * (your equity) * (pot size before you shove + the bet he calls)
3. (% he calls) * (his equity) * (- the bet you shoved )
Say there’s a $5 pot on the flop, my opponent bets $3, I shove to $14 (and he has me covered), he folds 55 percent of the time, and I have 35 percent equity when he calls. Here are the three parts:
1. 0.55 * $8 = $4.40
2. 0.45 * 0.35 * ($8 + $11) = $2.99
3. 0.45 * 0.65 * (-$14) = -$4.10
$4.40 + $2.99 – $4.10 = $3.29 and that is what the EV of a shove would be.
If you would like to ask me a question on equity, then please leave your query in the comments box below.