Equity

Poker Orifice said:

Pretty sure I've got a few decent articles saved on my other computer.... I'll dig them up and post one soon (in a game at the moment, lol)

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rufcut68 said:

What is it ? Equity is what share of the pot is rightfully yours. This is what you will win or lose on average for a particular play over a large sample size. Simpler situations of equity would involve hands in which players are all in, as I'll show in a moment. Further, equity calculations are more intended for cash games rather than tournaments. Although equities can be calculated, ICM comes into play there.

How is it calculated? Generally a program, like Pokerstove would be used to calculate equities. For example, let's say you're playing NL and are dealt AA with a stack of 150bb. The player UTG has 125bb and shoves all in. Now this is as easy a decision as you'll have, since you have the nuts you know you are calling. The current pot is 128bb, and you have to put in 125bb to call. In this spot, you know that you will win around 80% of the time.

Using the winning %'s yields the following equity calculation:
.80 (+128bb) + .20(-125bb)

*This is not taking rake into account*
102.4bb + (-25bb) = 77.4bb

The equity of calling in this hand is 77.4bb. This means that if you got into the spot 100 times, you should expect to have made about 7,740 blinds because you make 77.4bb "every" time. Now compare this figure of +77.4 to what the actual result. You are going to either end the hand +128 or -125, both of which are rather far off from your EV.

However, as sample size approaches infinity, the amount won per hand played this way will approach 77.4bb. And that's equity in an abbreviated nutshell.

In practice, equities are going to be based on your estimate of your opponent's range, and then you can use that equity to determine what the best choice is at that moment. Let's say the same scenario played out where UTG shoves all in, but this time you have QQ, and your opponent has 75bb after taking a beat on the previous hand. Well now you have a great hand, but can you call this shove? How do you decide whether to call or not? It all boils down to what range you estimate your opponent will make this play with. You must calculate a range in order to calculate your equity. We did not have to estimate a range in the previous example, as we held the nuts, therefore our opponent's range was irrelevant.

Now assume we know for a fact that this player will open shove here with TT+, AKs. Do we call here? Do we fold? This is where EV comes through. Running the numbers in pokerstove shows QQ as 50.55% equity against this range. The equity of calling here is about 3 blinds, which after rake, may or may not be worth it depending on your stance with variance. The key here is our estimation of our opponent's range. If we are incorrect with that, then the whole equation is flawed.

If, in fact, he is shoving AKo and 99 as well, then our equity jumps to 56%, and it's definitely a call. However, should he be playing a tighter range than we thought, say only KK/AA, our equity is a miserable 22.6% and we must fold.

As you play more, and develop your hand reading, you can improve your ability to estimate ranges. As you can see here, this will help significantly in allowing you to make the most correct decisions at the table, and maximizing your EV on every play.

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