Thursday, July 19, 2012

Thinking In Terms of Equity

Waaaaaay back on January 1st of this year, I posted my Poker Resolutions for the upcoming year (re-read it: here). Number #17 on the list was "Think of poker decisions in terms of Equity and EV."

Recently I received an email from a reader that said, in part:

You've explained equity to me at least 10 x if not 100. I see it on stove. I see it in ICM. I read it in Miller. P 110. 
But I am unable to explain it. Please help.

Okay, so what is Equity? And why does it matter?

In simple terms, Equity is your share of the current pot at that moment in time. In more complex terms, it's, well, a little more complex to explain. Let me try.

There are essentially two types of Equity we're concerned with in poker: Pot Equity (sometimes called Hand Equity), and Fold Equity. Your Total Equity in a hand, therefore, is simply your Pot Equity plus your Fold Equity. Let's look briefly at each:
  1. Pot Equity. Let's say you're dealt AKo and your opponent holds JTo. Using PokerStove, we can see that before a flop is dealt, your (Pot) Equity is 65% vs. your opponent's 35%. People frequently assume this means your chance of winning the hand at that moment in time, and while this is a reasonable way to think of the situation, it's not technically accurate. What the 65% number actually represents is your theoretical "share" of the current pot at that instantaneous moment in time. If the pot was $100, then $65 of it "belongs" to you in the long run (i.e., if you were to run this scenario out a few thousand times). If the flop came out J-T-4, however, your Pot Equity on the flop would plummet to just 21%, because your opponent flopped top two pair; your share of a $100 pot at this point in the hand is now just $21. If the turn brings a Queen, your Pot Equity is now back up over 90%. And when the river drops another Jack on the board, your Pot Equity, or rightful share of the pot, is now a big fat goose egg, i.e., Zero.
  2. Fold Equity. The layman's explanation for Fold Equity is simply the probability that your opponent will fold if you bet a certain amount. The more technically accurate definition is that it represents your share of the pot given the propensity of your opponent to fold to a bet of a given size. In the aforementioned example, your Pot Equity was zero on the river. But let's pretend that the Queen, Jack, and Ten on the board were all of the same suit. Let's also assume that the Ace in your hand is also of that same suit. Alas, your King is not, so you're still beat in the hand. Your opponent doesn't know that, however, and suspects that there is a possibility that you have a straight flush. If you bet big here, there is a chance a paranoid opponent may fold. How big of a chance? Well, unlike Pot Equity, there is no handy program like 'Stove we can employ to spit out the answer. Instead, how much Fold Equity you have depends on less tangible factors, like the emotional state of your opponent, what he perceives your range to be, and so on. It also (obviously) depends on your bet size. In this example, we might say that your Fold Equity on the river is nearly zero percent if you bet small, but might be as much as 10-20% if you bet a very large amount and made your opponent believe you could have the nuts.
So why does knowing what your Total Equity is matters? Because, as you will recall, there are two ways to win in poker: 1) show down the best hand (i.e., have big Pot Equity); or 2) get your opponent to fold (i.e., have Fold Equity).

Note that in the vast majority of poker hands we play (i.e., if we don't have total air or the nuts), we're somewhere in between, trying to win, with a combination of both Pot and Fold Equity. This is where things like Show Down Value hands and Semi-Bluffs come into play. Here's a simple graphic I ginned up to hopefully explain better:
Your Total Equity in a poker hand is the sum of your Pot Equity and your Fold Equity.
Finally, I'll leave you with an Equity rule of thumb that is often repeated by professional players: If you think you have more than 50% Total Equity in a hand at any given time, you should bet. I'll leave it to the reader to figure out why this is true....

All-in for now...
-Bug

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