WSOP 2018
2018 World Series of Poker

Subject to Change: Estimating Equity in No-Limit Hold’em Hands

Subject to Change: Estimating Equity in No-Limit Hold’em Hands
  • At any moment in a hand of hold'em, your hand has a certain yet-to-be-realised value or "equity."

  • A hand of hold'em isn't as complicated as selling a house. Or is it? Explaining "equity" in poker.

Last week’s article from the “Strategy Vault” shared a past discussion with Andrew “BalugaWhale” Seidman about floating versus bluff-raising after the flop. There Seidman related his thought process when after having called a preflop raise from position, he misses the flop and watches his opponent makes a continuation bet. Folding is always a choice here, but he focuses on instances when he’d rather “float” or call the bet with an intention of bluffing on a later street, or go ahead and bluff right there by raising.

Seidman’s explains how decision in such a spot is affected in part by how his opponent plays, and also by the “equity” he has with his hand that missed the flop. You can go back to that article to see how the combination of his opponent’s style and the relative equity of his hand affects his thinking, but I wanted to stop and linger a little over that term — equity — and talk about how it relates to poker, generally speaking.

What is “Equity”?

The word itself actually means “fairness” — or the quality of being fair or impartial. That idea comes to us sometimes when things don’t seem so fair at the poker table. You get your stack in with {A-Spades}{A-Hearts} versus an opponent’s {K-Clubs}{K-Diamonds} and a king spikes on the river — not fair!

Equity also refers to someone’s “share” of something, as in shares owned in a company. With your aces you might have claimed a “rightful share” to most of the pot while your opponent with kings has much less of a “right” to what’s in the middle. But after the community cards came and that king fell, you lost your equity and he got every chip.

That situation refers to equity after the all-ins have already come. What about during a hand, when there are still decisions to be made? Of what relevance is equity then?

The first time I ever really bothered to think seriously about what equity meant probably came at some point after buying a home. For those who haven’t gone through the process, most of us don’t buy a home outright, but perhaps make a down payment (some % of the total cost) and take out a mortgage to cover the rest. From there we make payments each month, with the majority of that payment actually going to the interest on the loan and the rest to the principal.

Ultimately your home equity refers to what part of the home you actually “own” as determined by that original down payment plus whatever you’ve paid so far. Also, if the house has gained in value since the time you bought it, that, too, helps build your equity in the home. (By the same token, if your home depreciates in value you lose equity.)

While buying a home can be pretty complicated, the general idea of equity is fairly simple. The equity you have in your home is essentially what you would earn if you were to sell it, something that’s affected greatly by what you “put into” it both at the time you bought it and with the mortgage payments you made afterwards. Before you sell the house you can estimate this figure by looking at the current market value of the house and subtracting your outstanding mortgage balance. If I think I can sell the house for $200,000 and I currently have a $120,000 balance, my home equity is $80,000.

That said, I don’t actually realize that equity until I do sell the house. And the longer I wait, the more things could change between now and then.

Equity = Current Value

Subject to Change: Estimating Equity in No-Limit Hold’em Hands 101

The idea of equity works similarly in poker. It essentially represents a theoretical amount you “own” of every pot for which you compete. I say “theoretical” because in the end not everyone gets to realize their equity in every pot — in fact, usually only one person does.

You hold {A-Diamonds}{K-Clubs} and your opponent has {7-Hearts}{7-Spades}. You raise from late position, he calls from the small blind, building a pot of $300. With five cards to come, you have just under a 45% chance of improving enough to beat pocket sevens. Your equity at this point is 45% of $300, then, or $135.

The flop then comes {A-Clubs}{8-Hearts}{2-Spades}, giving you top pair. Now with two cards to come, the PokerNews Odds Calculator shows you have a better than 91% chance to win. Suddenly your equity has risen to 91% of $300, or $273. It’s like the market value of your hand just went way, way up. (Unlike what happens when buying a home, equity values change a lot faster in poker hands.) Or you might think of that ace on the flop being a big fat payment lowering the principal of your mortgage. In any case, the future is looking bright.

If you can find a way now to increase the size of the pot, you will also increase your equity. If you bet $100 and your opponent calls, the pot grows to $500 and your equity increases again to $455. For every dollar that goes into the pot here, you increase your equity by 91 cents.

Equity = (Usually) an Estimation

Of course, in an actual poker hand you wouldn’t know your opponent has pocket sevens, so you can’t know exactly how much equity your ace-king gives you. Instead you estimate — top pair, top kicker is likely ahead of most hands your opponent has here, you think, so you probably do have more equity than he does, considering his likely range of hands. That makes it preferable to try to build the pot further and increase that equity.

It was a similar estimation that had inspired you to raise preflop with {A-Diamonds}{K-Clubs} in the first place. Ace-king is a premium hand, one that stands to be better than most others before the flop, and so your equity would increase by raising and increasing the size of the pot. Home owners looking at a house’s current market value are also making an estimation about how much equity they have in the home, understanding — just like the person with ace-king before the flop does — that it could change in the future.

Going back to Seidman’s discussion, he looks at situations when he missed the flop but may still have equity in the form of a draw that would improve his hand. Thus when he has {J-Spades}{9-Spades} after a {10-Hearts}{10-Clubs}{6-Hearts} flop he estimates he has practically no equity, while having that same hand on a flop of {10-Spades}{10-Hearts}{6-Spades} gives him a flush draw and considerably more equity — a difference (that along with his opponent’s style) will affect his decision whether to call or raise after the continuation bet comes.

Equity does not equal cash in pocket. You still have to close the deal, so to speak, which can be complicated — whether you’re selling a house or trying to win a hand of hold’em. But being able to estimate your equity at any given moment in a hand by accurately comparing its value with the value of others’ hands better informs your decision-making going forward.

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