Outs/Equity

[LesWormMurphy]

Is equity ever something you can narrow down precisely, based on outs? For example, I've read that 11 outs is 23.9% equity.

If so, is there a link (or can someone post) where I can see how equity is valued based on outs alone? I understand that the amount of people in the hand is equally important but I'd like to acquaint myself with the equity I have based on the outs I have.

Thanks.

[AKQJ10]

My first two paragraphs answer your question; my last two are on a related topic that some may find interesting, or not.

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Is equity ever something you can narrow down precisely, based on outs?

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If your primary draw is to the nuts and your hand is worthless unless it hits its primary draw, sure. In that case just figure your probability of winning the pot. If there's one card to come, divide the number of outs by the number of unseen cards left in the deck and that's your pot equity. 4 outs / 46 cards left = 0.086, so you "own" 8.6% of the pot. By that token, [ QUOTE ]
For example, I've read that 11 outs is 23.9% equity.

[/ QUOTE ]is exactly correct, with one card to come. But you'll almost never have 11 sure outs with no chance of winning otherwise.

More often, you can't calculate equity precisely because your primary draw may not make a nut hand, your secondary draws are worth something, your hand may already have showdown value, etc. etc. Then you need to estimate the effective number of outs, regardless of whether you're calculating odds or equity. E.g., suppose you have 9 outs to a flush, but two of them pair the board. A full house or better is unlikely so I'll figure based on 8 "effective" outs. 8/46 = 0.173, so with one card to come you "own" 17.3% of the pot. (Generally you'd apply equity to the decision to raise with two cards to come, though -- rarely can you count on the 4 opponents necessary to raise for value with a flush draw on the turn.)

Truth be told, though, I think it's easier to think in terms of odds than in terms of equity. Most people already talk about pot odds when deciding whether to call, but for some odd reason 2+2 orthodoxy seems to be to talk about pot equity when deciding to raise. Why not just talk about "fresh money pot odds"? (Term coined by Buzz on the O8 forum.) If the action to me in a 3-handed pot is bet-call, and I'm considering raising, I need to be getting 2:1 fresh money odds to raise for value. That to me is very sensible -- it's already how your calculate pot odds -- whereas to say, "You need to calculate pot odds to decide whether to stay in, and then you need to estimate your pot equity and compare it to 33.3%" seems odd. I mean, they both make sense and will give the correct answer, but why talk about odds for one part of your decision and probability (equity, EV) for the other part?

(Note that you could also talk about pot equity in deciding whether to stay in the hand. Instead of saying, "I'm getting 8:1, bump it to 11:1 on implied odds, so I can call with my gutshot," you could say, "My gutshot has between 1/11 and 1/12 of the pot equity. My share of the 8-bet pot -- figuring it will grow a bit to about 12 small by the showdown -- is a little greater than one small bet. I need to call one small bet, and I can do so." Odds and probability, probability and odds, two sides of the same coin -- but most people seem to find pot odds more intuitive. Pot equity is an important concept, but in practical terms it can't help you make a decision that fresh money odds can't. So once you've got people thinking in terms of odds, why switch them to probability with the decision to raise?)

[aargh57]

AKQJ10,

Thanks for that post, especially the last paragraph. I was always a little confused about the discussions of equity. I just want to give an example to make sure I understand you're concept of "fresh money odds" correctly. Lets say that I have a flush draw on the turn and there are 6 BB in the pot and I have the button with 3 opponents. If the first two check and the 3rd bets my first decision is whether to call or not. Given now 7 to one I should compare this to my odds of catching my flush (I'm assuming I can't win if I miss and can't win with a bluff) which would be about 4 to one so I should clearly call(I'm also asuming no one is check/raising). If I raise, I need 4 to one fresh money odds and since there are only 3 opponents I can't get this, so I should just call and not raise, correct?

[AKQJ10]

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If I raise, I need 4 to one fresh money odds and since there are only 3 opponents I can't get this, so I should just call and not raise, correct?

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Congratulations! You successfully navigated my long and rambling response. And yes, you're correct -- you might raise as a semibluff if you assessed some decent probability of the bettor folding, but you couldn't raise purely for value.