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Equity

  
 
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ellisd
Old 02-20-2006, 11:25 PM     Post subject: Equity #1 (permalink)  

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ellisd
Can someone please explain equity using mathematical terms. I often see the term thrown around when describing draws and have deduced it to mean that it's a fraction of the pot belonging to a player (in the long run.)

When is a good time to raise or C/R with a draw using equity?
How do you determine equity or fold equity?
How would a player easily go from odds to equity? Like taking your odds and multiplying it by the BB. If that equals less than the pot call, but instead using the players in the hand...?

Example:
Player: Ks,Js
Flop: 6d As 7s
Turn: 2c
Players: 3
Pot 6BB
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euphoricism
Old 02-21-2006, 02:35 AM #2 (permalink)  
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People knew to the forum are NOT supposed to ask these good questions. Stop it!

Ok, I don't think I can properly answer your question, so I'll leave it to the math guys, but I just wanted to chime in that you're asking the right questions that make me think you're going to turn into a damned good player.
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dsaxton
Old 02-21-2006, 05:12 AM #3 (permalink)  
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Equity is basically another term for "expectation," which refers to the average outcome of a random event when it's repeated an infinite number of times. This number is generally found by multiplying each payoff by its corresponding probability, and then taking the sum of these values.

For example, suppose an experiment where you flip a coin, and whenever tails came up, you win $1, and whenever heads came up, you lose $1. If you were to continuously perform this experiment, and take the average profit of the previous flips on each iteration, the number would converge to zero. In this situation, the "expectation" of each individual flip is said to be zero.
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ArcticKnight
Old 02-21-2006, 06:15 AM #4 (permalink)  
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On Fold Equity

Correct me if I'm wrong folks, but I think fold equity is that extra equity edge you get in your overall equity when your bet (or raise?) might result in a fold. (knowing that a check or call gives you no such fold equity).

It's not possible to quantify in terms of outs or odds, so as a player you need to instinctively decide (perhaps in % terms) how much added fold equity you have when, for example you are holding AK or AQ and considering whether to bet the turn on a 6h, 8s , Jd, 2c board when your opponent has called your flop bet.....


In NL I think there is more discussion about this, as it's more likely that someone with AK, for example, could put a player all-in pre-flop. He then has two ways to win. He can win the hand at showdown, or he can cause the original better/raiser holding a hand like 44, 77, AJs etc to fold preflop, thus using his fold equity. The all-in caller only has one way to win…
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Xanadu
Old 02-21-2006, 06:15 PM #5 (permalink)  
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Fold equity is a very important concept. It is also one of the most difficult parts of poker to quantify mathematically. I had been planning on putting together an analysis of fold equity, so this question is a good opportunity. I think basically the easier way of thinking of fold equity is not to ask 'how much fold equity do I have from this bet/raise?', but the reverse question of 'how much fold equity do I need to have to make this bet/raise have a positive expected value, and from my knowledge of my opponents can I reasonably expect them to fold that often?'. I'll start putting my analysis together later today.
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pokerfanatic
Old 02-21-2006, 06:23 PM #6 (permalink)  
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I’m not sure if you're going to get a 100% answer from anyone actually equity is just that equity...

Main Entry: eq•ui•ty
1 a : justice according to natural law or right; specifically : freedom from bias or favoritism

so really its not that specific to start with. However here is a link on fold equity that I think does a decent job explaining what it is... Pot equity gets more in depth and harder to explain decently.

http://pokernerd.blogspot.com/2005/0...-i-had-to.html
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euphoricism
Old 02-21-2006, 07:24 PM #7 (permalink)  
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Quote:
Originally Posted by pokerfanatic
I’m not sure if you're going to get a 100% answer from anyone actually equity is just that equity...

Main Entry: eq•ui•ty
1 a : justice according to natural law or right; specifically : freedom from bias or favoritism
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Xanadu
Old 02-21-2006, 07:33 PM #8 (permalink)  
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pot equity = (expectation of winning)(pot size)

Anyone who has had a decent course on prob/stat should know what expectation (estimation) means. Some might argue that ...
pot equity=expectation of winning
This is one of the great things (IMO) about the field of prob/stat. It is the only mathematical field that I know of that actually has meaningful controversy about the correct manner of calculating things. For example, is it mathematically correct to use a Bayesian estimator?

For a bet to be a value bet,

(expectation of winning)>(1/(1+ # of expected callers))

Taking fold equity into account makes this much more complex.
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ellisd
Old 02-21-2006, 10:22 PM #9 (permalink)  

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In the Theory of Poker, Sklansky goes on to say in one of his flush draw examples that there are 4 people in the pot and a 35 % one card chance to make the flush. Correct me if I'm wrong, but I remembered he justified a bet because the percent amount equal to the probablilty of the player making the draw was greater than the percent people in the pot. However, I hardly feel this topic has much importance at a low limit table and most raises for equity can be based on gut.

Thanks for the encouragement euphoricism, now all I need is a bankroll.
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pokerfanatic
Old 02-21-2006, 10:24 PM #10 (permalink)  
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Quote:
Originally Posted by Xanadu
pot equity = (expectation of winning)(pot size)
What I mint by my comment is not the concept is hard the math behind it is complex and very lengthy, if you have read King Yao’s book he has equity equations all though the damn thing...

Great book BTW
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dsaxton
Old 02-21-2006, 11:44 PM #11 (permalink)  
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Quote:
Originally Posted by ellisd
In the Theory of Poker, Sklansky goes on to say in one of his flush draw examples that there are 4 people in the pot and a 35 % one card chance to make the flush. Correct me if I'm wrong, but I remembered he justified a bet because the percent amount equal to the probablilty of the player making the draw was greater than the percent people in the pot. However, I hardly feel this topic has much importance at a low limit table and most raises for equity can be based on gut.

Thanks for the encouragement euphoricism, now all I need is a bankroll.
If you bet and get called my 3 other players, you expect to make money since you will win the pot more than 1/3 of the time. You risk one unit to increase the pot size by four units. You expect to win more than 1/3 of the 4 unit increase in the pot size, which is greater than the single unit you risk to do so. In practice, you can't be certain of getting sufficient callers for a bet with a drawing hand to be profitable, so it isn't quite as simple.
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donnybaker
Old 02-22-2006, 04:05 AM #12 (permalink)  
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Quote:
Originally Posted by pokerfanatic
I’m not sure if you're going to get a 100% answer from anyone actually equity is just that equity...

Main Entry: eq•ui•ty
1 a : justice according to natural law or right; specifically : freedom from bias or favoritism

so really its not that specific to start with. However here is a link on fold equity that I think does a decent job explaining what it is... Pot equity gets more in depth and harder to explain decently.

http://pokernerd.blogspot.com/2005/0...-i-had-to.html
Thanks for this link! I learned a lot about fold equity. A must read for SNG or MTT players!

Quote:
Originally Posted by Poker Nerd
Unless you are attempting to pick off a bluff, if you will call an all-in, it is always better to move all-in yourself first. Put the pressure on your opponent. It's easier and more fun.
Good stuff!
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