THINKING 'BOUT FOLD EQUITY

[chimpanzepoopdic]

Lately I have thinking much about fold equity. Please help discuss the following ideas that I am trying to wrap my chimp brain around.

Fold equity is an estimation of the % of time you think your opponent will fold to a particular bet in a particular situation, allowing you to win without a showdown. Yes/No?

For example on the turn say you have a 28% chance of improving your draw on the river to the winning hand and feel if you make a ½ pot size bet that your opponent will fold 30% of the time, due to previous action, chipstacks and so forth (your fold equity would be 30%). Therefore you estimate the equity on such an action as 58%. If you felt he was really weak you might estimate that a pot size bet would win the pot uncontested say 50%, add that to your draw and you could assume that the equity on such action is 88%. Of course once you are called your fold equity goes out the window.

Someone else has to give up equity in your estimation in order for you to gain equity.

Say you are on the flop and the PF raiser makes a continuation bet into you. You realize that you have a premium draw and believe your opponent has you currently beat. Can this be expressed as follows?
x=your equity
y=your opponents equity
z=your fold equity, or the % of time you feel your opponent will fold to a particular bet in a particular situation.
x+y=100
(x+z)+(y-z)=100

Are Bluff Equity and Fold Equity actually one in the same? I think they are.

If you feel like there is no way this guy will fold then you will have zero fold equity but never a negative.

On the river you can have Bluff Equity/Fold Equity if you are behind but never if you are ahead.

Please discuss.

[Acevader]

The easy way that I figure it out it to calculate how much fold equity I need to break even. So lets say I raise 78h 4bb on the button and the BB calls. The flop comes Kh,9s,6d and the BB leads out for 8bb and the action is on me. I find BB does this in two situations, 1) where he has a monster, set, top-two or AA. He hopes I have a king with a good kicker and will raise him. 2) When he has something marginal such as 1010-JJ, KJ, etc. He doesn't want to raise or start calling CB's so he's asking us the question.

I'll raise here nearly everytime and I'm going to assume that if he calls he'll check the turn to me. I expect him to do this with the monster as well as he should allow me to hang myself given that I should't have a draw (in theory) as preflop raiser. I calculate as follows: The pot stands at around 17bb and its 8bb to call. I'll usually go 8bb+20bb. I am therefore risking 28bb to win a pot of 45bb and thus need this play to be effective 62% of the time to be break even. My draw has about 16% equity for the turn card so I need him to fold around 46% of the time. I put it at about 50:50 monster/tester so its not a bad bet. However, in this case I see this bet as doing more for me. It'll often buy me a free river card as he'll usually seek to trap with the monster and seek to re-evaluate if he looks me up with a weaker hand. So in this case I have the back up of knowing that even if my raise (which we've calculated to be fairly marginal) isn't effective I still have another opportunity to win the pot.

The key thing is that the decision making process started with me deciding on an appropriate bet and then calculating the break even point from there. I can then use this to inform my decision making process and act accordingly.

[Rainclouds]

[ QUOTE ]

For example on the turn say you have a 28% chance of improving your draw on the river to the winning hand and feel if you make a ½ pot size bet that your opponent will fold 30% of the time, due to previous action, chipstacks and so forth (your fold equity would be 30%). Therefore you estimate the equity on such an action as 58%.

[/ QUOTE ]
You can't just add up the equities; if you have 30% to win but you are 100% sure someone will fold, you will end up with an equity of 130%! That can never be right [img]/images/graemlins/wink.gif[/img]

Also, the potsize is different when someone calls or folds, so you have to account for that in your calculations.

Yesterday I did a calculation for this in this thread; use it as an example.

[w33ktight]

should i be using lots of math like this?

when i think about fold equity, i think about the guys range of hands, how likely i am to hit, and how many hands in his range he folds. i dont use much math or anything, is that bad

i probably use lots of math that i don't realize im using, I just know it's the right play to make from experience.

(for instance pushing any 2 in some spots when everyone folds to you in the small blind in a mtt or sng)

[Rainclouds]

[ QUOTE ]
should i be using lots of math like this?

when i think about fold equity, i think about the guys range of hands, how likely i am to hit, and how many hands in his range he folds. i dont use much math or anything, is that bad

[/ QUOTE ]
No, in the heat of the battle, estimations will do just fine. The more experienced you are, the more accurate your estimations will be. The most important factor anyway is your judgement of how likely someone is to fold; there is no math to that.

[Acevader]

Great question weektight and the answer IMHO is no!! You should know what they mean though and how to use them though. Rainclouds other post is excellent but I'm sure he'll admit he can't run those calculations in 30 seconds. You therefore need to have 'guide' maths as I call it to help inform decisions but which cannot be definitive.

This is why I use the x2+2 method for outs calculations as it can be done in my head instantly and gets me with 1-2%. This can inform calling decisions. In my example above it doesn't take more than a few seconds with a handy calculator (or great maths skills) to calculate how often a bet/raise needs to be effective. Risk/gain if effective x 100 = the break even percentage.

I use this in combination with 'calls CB' stats in hud. If I've raised preflop and find two villians calling then I'm in a tricky spot to CB if I miss. But if they are say 25% and 35% respectively to call a CB then I'm in pretty good shape to bet pot. Unless I'm mistaken (raincloud?), the odds of either of them calling is 0.25+0.35/2*100 = 30.% If the pot is 20bb then I can bet 20bb meaning I need tht bet to be effective 50% of the time. I know in pure mathematical terms they will bin to that CB 70% of the time. I then use that info, examine the board and make a decision accordingly. Perhaps there is something about the board that eats into that edge enough to make a CB risky or -EV.

Please wait for verification of my maths as its not my strong point and hasn't been scrutinized before.

[Rainclouds]

[ QUOTE ]
Unless I'm mistaken (raincloud?), the odds of either of them calling is 0.25+0.35/2*100 = 30.%

[/ QUOTE ]
Actually, you have to calculate the chances that both [edit]FOLD[/edit] and substract that from 1. The odds are 1-(1-0.25)*(1-0.35) = 51%

Edit: I messed up some things, it's good now [img]/images/graemlins/wink.gif[/img]

[Acevader]

Right I think there must be something wrong with my maths in the 'two villians' example.

If we have an event A that is 50% probable and event B that is 50% probable then the probability of BOTH events happening are 0.5*.5*100 = 25%. I'm pretty sure this is correct.

In the above example I want to know the probability of A OR B occuring in which case I added them, divided by 2 and reached what is in effect an average of the 2. This seemed logical but I don't think it can be right because 0.5+0.5/2*100 is still 50%. How can you have two villians at 50% and still the same odds of an event occuring if there were just one? Seems illogical. However, if you stretch it to 3 villians at 50% then by this method its 75% probable that one of them will call. This does, seem, 'right' or logical to me? [img]/images/graemlins/confused.gif[/img]

[Acevader]

^^Post overlap^^

Thanks rain, that's what I was looking for.

So in my example we need to bet 2/3rd pot [img]/images/graemlins/laugh.gif[/img]

[Acevader]

P.S rain you have a typo in your maths (1-0.65) should be (1-0.35)