EV calculation

[iceman5]

Can someone give me a fairly simple formula to figure how often I need villian to fold for this all in to be break even EV?

Battle of blinds. I complete in SB with 77. BB raises to $14 and I call.

Pot $28. Flop 865 rainbow.

I lead $20, he raises to $60. I push in for $326. We have equal stacks.

Figure that when he calls he has a high overpair so Im 40/60 (close enough).

What percentage does he have to fold for me to break even. I can estimate in my head, but Id like to know the formula for future reference.

Thanks.

[fsuplayer]

dont know how to do the math myself, but id say its like 5% or so. hell, maybe less.

[xorbie]

This is a pretty standard calculation. I'm assuming you started with $340 each and that you push flop for $326 total. You bet $306 to win his $266 + $108 already in pot. If he folds, you end up with $306 + $108 = $414. If he calls, you win .4 * $680 = $272.

So your EV is -306 + 414x + 272(1-x) = 142x - 34, x is how often he folds. Break even point is x = ~25%. So pretty high actually.

[FoxwoodsFiend]

I'm pretty sure the formula is this:
x=probability he folds
W=chances you win if he calls
P=pot before bet
A=amount you're raising
B=Bet you're facing
EV of a bluff:
xP+(1-x)(W(P+A-B)-B)

Is this right and is there a simpler way to do it?

[punter11235]

I assume that "I pushed in for 326 means that you bet 306 more".

Lets denote :
E - our equity in $ if called
P - probability of opponent folding
Pot - pot including our last bet

Now :

EV = P*Pot + ((1-P)E - our bet)
If you are interested in breakeven point you need to solve it for EV = 0
The solution is :

P = (ourbet - E) / (Pot - E)

The problem is that you have to know your equity to calculate breakeven probability of opponent folding.
For the sake of simplifying the calculations lets assume your equity is in fact 40% when called. Then :

Pot if called = 680, E = 272$
Pot = 326 + 28 + 60 = 414$
our bet = 306$

P = (306$ - 272$) / (414$ - 272$) = 0.239 = 24%

Bear in mind that assumption about equity was pretty optimistic. So you need your opponent folding about one time in four to show profit here also to make this play worthwhile your actual EV must be higher than EV of calling which should be on plus side also in the actual hand.

Best wishes

EDIT : my opinion is that its bad push against most opponents

[iceman5]

[ QUOTE ]
I assume that "I pushed in for 326 means that you bet 306 more".

Lets denote :
E - our equity in $ if called
P - probability of opponent folding
Pot - pot including our last bet

Now :

EV = P*Pot + ((1-P)E - our bet)
If you are interested in breakeven point you need to solve it for EV = 0
The solution is :

P = (ourbet - E) / (Pot - E)

The problem is that you have to know your equity to calculate breakeven probability of opponent folding.
For the sake of simplifying the calculations lets assume your equity is in fact 40% when called. Then :

Pot if called = 680, E = 272$
Pot = 326 + 28 + 60 = 414$
our bet = 306$

P = (306$ - 272$) / (414$ - 272$) = 0.239 = 24%

Bear in mind that assumption about equity was pretty optimistic. So you need your opponent folding about one time in four to show profit here also to make this play worthwhile your actual EV must be higher than EV of calling which should be on plus side also in the actual hand.

Best wishes

EDIT : my opinion is that its bad push against most opponents

[/ QUOTE ]

Whether or not calling is better wasnt the point of the post. Its a whole different question. I just used this as an example to get the formula. Thanks guys.

[ddubois]

I made a spreadsheet for this a long time age:
http://ddubois.bounceme.net/poker/OddsBets.xls

The formula has a twist to it:
((pot*foldpercent)+((1-foldpercent)*mywinpercent*(pot+MIN(mystack-actiontome,hisstack))))-((1-foldpercent)*(1-mywinpercent)*MIN(mystack,hisstack+actiontome))