calculating EV of a bluff

[conslice]

if you were to be bluffing with a draw hoping for a fold but abotu a 3/1 underdog so 25% to make your hand if u do get called. how do u calculate how often u expect them to fold combined with your % to drawout if he does call to find out if a bluff is +EV. any kind of formula type thing would help by one of u math gods

[That guy]

To keep the numbers easy:

say there is 33% chance opponent will fold if you move all-in and if he calls, you will win 25% of the time...

easiest way to calculate is to figure out how often it WON'T happen and then subtract from 1...

so there is a 67% chance opponent will NOT fold (1-.33)
and there is a 75% chance you will NOT win if called (1-.25)

Thus,
.75 x .67 = you are 50% to win this pot if you move all-in...

thus, since you expect to win 50% of time, move all-in (the existing pot is your overlay). Use standard pot odds calculations when <50%.

[creedofhubris]

[ QUOTE ]
To keep the numbers easy:

say there is 33% chance opponent will fold if you move all-in and if he calls, you will win 25% of the time...

easiest way to calculate is to figure out how often it WON'T happen and then subtract from 1...

so there is a 67% chance opponent will NOT fold (1-.33)
and there is a 75% chance you will NOT win if called (1-.25)

Thus,
.75 x .67 = you are 50% to win this pot if you move all-in...

thus, since you expect to win 50% of time, move all-in (the existing pot is your overlay). Use standard pot odds calculations when <50%.

[/ QUOTE ]

You're not figuring in the size of the pot here vs. the size of the bluff, which is key.

[donny5k]

Let x = % of time he'll call your all-in, P = potsize before your allin, B = amount of money you are betting allin.

EV = x * ((0.25 * (P + B)) - (0.75 * B)) + ((1 - x) * P)

This is assuming you are facing a bet and your choices are fold or move allin.

EV of bluff = ((Total in pot before betting) * (percentage of times opponent Folds)) + ((Total in pot before betting) + allin Bet) * (1 - percentage of times opponent Folds) * (percentage of times you Win at showdown)) - ((allin Bet) * (1 - percentage of times opponent Folds) * (1 - percentage of times you Win at showdown)).

More elegantly: EV(bluff) = TF + (T + B)(1-F)(W) - (B)(1-F)(1-W).

So, if the pot is 1000, you put another 1000 in on a semi-bluff you think will win at showdown 25% of the time, the EV would be calculated like this:

EV = 1000F + (2000)(1-F)(.25) - (1000)(1-F)(.75).

To find out how often your opponent has to fold to make this semi-bluff break even EV, set EV = 0 and solve for F.

0 = 1000F + 500(1-F) - 750(1-F)
0 = 1000F - 250(1-F)
0 = 1000F - 250 + 250F
250 = 1250F
F = .2

So, when considering whether to go allin for 1000 more into a pot of 1000 which you have a 25% of taking down at showdown, your opponent only needs to fold more than 20% of the time for your bet to be positive EV.

[n1bd]

I like this formula because it's pretty easy to remember. It calculates the minimum probability of your opponent folding for which your bluff is profitable.

F = (B - E) / (P - E)

where

F = break-even probability of opponent folding
B = amount of hero's bet (or, if raising, amount of call + raise)
P = pot size when opponent folds, including hero's last bet/raise
E = equity in pot when called (in terms of $s, not %) = pot size when called * probability of winning

[1800GAMBLER]

It's also worth meantioning that while all the calcs above given are correct, factoring in the percentage success rate of your bluff if you wait another street is very important in these decisions.

great link

[_dave_]

Fimbulwinter made a very detailed post on this topic recently in the SSNL forum - I found it useful and interesting, hopefully you will too.

Calculating EV Part II: Making an All-In Raise

enjoy,

Dave.