I believe that I have this correct but I was hoping someone could double check it for me.

30 bb effective

Hero (UTG) opens for 2 BB
UTG +1 3bets to 4.5 BB
folds back to Hero

If Hero ships allin he expects to pickup blinds and antes, assume 2.75bb, and the rest of the dead money (9.25 bb total) 60% of the time.

The other 40% of the time, when hero is called, he expects to have 35% equity against villains calling range.

.60(9.25) + .40(.35(62.75) - 28)= +3.13bb ev

If my above math is correct, how do i figure how often villian has to fold for play to breakeven? Thanks in advance.

Your math is correct; required fold equity for BE is basically the same equation with another unknown:

x*9.25+(1-x)*(.40(.35(62.75) - 28)) = 0 and solve for x

Answer is 20.7%

thanks bud. would you be able to show me how you solved for x? i cant remember how to solve for unknown. thanks again

It's just basic algebra:

x*9.25+(1-x)*(.40(.35(62.75) - 28)) = 0
--> x*9.25+(1-x)*(-2.415) = 0
--> x*9.25+1*(-2.415)-x*(-2.415) = 0
--> x*9.25-2.415+x*2.415 = 0
--> x*(9.25+2.415) = 2.415
--> x = 2.415/(9.25+2.415)
--> x = 0.207

what does the -28 part signify?

This is what not having a math class for over a year does to me. My sister asked me for help with like 8th grade algebra last night and it took me a bit to just recall the standard stuff.

You're not gaining the extra 28 BBs (30-2) in your hand when you win the pot. They were yours to begin with.

Contrast that with your 2BB opening raise, which is included in the dead money in the first part of the equation, because you can't get it back when you fold.

Cool thanks

See it this way too if its easier to understand why; (also its not 20.7% only, you left a 0.4 in there that was the 1-x ) (compare avg positions with a push and a fold option, a call is also another alternative that maybe necessary to know on occasion as it may sometimes prove better than the other 2)

You have 30bb and used 2bb so 28bb left to decide what to do. Whatever you do will have some expected result. To be better than folding you need it to be higher than 28bb.

So if you push and he folds x fraction of the time the expected result of the push will be

x fraction of time a move to 28+9.25 + (1-x) fraction of time to 62.75*Equity when called.

So this must be larger than 28 or;

x*(37.25)+(1-x)*0.35*62.75>28 or x >39.5%

So he must be folding more than 39.5% of the time. If he folds 60% (=called 40%) the above gives +3.135bb as you said.

So the threshold is 39.5% fold probability.

thanks masque for correcting that. i believe pablito just forgot to replace that 0.40 with (1-x). i could not remember how to do the basic algebra and had to have my brother refresh me. thanks again guys.

lol

if you fold you win/lose 0.

If you shove and villain folds you win 9.25 BB

If you shove and you are called you:
win 37.25 BB 35 % of the time, and
lose 28 BB 65% of the time

The formula (where P = % villain folds) to determine break even is:
(P * 9.25) + ((1 - P) * ((37.25 * .35) - (28 * .65)) = 0
9.25P + ((1 - P) * (13.0375 - 18.2)) = 0
9.25P - 5.1625 + 5.1625P = 0
14.4125P = 5.1625
P = 35.82 %

So if villain folds more than 35.82% of the time you have a +EV.