Calculating how much FE needed for breakeven shove

This has probably been done but I'm not the greatest math guy and I'm lazy. Had discussion with a friend about a hand in a live game that a third party played.


Spare you the details but Hero has on board of turn
BB (raised over limpers) bets $70 into pot of $125. Pot is $195, effective remaining stacks $405.

Friend came up with this formula:
0 = XP + (1 - X)(-LV + WH)

Where...

X = Breakeven Folding Frequency
P = Current Size of the Pot
L = Maximum Loss
V = Villain's Equity
W = Maximum Gain
H = Hero's Equity

So, we need to solve for X obv.

0 = 195X + (1 - X) (-405 x 0.65 + 530 x 0.35)
0 = 195X + -77.75(1 - X)
0 = 195X + 77.75X - 77.75
0 = 272.75X - 77.75
X = 77.75/272.75 = 0.285 BE point for FE. (or 29%)


So we need him to fold around 29% for a breakeven shove. Does this seem right? It jives with my half-ass way of figuring it out.

you wanna shove this turn and want to know how much FE you need to make the shove 0EV at least?

first you need a range for him on this turn.

X*195+Y*(195+405)+(1-Y)*405=0

X=FE
Y= your equity vs his turn range for calling a shove.

every time he folds you win pot=195, when called Y times you win pot+405(his stack left) and you lose (1-Y) times 405 your stack shoved. thats why X is FE and Y is our equity vs his calling range. when we equal all this to 0, the shove is 0EV for X value we get by resolving ecuation, if X is higher the value got from our ecuation then the shove is +EV and -EV if X is lower the ecuation value.but all this depends also on the acurracy of our range for him.

Originally Posted by Razvan729

you wanna shove this turn and want to know how much FE you need to make the shove 0EV at least?

first you need a range for him on this turn.

X*195+Y*(195+405)+(1-Y)*405=0

X=FE
Y= your equity vs his turn range for calling a shove.

every time he folds you win pot=195, when called Y times you win pot+405(his stack left) and you lose (1-Y) times 405 your stack shoved. thats why X is FE and Y is our equity vs his calling range. when we equal all this to 0, the shove is 0EV for X value we get by resolving ecuation, if X is higher the value got from our ecuation then the shove is +EV and -EV if X is lower the ecuation value.but all this depends also on the acurracy of our range for him.

He only has 335 left in his stack sir.

Looks good. I prefer to always call x our equity and use F or FE for fold equity but that's w/e.

Formula is same thing just

eV = P*FE + (1-FE)((P+2S-B)(x) - (1-x)(S))

eV = eV ldo
P=Pot
FE=Fold equity
X=our equity
S=stack
B=The last bet or raise they made.

sorry I forgot to mention that we assumed we have 35% equity vs. his calling range.