Calculating how much FE needed for breakeven shove

[baudib]

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.

[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.

[Icanhastreebet]

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.

[Icanhastreebet]

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.

[baudib]

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