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.