b * (1-x) = p * x, where x=equity 0<x<1, p is pot before our call and b is the bet amount we have to call.
So for this shove we fill in pot and bet since we know those
2.68(1-x) = 3.40 * x
2.68(1) - 2.68x =3.4x ;multimply b or 2.68 into 1 and x
2.68= 6.08x ;add 2.68x to both sides
x= .4407 ; divide both sides by 6.08 to get x alone =
as you mention we should account for rake too which could look like this
b * (1-x) = px -.05(b+p) ; that assumes 5% rake and b+p is total pot
2.68(1-x) = 3.4x - .05 (6.08)
2.68(1) - 2.68x =3.4x - .30
2.98= 6.08x ;
x= .4901
rake is
At first this surprised me but the pot is .42 on the flop and almost that entire amount will be taken in rake (.30) so thats why we need so close to 50% equity to stack.
fwiw I'd still stack here at the micros, someworse flushdraws stack here and we could have 19 outs with gutshot, pair, fd. his sizing is really stupid for anything other than a strong draw. does he have 98s and crap in his range? QQ makes some sense and kk++ seems like it will be 4bet pre often.
edit, I am lazy but both the above calculations fail to account for our 30 cents that went into the pot on the flop when we lead.
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