Hi, I'm trying to figure out a general equation for how much I should bet X when opponent folds Y% times and I have Z% equity on the flop. I also want to solve this equation for all X and Y and see what a graph looks like.

First, is it even possible to do, and second what is the math for the first part. Not sure if I have this right.

Suppose I have

**K** **Q** in BB against a BU open range, I call pf and flop comes

**4** **9** **J**
Now I decide to donkbet semibluff my two overs and I estimate my opponent will fold 50% of his hands - so I should bet pot if I only considered fold equity - to make a better hand fold (maybe small pockets or missed AK with no hearts) or take down the pot right away.

I also have a fair bit of equity on the flop maybe 41% according to Equilab, so I don't need to bet full pot, my semi bluff is part value, part bluff?

so I have

EV(folds) + EV(calls)

say the pot is P$ and my bet is X$

my equity if folds is 100%

my equity if calls is 41%

if folds I win $P? or $1/2P??

if calls I win P$ + X$ (or 1/2P$ +X$?) profit 41% of the time and lose same amount 59% of the time (assuming no turn and river action - maybe this is where the math breaks down..)

so my EV on flop (no turn and river)

50% X (P$) + 41% X (P$ + X$) - 59%(P$+X$+)

= 0.5P + 0.41P + 0.41X - 0.59P - 0.59X

= 0.32P - 0.18X

for a pot of $16 and a bet of 10$

P= $10.00 ($16 minus my say 6$ contribution)

= $3.20 - $1.80 = $1.40

so with 50% fold equity and 41% equity a 2/3 pot bet is worth $1.40

if my fold equity was instead 30% and my bet was the same my bet would be worth

= 0.12P - 0.18X

= $1.20 - $1.80 = - $0.60, not a great bet equity wise, but our EV could improve or worsen on the turn and we might get more action - so maybe it's not even worth doing the math and plotting the surfaces?

thanks for reading even if you don't respond. thinking on a thread helps me figure this stuff out.