Bottom set on monotone flop, lay down or move in?

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How sure do I need to be here that he's got a made flush for me to fold?

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I think there are three holdings you are likely up against here. First is a made flush protecting against a higher flush. Second, a flush draw like Ahx. Third, top pair like black A9, a lower pair, a pocket pair or a bluff.

If you are against a made flush, you still will improve to quads or a boat 34.4% of the time, making the EV of your call -288.84 chips. If you are against a flush draw like Ahx, you will win the hand 71.7% of the time, with an EV of 569.38 chips. If you are against a pair like A9, you are the overriding 94.3% favorite, making the EV of your call 1053.02 chips.

To figure out how often villain needs to have a made flush to make your call correct, we have to solve this equation:

(likelihood of a flush)(-288.84) * (likelihood of a flush draw)(569.38) * (likelihood of a pair or bluff)(1053.02) > 0

First, lets somewhat-arbitrarily assign the likelihood villian is on a pair or worse at 10%. This seems a little low here, but it's better to err on the side of a good opponent than a bad one.

This leaves us with two equations to solve (x = likelihood of made flush; y = likelihood of flush draw):

-298.84X + 569.38Y + 105.302 > 0

and

X + Y = .9

So, restated in terms of X:

-288.84X + 568.34 (.9-X) + 105.302 > 0

or

X > .7196

Therefore, you would have to put your opponent on a made flush given his push on the flop more than 71.96% of the time for your call to be wrong. There is no way he has that big a hand this much here, and your call was clearly right. NC. Nice suckout, too.