Maximizing cEV in check behind vs betting scenario.

[DevinLake]

Here's the scenario.

You get to the river of a cash game hand where the pot is $300. You have a hand with show down value. Ie, it's the best hand x% of the time. However, because there are weak hands in the villains range, you feel that betting will fold out weaker hands that beat yours y% of the time.

So, your cEV for checking behind is x*300.

Your cEV for betting (I'm assuming the bet is $200) is (300)(x+y)-200(1-x-y). I'm also assuming all worse hands fold so you lose every time you are called.

What I'm trying to do is figure out some sort of equilibrium between x and y that maximizes cEV. But, I'm not sure how to set the constraints either.

The more I think about this, the more I think it's probably a stupid question and you can't really find an equilibrium. But, I'll see what you guys think/suggest.