Maximizing cEV in check behind vs betting scenario.

[DevinLake]

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You should bet if 500y + 200x > 200 (x,y decimals)

Note that x being larger makes it better to bet. This may seem slightly weird but it comes from having a fixed y% of his whole range that is best & folds. That's what you're gaining irregardless of x & you're risking slightly less if x is larger.

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Yea, I realize all this. I was just trying to figure out a way to determine if their are distinct values for x and y that yield the larges gains in cEV by betting rather then checking behind.

But, I realize this is a linear function, and the maximum is only constrained by how we define x and y. Obviously, the best scenario is when x and y are a maximum. However, the only relationship we can really say about x and y is that x+y<=1.