There's a play I do that is small volume but scales with partners. I usually offer a flat $X or a Y% cut in the profits (freeroll). Although most people (2/3) have taken the flat amount my concern is that the freeroll is obviously better. I have thought about this since I started recruiting others but I haven't been able to figure out, given a utility function as a Kelly fraction, what the risk premium for taking the % cut should be.
A few times I have tried looking around for a CE formula that's applicable. The issue is that most of the formulas I have found apply to binary events (event with some fixed percentage chance of winning). The outcome of the play is a normal distribution not a binary win-loss.
Anyone have any idea how I would go about calculating the CE for a play with a distribution N(?, ?)?
EDIT: doesn't display properly, but it should read 'distribution N(mu,sigma)?'
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