Certainty Equivalent Calculation

[NotEnoughHeat]

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)?'

[DSchles]

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)?'

Does this help?

Certainty equivalent is: CE = mu - (0.5/risk tolerance)*sigma^2.

Go here: http://www.web-books.com/eLibrary/ON...9/079MB59.html

Don

[NotEnoughHeat]

Does this help?

Certainty equivalent is: CE = mu - (0.5/risk tolerance)*sigma^2.

Go here: http://www.web-books.com/eLibrary/ON...9/079MB59.html

Don

What's the unit for risk tolerance in this equation?

A particular instance I have ran into is $360 EV for a play with about $130 SD.

Plugging in a Kelly fraction doesn't seem right because if my kelly fraction is 0.5 then the bracket reduces to 1. With a VAR of 130^2 = 16900, and a much smaller EV, it suggests that I would pay huge sums to avoid this gamble. What's going wrong here?

[RS]

I'd run several simulations on the game. On the side, include the different options (% free-roll or flat payment).

[NotEnoughHeat]

I'd run several simulations on the game. On the side, include the different options (% free-roll or flat payment).

Thanks. For some reason it never occurred to me that it might be possible to sim this on CVData since the base game is blackjack.