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I'm not convinced about the formula for CK. It seems too simple.

Sorry, too complicated. My computing has been reduced for the time being to an android tablet which really sucks. I'll tackle the Kelly eq when it reduces to a quadratic but not when it's a cubic or higher. I'll never complain about Windows again (at least not until I get back on a Windows...

Kelly == 0.1963808 Expectation == 1.81572481 k*E == 0.35657349 :cool: There is overbetting here (betting fraction == 22% > k) but the proportions are very good.

No. Reread the definitions. They're based on a unit bet. To put it another way, x == R/(R+F+S), and so on.

The Kelly equation I posted indicates the total betting fraction (k) that grows a given asset allocation {x,y,z} the fastest in this roulette game. So it doesn't find the optimal allocation {x_opt, y_opt, z_opt}. x_opt, y_opt and z_opt are the values that maximize k*E.

Oy! Sorry, I have to do it my way. Let x == fraction of unit bet on Red , Let y == fraction of unit bet on R-14 , Let z == fraction of unit bet on R-16. x + y + z == 1 E == (4/37)(35z+x-y) + (3/37)(35y+x-z) + (16/37)(x-y-z) + (14/37)(-1) Now comes the hard part: 0 ==...

OK but we don't have the many-horses situation. Red is not mutually exclusive with either R-14 or R-16. I had to solve the Kelly equation the hard way, so I made the assumption that the bet on Red was exactly half of the betting fraction. This reduced the 16 unfavorable red outcomes to...

Thanks, nonlinear5. :) Strategy MedianProfit k*E C 1849 0.35601508 B 1344 0.28061395 A 162 0.05917 Just as I suspected, your original performance metric predicts exactly what the best strategy is, even when Kelly sizing itself isn't used. Trust your first...

Thanks for the thorough testing. Yikes! I didn't expect this. I think the problem is the average. I should have specified the median, because 'average' usually is interpreted as the mean (even though, strictly speaking, 'average' can indicate the mean, the median or the mode). And the mean...

Profit. Starting with $1000, what is your final bankroll after ten spins? On average, of course. Which strategy is best and which is worst? Thanks.

OK let's try a different question. Which of the three strategies below is best according to MCS? A) bet 10% on Red ; B) bet 5% on Red and 5% on R-16 ; C) bet 5% on Red, 3% on R-16 and 2% on R-14. Now we can make an apples-to-apples comparison looking only at asset allocation and with...

The answer you arrive at depends on how you approach the situation. 1) Is this a real-life event where you're playing with your own money and you're free to gamble it away with no other consequence? 2) Is this an interview question where your prospective employers are looking to see how...

The BEST strategy! (... so far) : Bet 13% of bankroll on Red ; Bet 7.8% of bankroll on R-16 ; Bet 5.2% of bankroll on R-14. Kelly == 0.2593 , Expectation == 1.37297 , k*E == 0.356 :cool:

Prove it.

You're mixing apples and oranges. Of course the Kelly fraction doesn't give asset allocation, its calculation is totally dependent on asset allocation. BUT it does reflect the quality of any given asset allocation. For all your complaining, you've yet to show a better method of determining...

I propose that the Kelly fraction is a far better measure of risk than standard deviation. At least the risk reflected in Kelly is pure downside, whereas the 'risk' reflected in standard deviation is only partially downside.

Agreed.

1% on Red? Sheesh! Why bother? (A) I'll stick with Kelly. (B) You might get better results with the downside deviation rather than the standard deviation. PMPT uses the downside deviation.

You just proved that it is. Kelly has the higher expected outcome. As to the greater std dev, so what? You've swallowed the economystic kool-aid that standard deviation is a measure of risk. In fact, standard deviation is a measure of uncertainty, and uncertainty can work in your favor as...

You should not use the word 'guarantee' in the context of MCS. MCS is a computer program, and as with all computer programs, it's Garbage In, Garbage Out. And even assuming you've made no bad inputs, how good is your random-number generator? I'll bet it's not the world's best. And even the...