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Ok, thanks. My Monte-Carlo disagrees somewhat with your more analytical solution (specifically with respect to the bet on red), so I am looking for he explanation of the discrepancy.

Your solution is much more elegant than mine, since it does not require any random number generation or Monte Carlo simulations. So, it's much faster and more accurate. Here is what I get with your proposed solution (top 20 strategies): R16 R14 Red F(R16, R14, Red) 8 5 11 0.11634 8 5 12...

And here is what I think is the answer to the original question. The "best" strategy is a close tie between these top 10 strategies: R16 R14 Red MedianProfit 8 8 5 2473.37 7 7 5 2472.91 8 8 4 2472.69 7 7 6 2472.38 8 7 4 2472.12 8 8 6 2470.02 7 7 4 2469.58 8 8 3 2468.00 7 7 7 2467.99...

Okay, I think I am closing on the solution. First, I found a bug in my Monte-Carlo simulation, so the previously posted results should be discarded. Second, I fixed the bug, and verified the code by running it against the various single bets on R16 (I have not tried the combo bets yet). The...

I stll think there is a certain equivalence here, because the continuous Kelly is a generalization of the descrete Kelly, and the continuous Kelly is simply return divided by squared standard deviation. I have an idea of how about how to test for this equivalence, which I will do tomorrow.

Right, I will take my suggestion back.

As it turns out, there is a well-known solution to this problem. See the "many horses" section in this article. In our particular case, the Red-16, Red-14, and Red can be thought of as 3 different horses, with the well-defined odds and edges. So, the Kelly criterion can be applied to this...

And here is another one, with an additional metric, roughly equivalent to Sharpe ratio: average profit divided by the standard deviation of profits. Strategy R16 R14 Red AveProfit MedianProfit MedianSharpe E 50 0 0 21481547 156 0.04 D 25 0 0 494454 2084 0.20 B 5 0 5 4339 1344 0.85 C 3...

Here is the same simulation, with both average and median profits: Strategy R16 R14 Red AveProfit MedianProfit E 50 0 0 21481547 156 D 25 0 0 494454 2084 B 5 0 5 4339 1344 C 3 2 5 3544 1849 A 0 0 10 272 162 In deciding which strategy to use, the median profit certainly looks like an...

Correct. The "average" result is skewed by just a few outliers which have an enormous profit, against the vast majority of the outcomes which result in a total loss of a bankroll. I'll re-run with the median, and post the results shortly.

OK, I added 2 more strategies for reference, and ran the simulation 10 million times. I also added a condition that if the bankroll drops below $1, no bets can be made. The utility function is the average profit after 10 spins. Here are the results: Strategy R16 R14 Red AverageProfit E 50 0...

Okay, I'll run it later today. Dom993, would you mind running it, too, just verify the validity? Let's run, say, 100000 simulations, each one for 10 spins of the wheel.

I can run the Monte-Carlo simulation, but to determine the "best" strategy, I have to use some performance metric. Which one would you like me to use?

The "continuous" version of Kelly also uses standard deviation: CK = r / s^2 That happens to be directly related to Sharpe's ratio: CK = r / s^2 = S / s CK = continuous Kelly r = return s = standard deviation of returns S = Sharpe's ratio Now, I know that you fight a campaign against the...

:)

Got 150, which apparently qualifies me as "genius". Click on the image to take the test. <a href="http://www.freeiqtest.info" title="IQ Test"><img src="http://www.freeiqtest.info/Badges/www.freeIQtest.info-150.gif" width="127" height="148" alt="IQ Test" border="0"></a>

I finally found what I was looking for, in a graphical form:

Ok, so you are uncomfortable with the high variance of the results when using full Kelly. Me too. But it doesn't disprove the hard mathematical fact that Kelly maximizes the compound rate of return, either over 1 trial, or over 1 million trials. Mine is to maximize the return-to-risk ratio...

But in the 30% of the outcomes, the payout on the Kelly bet is many times larger than the payout on the fixed $50 bet, isn't it? Why are you ignoring these 30% of the outcomes?

What's the formula from which this relationship is derived? And how does the growth rate scales when Kelly is reduced? As Kelly is reduced, the growth rate decreases slower than the variance, which implies that the risk-adjusted growth (growth divided by variance) goes up. I'd like to know at...