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Hey, Visaria, can you point me to the way of calculating the relationship between Kelly and the standard deviation? What I am looking for is a way to maximize the (growthRate/stdev ) ratio. That is, the question is, by how much do I need to reduce Kelly so that I can maximize the quantity which...

Kelly prescribes betting 8% of the bankroll on Red-16. 8% of $1000 is $80. With that single $80 bet, you have an 89.2% probability of losing $80, and a 10.8% probability of making $2800 (80 * 35). Therefore, the expectancy of that single bet is: 0.892 * (-80) + 0.108 * (+2800) = $231. QED...

I've already qualified this. If the goal is to maximize the return with no regard to risk, and if you are willing to destroy hundreds of accounts in this game, then betting 100% is indeed the right strategy. For example, there is 1 in 791 chance that you hit R16 three times in a row, which...

Here are the top 10 strategies, if the goal is to maximize the risk-adjusted return, rather than the absolute return. The score is the average return divided by the standard deviation of returns. The top strategy is to bet 1% of the bankroll on Red. This strategy would probably resonate with...

I believe that the above Monte-Carlo simulation results are totally valid. In the extreme case of a 100% allocation, they simply show that if you are willing to blow your account thousands of times, eventually you would make enough to recoup all the losses. In other words, it assumes that you...

And here are the results, which are the top 10 strategies, for each of the max allowed drawdown: Max allowed drawdown: 25 R16 R14 Red AveProfit 3 0 0 1609 2 1 0 1449 1 2 0 1224 2 0 2 1053 2 0 1 995 0 3 0 953 2 0 0 938 1 1 2 885 1 1 1 833 1 1 0 781 Max allowed drawdown: 50 R16...

Ok, here is the Java code for the Monte-Carlo simulation. It creates 176851 strategies with the different allocation of capital to R16, R14, and Red, and then spins the wheel 10 times. This counts as one trial. At the end of the trial, the profit is calculated for each of the 176851 strategies...

Right, that's what I thought, too, but after running the Monte-Carlo simulation on this problem, the results are totally not what I expected. The top strategy is this combo: {R16:60%, R14:30%, Red:10%}. So, it's a bet of 100% of the bankroll on every bet that maximizes the average profit over...

Yeah, that's it, thanks Visaria.

Yes, although I am not sure if it should be adjusted for volatility (risk), or if it's already adjusted for volatility by incorporating the Kelly. From what I remember, cutting Kelly by 50% reduces the risk by 75%. So, if we are seeking the maximum risk-adjusted return, perhaps we should account...

Correct.

It's still a good interview question. What matters here is how the interviewee thinks, and not how accurately he/she understands the assumptions of the stated problem. And indeed, it's very directly related to the problem of the optimal capital allocation in the portfolio of strategies.

You postulate that Kelly doesn't apply because of the limited number of trials, but then proceed with the 100,000 trials simulation to come up with a more legitimate answer? Both Kelly and Expectancy are invariant with respect to the number of trials. Think of it this way: you can play only 10...

Yes, your original proposal (a combo bet of 8% on R16, 5% on R14, 24% on Red) is almost certainly an overbet. I am not sure if it's possible to solve for the optimal combination bet analytically, but it can certainly be done numerically using a simulation.

Ok, thanks for the clarification. Here are my calculations. Optimal bet fraction = Kelly = p - (1- p) / b, where p = probability of winning b = odds on the bet Expectancy = p * b - (1 - p) My custom score = Expectancy * Kelly Then, Kelly(red) = 23/37 - (1 - 23/37) / 1 = 0.24 = 24%...

Okay. And what about the rule about about R-14 and R-16? There are 3 R-14 spots. So, if I bet on one of these R-14 spots, and the ball stops at the other R-14 spot, do I get a 35:1 payoff, or not?

The rules are still not clear to me. If I bet on either R-14 or R-16, and the outcome is some other red number, I still get the 1:1 payout, right?

The way I read it, the bet on either R-16 or R-14 wins 1:1 if the outcome is any red, except when the outcome is R-16 and R-14, in which case the bet wins 35:1. Therefore, it doesn't make sense to bet on just Red.

Manis and carss. I like that. Manis Manis was the trained orangutan that played Clyde, Clint Eastwood's orangutan sidekick from the 1978 box office hit Every Which Way But Loose. Its 1980 sequel, Any Which Way You Can (1980), did not feature Manis, as he had grown too much between productions...

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