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I suppose I misread. So, what's your "absolute best" strategy?

The rules as stated in the beginning do not allow borrowing. They clearly say that the maximum bet can't exceed the bankroll. We don't have the solution for this yet.

Yeah, clearly it is. It got us all fooled for weeks, and we still don't know the answer. Well, it's coming.

I'll see if I can set it up for simulation. Should not be that difficult. Thanks for your participation in this thread, SplawnDarts. I've learned a few good things from you.

I didn't understand where the arbitrage comes from until I worked out this bet. Indeed, this is a risk-free bet, you win every single time! This is almost disappointing, as the best strategy turns out to be borrowing as much as you can, and betting 100% of your bankroll, on every bet. So much...

So, bet a small percentage on all black numbers, with the bulk bet on R16, R14, and Red?

It's an approximation only when it takes the analytic form of (r / s^2), because it makes an assumption that the returns are normally distributed. If you solve it numerically as I outlined above, no such assumptions are made, so the CK is exact, in the sense that it maximizes the compounded rate...

In one of your other threads, SplawnDarts gave a recipe for calculating Kelly from any series of trade returns: Let's verify this recipe. Suppose that the rules of our roulette game are simplified. The only allowed bet is that on R16. How much do we bet? The precise solution is given by...

Well, we are measuring the risk-adjusted performance, as signified by the rate of growth (rather than by the absolute profit). By including the bets with negative expectation (such as Green-0), the expected profit is reduced, but the risk is reduced by a larger degree. The ratio of the two...

Looks like the (k*E) metric has its merit, right?

You are right in that there is nothing special about Green-0. A bet on Green-0 is just as good as a bet on any other number, as long as it's not R16, R14, or Red.

Red is part of the solution, too. It's just that we are experimenting with various rules, such as excluding bet on red altogether.

I don't know what the above equation is. We are looking to maximize the rate of growth g, which is the log of the terminal bankroll so I believe my version (well, SplawnDarts' version) is correct: F(R16,R14,Red,Green) = (4/37) * log1p(35 * R16 - Green - R14 + Red) + (3/37) * log1p(-R16...

Maybe (k*E) does not exactly correspond to LN(bankroll), which is the rate of geometric growth.

It still does: R16 R14 Red Green F(R16,R14,Red,Green) 8.4 5.7 0.0 0.3 0.110270 8.5 5.7 0.0 0.3 0.110269 8.4 5.8 0.0 0.3 0.110268 8.5 5.8 0.0 0.3 0.110266 8.4 5.7 0.0 0.4 0.110262 8.3 5.7 0.0 0.3 0.110261 8.5 5.7 0.0 0.4 0.110261 8.4 5.8 0.0 0.4 0.110260 8.3...

I started with the Monte-Carlo simulation, generating a random number between 1 and 37 (inclusive), millions of times, and noting where the LN(bankroll) reaches the maximum. That works, but it converges slowly, and is not precise. Then SplawnDarts suggested a much better solution, which does...

I confirm SplawnDarts' results. Here are the top 5 combos, if bet on Green is allowed: R16 R14 Red Green F(R16,R14,Red,Green) 8.1 5.4 11.4 0.6 0.117290 8.1 5.4 11.5 0.6 0.117289 8.1 5.4 11.3 0.6 0.117289 8.1 5.4 11.6 0.6 0.117288 8.1 5.4 11.2 0.6 0.117287 Unexpected and very...

You must have missed this:

RAM is cheap, and your 8GB is definitely on the low side. Windows 7 Professional 64-bit supports up to 192 GB. That max would be an overkill, but 32 Gb would make your apps run much smoother. I don't think it matters whether it is 4x8 or 2x16. However, your machine is likely to have specific...

The discrete Kelly is applicable in a very special case when the outcome is binary -- either the entire loss of a bet with a well-defined probability, or a payoff with another well-defined probability. That's what makes the discrete Kelly so simple. The continuous Kelly is a general case when...