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No but so what? That's like asking if you inherited a huge fortune, would you have to work for a living? Again the answer is no but so what? For those of us who aren't rich and who don't have a holy-grail trading strategy, a job and a good performance metric help a lot.

System Achievement Score

k*E for R-14 is 0.10520714. k*E for R-16 is 0.23894396. k*E for {R-14, R-16} is 0.35349969. Once again, the whole is greater than the sum of its parts.

Well yes, that confirms what I said: F > k14 and S > k16. The real question is where this synergy comes from.

http://www.elitetrader.com/vb/showpost.php?p=3960777&postcount=111 http://www.elitetrader.com/vb/showpost.php?p=3960803&postcount=114

We agree.

Excel. Doesn't get any cheaper than that. Runner-up: AmiBroker.

A Tale of Two Horses II At long last, so have I. I tried different ways but got nowhere with my unit-bet analysis. So I went back to the relationship established by Splawndarts and, with the aid of an on-line equation solver, I got the following results: F == 5.72% and S == 8.43%...

My approximation doesn't output leverages, especially in the three-digit range.

Not at all. Here's what you posted. Nowhere in the link you provided is ln(r) or log(r) mentioned. What is talked about is log(1+r), which is vastly different from log(r), and which I already said is one step in the derivation of the Kelly equation. The derivation of the Kelly equation is...

Yes I said that. If r == ln(p2/p1), then what do you mean by ln(r)?

There's a huge difference between log(r) and log(1+r). And the Kelly equation is the result of first taking the logarithm of the gain before taking the differential. It looks like you're conflating a derivation with a final result. And do you trust this number? And how is this leverage...

I need the same type of rigorous mathematical proof that I supplied to you, not just speculation. Three things: Ln(r) makes no sense to me. Why do it, if we already have r? More to the point, returns are often expressed not as percent price change but as the logarithm of price change...

http://www.elitetrader.com/vb/showpost.php?p=1577681&postcount=1 http://www.elem.com/~btilly/kelly-criterion/#complex_kelly

I propose the System Achievement Score. SAS == 4*k*max[ 0, E ]*PF*min[ 1, N/mant ] , where SAS is the System Achievement Score, k is the solution to the Kelly equation (see below), E is the expectation (see below), PF is the profit factor (see below), N...

I think you are correct. I have faith in the numerator but there is something wrong with the denominator. I didn't expect Visaria to give up so easily. :p I'll work on this problem later when I have more time.

Nope, not even close. For {R-14, R-16}, k*E == (36z + 71)(36z + 71)/(37(47952zz - 47952z +1295)). where z is the fraction of a unit bet that is placed on R-16, 1-z is the fraction of a unit bet that is placed on R-14. k*E is only positive when z > 35/36 or z < 1/36. k*E clearly...

What about the score we agreed upon? Median bankroll after ten spins.

I welcome evidence to the contrary. My analysis was not easy and it's possible I missed something.

R-14 versus R-16 Or A Tale of Two Horses Suppose we had the same scenario as depicted in the OP with the exception that you can't bet on Red (casino management feels a winrate greater than 50% is too attractive). So you can bet on any of the 34 numbers, you can bet on Black, or you...