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Haha. You are starting to sound like certain famous posters here, who make it their purpose to obfuscate everything they say. I still don't know what the purpose of this discussion is, so I'll treat it as chit chat.

Did you figure out what the K*E is for {R16: 8.1% R14: 5.4%, Red: 10.8%}, which by consensus, appears to be the best 3-way combo?

Thanks for posting this. It's very humbling to watch.

So, your approximation is a better one, then?

You are becoming defensive, dude.

Both can be used, depending on how you calculate the return: LN(1 + (price2 - price1) / price1) = LN(price2 / price1) = LN(price2) - LN(price1)

See here: http://www.bjmath.com/bjmath/thorp/paper.htm, equation 7.4. See here: http://quantivity.wordpress.com/2011/02/21/why-log-returns/ Some of my strategies have Kelly-optimal leverage of 180.

One thing that I'd note is that your approximation of Kelly: k ~ sum[Ri]_n / sum[Ri²]_n resembles the continuous Kelly: CK = R / (s^2) Note that: -- your nominator sum[Ri] is proportional to R -- your denominator sum[Ri²] is a component in (s^2) I think that if you started with ln(r)...

I think I hijacked this thread, sort of. Sorry about that, kut2k2. The original problem seems to have been solved, so we have proceeded to discuss other (related) problems. tradingjournals: the A and B strategies have nothing to do with the roulette game. Rather, it's a totally different problem...

By definition, the return on a single bet A is about 10 times of the return on a single bet B. So, let's say that A and B do indeed collide in a sense that if you bet on one, there is not enough capital to bet on the other. If you bet only on A, you make return R, with a standard deviation S...

Understood and agreed. My preference for using Sharpe^2 instead of Sharpe is motivated by the more straightforward interpretation of the former. Since Sharpe^2 measures the "leveraged expectancy" (that's the best that I can describe it), it scales more intuitively to me. For example, if strategy...

How did you come up with this, and how do I solve for k?

Right, but what is the "base" metric for a betting strategy? I am arguing that it should be r/s, or better yet, (r/s)^2, since it captures the relative value of a strategy better.

Right. And furthermore, I propose that (R^2 / S^2) can be used as a universal performance metric for strategy selection, including any trading strategy, and even more generally, including any betting strategy, such as the one stated in the beginning.

It takes between 50 ms and 600 ms for me.

I think I am onto something. I found a confirmation of (r^2) / (s^2) = Sharpe^2 as a "special quantity" in here (see section 7, "Wall Street: the biggest game", equations 7.4): http://www.bjmath.com/bjmath/thorp/paper.htm

Help kut2k2 and myself to come up with a generalized approach to rank trading strategies (not necessarily the ones with a binary outcome) . This is where I'd like to see the direction of this discussion.

I don't know what this means. Is the purpose of this thread to illustrate that there is no way to run a profitable trading business?

Yeah, same here. The last question (about the 10 overlapping hexagons, or something like that) was insanely difficult. I figured that it would take me an hour to find the correct answer, so I just guessed.

I think there is an error some place in your derivation of k*E. Based on your formula, my results indicate that there are only 2 combos which are profitable, at z=0, and at z=1. So, it says that all combination bets are losers. This is clearly not right.