What is your strategy?

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kut2k2 said:
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%

Surprisingly, at least to me, both F and S are larger than their respective single-bet Kelly fractions.

Specifically, F is 4.4% larger than k14 and S is 2% larger than k16.

This implies some sort of synergy is created by combining mutually exclusive bets. Any thoughts?
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must have missed something, what do u mean by F and S?
 
kut2k2 said:
F == 5.72% and S == 8.43%

Surprisingly, at least to me, both F and S are larger than their respective single-bet Kelly fractions.
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Well, hardly. Single bet Kelly fraction is 5.5% and 8.3% for r14 and r16, respectively.
 
Visaria said:
kut2k2 said:
F == 5.72% and S == 8.43%

Surprisingly, at least to me, both F and S are larger than their respective single-bet Kelly fractions.
More...
Well, hardly. Single bet Kelly fraction is 5.5% and 8.3% for r14 and r16, respectively.
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Well yes, that confirms what I said:

F > k14 and S > k16.

The real question is where this synergy comes from.
 
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.
 
kut2k2 said:
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.
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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?
 
Kelly in discrete case is mean/odds, but in continuous case it is mean/(sigma^2). Why is the formula not the same even if in both cases the aim is to optimize the geometric return.
 
tradingjournals said:
Kelly in discrete case is mean/odds, but in continuous case it is mean/(sigma^2). Why is the formula not the same even if in both cases the aim is to optimize the geometric return.
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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 the outcomes are spread across the probability curve. With the assumption that these outcomes are normally distributed, the mean/(sigma^2) is the analytical solution for the "optimal leverage", in the sense of maximizing the geometric growth. If you remove the assumption of the normal distribution, it's still possible to figure out what continuous Kelly is, using numerical methods, instead of the analitycal ones.
 
I've read elsewhere that taking a negative-expectation bet (e.g., a small bet on Green-0) combined with the proper bet sizes on the positive-expectation numbers can somehow boost the overall gain. Has anybody else heard this? More to the point, can anybody confirm this? Thanks.
 
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