Kelly critical fractions
> The way my software works is it does a quick approximation for all possible plays. It then does the top choice, in this case splitting, using the best algorithm. If it is a close play, it also does the runners-up that way. However, here it decided that Splitting was so much better than either doubling or hitting, then no-one would be interested in the hitting/doubling numbers.
Interesting. That is essentially the same method Griffin used to create his basic strategy charts -- quick/dirty approximations combined with slow/accurate computations. This led to the two known (but very minor) errors in his basic strategy, due to misjudgements that the approximate results were "far enough apart" to preclude a strategy error.
It is nice to not have to worry about approximations most of the time. One of these days I've got to upgrade my pair splitting so that I never have to worry about approximations. Ah, the luxury of a blazing fast algorithm... ;-)
> BTW, I did not realize until just now that even with S17, the exact numbers show that doubling is the BS. To respond to Don's issue of Risk-Aversion, the critical fractions are also listed.
Do you support log-optimal strategy at all decision points, or are you approximating the critical fractions? Also, do you support any other utility functions, or only the linear and log() cases? I have support for power utility functions in addition to Kelly.
> Dble Mean = 19.07086 % SD = 1.946
> Hit Mean = 18.80238 % SD = 0.956
> Risk Averse Data - Critical Banks
> Dble: 535.08 ( 0.187% ) with Var Method
OK, I guess that answered one of my questions. I compute the crossover at 0.19036% for this decision.
> //Following H17
> Dble Mean = 20.63118 % SD = 1.946
> Hit Mean = 18.95811 % SD = 0.955
> Risk Averse Data - Critical Banks
> Dble: 85.90 ( 1.164% ) with Var Method
This is closer -- I get 1.1661% as the crossover here.
> Since this rule would only be used after splitting, we should probably use a 308-card remainder: Remove 2 aces and the dealer 6. Split the Aces and draw another Ace. I thought the Homer's rule did not Re-splitting fo Aces. If Re-splitting were allowed, then we should remove 4 Aces, the dealers 6, and another Ace, as done by Cac. The critical fractions would be much higher then.
The critical fractions go up to 0.809% for S17 and 1.693% for H17.