I don't follow what you're doing but the Kelly Bankroll (Poundstone's "Fortune's Formula") can be calculated for any option by summing up this formula (the natural log of bankroll growth) for all possible results:
prob x ln((BR+Win-1)/BR)
then iteratively solving for the value of BR (Bankroll) that results in the largest sum (maximum bankroll growth). Your bankroll can be larger than this value (less growth but less risk) but should never be less (less growth and more risk).
Alternately you can use Jazbo's perl script which does the same thing:
http://www.jazbo.com/poker/kellyp.html
Or the approximation for Kelly Bankroll:
variance/edge
Another approximation is the Certainty Equivalence:
EV - Variance/(2x BR)
Every option has a Certainty Equivalence, the option with the highest value is the best for bankroll growth. Note that if you have an infinite bankroll (too big to fail) the formula reduces to EV (Expected Value), or maxEV (Bob Dancer) strategy.
http://members.cox.net/vpfree/FAQ_S.htm
--- In vpFREE@yahoogroups.com, Tom Robertson <007@...> wrote:
>
> I'm analyzing something having to do with a hand in
> 1-2-3-4-4-9-15-25-200 Deuces Wild. The hand is 973s8W, in which the
> "best" play is to keep the deuce, but only by a tiny margin over the
> straight draw. My question is the bankroll required, according to the
> Kelly Criterion, to draw to the deuce instead of the presumably lower
> fluctuation straight draw. I've come up with an answer of 35,624
> units, which seems reasonable, but I'm not sure I've done it right.
> My method was to take the additional frequency of each ending hand
> that drawing to the deuce results in over what drawing to the straight
> results in, but that required the total frequency of ending hands be 0
> instead of the normal 1 that I'm used to in working with the Kelly
> Criterion and that the frequency for the straight be negative, neither
> of which I'm sure works correctly. Is there a better way of going
> about it?
>
