> It has been repeatedly stated in blackjack
> literature that a Kelly betting approach is,
> in a purely theoretical sense, the fastest
> way to grow your bankroll.

Grow the logarithm of your bankroll, which isn't exactly the same thing, but I digress.

> However, it is my
> understanding that the Kelly Criterion
> assumes an SD of exactly 1 or, in other
> words, a 1 unit up or down move at the
> conclusion of each trial.

No, that isn't true. It has no such restriction, and, clearly, for blackjack, the variance of a hand is greater than 1.

> Has anyone ever
> corrected for this approximation and
> determined an exact optimal bet as a
> function of EV and BR size, assuming a goal
> of maximum bankroll growth, for blackjack
> with different numbers of decks in play and
> for different benchmark rules?

Yes, absolutely! You can read all about it in BJA3 -- in the greatest possible detail imaginable.

> Also, has anyone ever determined SD as a
> function of EV in blackjack? This would, of
> course, have to be approximated by
> evaluating the SD of a blackjack hand as a
> function of the count. This could also imply
> a sort of second-degree functionality of EV
> in determining an optimal bet size. I do not
> expect this change in SD to be very
> significant, but it is intuitively obvious
> that a change in deck composition can change
> SD.

See above. It's all been done -- years and years ago.

> I'm not going to claim that any of this is
> actually useful, I'm merely curious.

It's very useful. You've just been somewhat out of contact.

Don