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. 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. 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?

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.

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