part of kelly is the certainty equivalence equation:
CE=(ER-1) - Variance/2xBankroll
example?
let's say you're playing full pay deuces with a bankroll of 3524 bets
(10% ror) and you're dealt this hand:
22299
what do you do?
you could keep it for a guaranteed 15-1 = 14 bets
or just keep the deuces and go for it, but is it worth it?
ER=46/1081 x200 + 40/1081 x25 + 67/1081 x15 + 108/1081 x9 + 820/1081
x5 = 15.057
VAR=46/1081 x(200-15.057)^2 + 40/1081 x(25-15.057)^2 + 67/1081
x(15-15.057)^2 + 108/1081 x(9-15.057)^2 + 820/1081 x(5-15.057)^2 =
1540
CE=(15.057-1) - 1540/7048= 13.84
and there's your answer:
the correct kelly strategy is to keep all five cards