Exponential growth & answer to your question

*This is somewhat a revelation to me. I personally would not use full Kelly betting even if I knew I'd get an ace, but just out of theoretical curiosity, could you please elabrote on this remark? *

I will in a minute, but I wanted to address what you said about avoiding full kelly betting, because it represents the common, and I believe, mistaken, wisdom about betting large fractions of bankroll on highly advantageous oppportunities.

When you bet a fraction l of your capital each time on a coin toss and win W times and lose L times, then the exponential rate of growth from Kelly's original paper is:

G = Lim{(W/N)log(1+l)+(L/N)log(1-l)

N->oo

= log(1+l)q + log(1-l)p

where p is the probability of losing and q is the probability of winning. You will see when you test this that for very high values of P resulting in a large l fraction the performance loss, as I think Thorp originally noted, is very dramatic in financial terms. Coin-toss games are simplifications but the wider principle holds for more complex games with large advantages *relative to the kelly bet divisor*.

Put in Layman's terms: Betting small when you have a rare opportunity like this costs you dear to the point of irrationality.

*BTW, the orginal post by twin jacks is NOT correct then based on your statement. The majority (~30%) of the advantage, ~40%, comes from getting a Blackjack, whose payoff is 3:2. Therefore the correct (full) Kelly will be somewhat smaller than 40% of your bankroll. Probably closer to what E.J. suggested in this thread or around 30%.*

My interpretation of this is that 40% is approximately correct. It is simply advantage when the ace is the first or second card divided by 1.3, which is the approximate kelly divisor in this case if a no-split, no-double strategy is employed. I believe your 30% figure may have arisen because you are looking at the main component of advantage rather than the "global" bet to determine the correct Kelly bet divisor.