Kelly criterion in the short run
I know that Kelly works in the long run, but what to do if we have ,for example, only 3 bets to take with different probability of winning?
More precisely, for example we have 100 dollars at the beginning, all bets are at even money (putting x dollars in the beginning, if win we get 2x dollars (our x dollars + additional x), if lose we get 0 dollars ...)
On first bet we have probability of winning 0.6, on second bet probability of winning 0.7, on third bet probability of winning 0.8.
What would be optimal strategy in this case?
$10 bet on first one, then $22 if we won the first one ($18 if we lost), then $39.60 if we won twice. Basically 10% of bankroll on first, 20% on 2nd, 30% on 3rd as Kelly Criterion says (ProbWinning - ProbLosing) / 2 = Bet as a % of bankroll
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