Let’s say we have a game where we win with probability $p=0.42$ and lose with $q=1-p$. Winning in the shell game has a probability of $0.33$. I now want to construct a series of bets between a minBet and maxBet so that I make profit. I have the constraint that the longest loss-sequence is not longer than $10$.
Is there a way of generating the best series? How can I make use of the fact that my longest sequence is $10$?