Suppose the casino has a game which allows the player to place only a maximum of 100 bets. Suppose I have devised a strategy that puts the odds in my favor. When I place a bet, I have X % probability of winning where X >50%. Given that I am a conservative person, I want to have at least 75% chance of making a profit. How to calculate X?
The player starts with USD100. Each bet is equal size at USD1. When the player wins, he earns USD1. When he loses, he loses USD1.
The player has to make 100 bets. He cannot stop even if he is deeply in profits until 100 bets have been made.
Answers that solve the problem using computer programming instead of analytically are welcomed as well.