Blackjack Bonus Wagering Strategy
A gambling site offers a 100% deposit match up to
000. You deposit
000, giving you
000 to play with. On each hand, you win (doubling your bet) with probability 0.45 and lose your bet with probability 0.55. The catch: you can only cash out once your cumulative betting turnover exceeds 0,000.
1. Should you take this promotion? Is the expected value positive?
2. What is your optimal betting strategy to maximize your expected profit while satisfying the
0,000 turnover requirement?
3. How does ruin probability factor into your strategy?
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