At a certain casino game if you bet \$x you will loose your \$x with probability .505 (so your fortune will decrease by x) and win \$2x with probability .495 (so your fortune will increase by x). You walk into the casino with \$25 dollars with the goal to get \$500.
Compute the probability for you to succeed if you use the following strategies
- You make repeated \$5 bets until you either win \$500 or you are wiped out.
- You make repeated \$25 bets until you either win \$500 or you are wiped out.
- You play bold strategy, i.e, Bet everything you can but no more than necessary
How would you approach this?