To gamble, you pay a dollar, and pick a number n from 1 to 100. The dealer rolls a roulette wheel 100 times. The roulette wheel is numbered from 1 to 100. You win a chip for every time the wheel comes up to be your number n.
You start with one dollar. At each unit of time, you use the strategy of betting your entire bankroll. [To be clear: the next unit of time doesn't start until you've bet your entire bankroll from the previous unit of time, no matter how rich you may have been.]
ObPuzzles:
1. (easy) In the long run, do you expect to gain or lose?
2. (easy) There's nothing special about the number 100; it can WLOG tend to infinity without affecting much.
3. (hard) Approximately what are the chances that you are bankrupt after t time units?
------------------------------------------------------------------------------- David Wagner dawagner@princeton.edu