All or None
You have $100 and, never mind why, you must convert it to $1000. Anything less is no good. Your only way to make money is to gamble for it. Your chance of winning one bet is p.
Here are two extreme strategies:
Maximum strategy: bet as much as you can each time. To be smart, if you have less than $500 you bet it all. If you have more, you bet enough to get to $1000.
Minimum strategy: bet $1 each time.
If p <.5 (the odds are against you) which is the better strategy?
What about p >.5 or p =.5?
Minimum strategy: bet $1 each time.
If p <.5 (the odds are against you) which is the better strategy?
What about p >.5 or p =.5?
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