There are $4$ closed doors, with $100\$$ behind one of them. You can pay $X$ to open a door. If the money is there, you can keep it. If not you can pay another $X$ to open the next door, and so on. What is the most I can pay and still win on average?
I think that it's $25\$$. Since the money can be behind any door, you have as much of a chance of getting it on the first door as any other door. Since there are $4$ doors, and equal chance of being behind any door, $100 / 4$ = $25$.