You are playing the following game. You are offered two closed boxes, each having a random amount of money between $0 and $100 inside. After picking one and noting the amount of money inside, you are asked to state whether the other box contains more or less money. If you are right, you win $1. If wrong, you lose $1. If you play a large number of times, is there a strategy where you can be almost certain to leave with more money than you started with?
If this is viewed as a continuous distribution, where the amounts can
include pennies or fractions of a penny, then the best strategy
evaluates easily (and geometrically) to 75% probability of winning on
each turn. Consider a graph of all box one values versus all box
2 values.
What about pennies?
