You and your arch rival are competing for the same girl. After years of battling, you both decide to settle it by tossing a coin.
Your rival produces a coin, but you don't happen to have one on you. You are certain that the coin your rival has produced is loaded, ie. it will come up with heads more than 50% of the time on average.
How do you arrange a fair contest, based purely on chance and not skill, by flipping this coin?
Variation: (COIN BIASING) You and your rival are competing for the same girl, and decide to settle it with a coin toss. Your rival has known the girl longer than you have, so you agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, you only have a fair coin. How can you conduct this contest such that the biased probability is manifested? What is the average number of coin flips needed to determine a winner?
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