coin unceasing riddle
Jacob and John are competing for the same girl. After years of battling, both decide to settle it by tossing a coin.
John produces a coin, but Jacob doesn’t happen to have one on him. Jacob is sure that the coin John has produced is loaded, i.e. it will come up with heads more than 50% of the time on average.
How do Jacob arrange a fair contest, based purely on chance and not skill, by flipping this coin?
Variation: (COIN BIASING) Jacob and John are competing for the same girl, and decide to settle it with a coin toss. John has known the girl longer than Jacob have, so Jacob agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, Jacob 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?
Let Jason do the tossing. He doesn’t know if or how the coin is loaded, so he also doesn’t know how to toss the coin to favor on of the sides.
Toss the coin N times (where N is even). Count the heads in the odd tosses for John and in the even tosses for Jacob. The one who has the greatest number of heads wins.
For the variation just multiply the number for John with a factor x (x>1) so his chance of winning the game increases.
Unfortunately I don’t have time to calculate the relation between x and p.
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