07 Jan '05 18:165 edits

Suppose somebody approaches you on the street and wants to flip a coin for money. He offers you better than even odds (say 2:1, but the actual odds are irrelvant to this problem) to choose tails. The coin may be biased by an unknown amount; that is, it may land heads, say, 60% of the time (again, an arbitrary and irrelevant figure). Finally, he will only play once, and you are not allowed to experiment with the coin beforehand - you can't flip the coin an arbitrary number of times in order to empirically estimate its bias.

Construct rules for playing a coin-flipping game, one time, such that you receive your advertised odds (for example, 2:1) in expected value. That is,

Of course, your solution should be a mathematical one, not a physical one like trying to influence which side the coin actually lands on.

I offer mad props to anybody who can solve this without having seen the solution before. This problem was first told to me by a former colleague of mine and I was unable to solve it on the spot.

Dr. S

Construct rules for playing a coin-flipping game, one time, such that you receive your advertised odds (for example, 2:1) in expected value. That is,

**create rules for flipping the biased coin that effectively eliminate the coin's bias.**(The restriction that you may only play the game one time should not be construed to mean that the coin may only be flipped one time, but it should be construed to mean that the game is required to terminate with a winner being declared with each player being equally likely to win.)Of course, your solution should be a mathematical one, not a physical one like trying to influence which side the coin actually lands on.

I offer mad props to anybody who can solve this without having seen the solution before. This problem was first told to me by a former colleague of mine and I was unable to solve it on the spot.

Dr. S