The Three Coins

Three coins are on the table; a quarter, a half-dollar and a silver dollar. Smith owns one coin and Jones owns the other two. All three coins are tossed simultaneously.

It is agreed that any coin falling tails counts zero for its owner. Any coin falling heads counts its value in cents. The tosser who gets the larger score wins all three coins. If all three come up tails, no one wins and the toss is repeated.

What coin should Smith own so that the game is fair, that is, so that the expected monetary win for each player is zero?

David L. Silverman, author of the excellent book of game puzzles called Your Move (McGraw-Hill, 1971), is responsible for this new and unpublished problem. It has an amazing answer. Even more astonishing is a generalization, formally proved by Benjamin L. Schwartz, of which this problem is a special case.

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