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 Three coins (Posted on 2015-08-20)
Three coins are lying on a table: a quarter, a half dollar, and a silver dollar. You claim one coin, I’ll claim the other two, and then we’ll toss all three.
A coin that lands tails counts zero, and a coin that lands heads wins its value
(in cents, 25, 50, or 100) for its owner.
Whichever of us has the larger score wins all three coins. If all three coins land tails then we call it a draw and toss again.

Which coin should you claim to make the game fair — that is, so that each of us has an expected win of zero?

Source: Martin Gardner, “Charles Addams’ Skier and Other Problems,” in Wheels, Life and Other Mathematical Amusements, 1983.

 Submitted by Ady TZIDON Rating: 2.0000 (1 votes) Solution: (Hide) Surprisingly, the game is fair regardless of which coin you choose. Prepare a table of the possible payoffs and see for yourself. BTW this game is fair with any set of coins, no matter how they’re divided, provided that their values show a successive doubling (e.g., 25, 50,100). From Martin Gardner, “Charles Addams’ Skier and Other Problems,” in Wheels, Life and Other Mathematical Amusements, 1983. The text, as quoted by me may be found at www.futilitycloset.com/2015/06/03/three-coins/

 Subject Author Date re(6): question Charlie 2015-08-23 15:08:46 re(5): question Ady TZIDON 2015-08-23 05:09:23 re(4): question Charlie 2015-08-22 07:40:37 re(3): question Ady TZIDON 2015-08-22 02:41:28 re(2): Fair Game (spoiler) Ady TZIDON 2015-08-22 02:37:05 re: Fair Game (spoiler) Steve Herman 2015-08-21 06:48:10 Fair Game (spoiler) Steve Herman 2015-08-20 21:55:19 re(2): question Charlie 2015-08-20 15:34:30 re: question Ady TZIDON 2015-08-20 15:00:40 question Charlie 2015-08-20 13:48:19

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