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.
(In reply to re: question
by Ady TZIDON)
In the referenced work, the two players are Smith and Jones and it is said that Smith OWNs one of the coins and Jones OWNs two of them. The coins coming up heads count for their OWNER.
The question is which of the coins should be owned by Smith to make the outcome fair; that means, in effect, which one should Smith supply, or, since they are already on the table, which one should Smith have supplied, so as to make the game fair?
The winner does not win $1.50, but rather the value of the one or two coins he did not supply; the loser loses the coin or coins he did supply.
Posted by Charlie
on 2015-08-20 15:34:30