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.
When one player wins all three coins, what does the other person lose? Whose coins were they to begin with? If they are just lying on the table, not belonging to anyone to begin with, there's no loss and therefore a positive expectation for each bettor. We need to identify the loser's loss in order to solve.
Posted by Charlie
on 2015-08-20 13:48:19