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 question
my interpretation of MG text:
the coins belong to the table, and after a round of games they stay on the table.
Claiming a coin should be understood as designating a token i.e. identifying a player. The amounts lost are paid out of the pocket and the coins remain "table's property"
Sample single game and result:
A's choice being a quarter, B by default has a 50c and 100c coins.
If the quarter was the only HEAD, then A WINS 1.5 $ by "taking all three coins".
I had some problems with the text, copied here verbatim, and reached my conclusions after reading the original answer.