In his letter of August 24, 1654, Pascal
was trying to show how a pot of money should be allocated when a
gambling game must end prematurely. Imagine a game where each turn
consists of the roll of a die, player E gets a point when
the die is even, and player O gets a point when the die
is odd. The first player to get 7 points wins the pot. Suppose the game
is interrupted with E leading 4–2. How should the money
be fairly split in this case? What is the general formula? (Fermat and
Pascal made several errors before solving the problem, but you should be
able to get it right the first time.)
In his letter of August 24, 1654, Pascal was trying to show how a pot of money should be allocated when a gambling game must end prematurely. Imagine a game where each turn consists of the roll of a die, player E gets a point when the die is even, and player O gets a point when the die is odd. The first player to get 7 points wins the pot. Suppose the game is interrupted with E leading 4–2. How should the money be fairly split in this case? What is the general formula? (Fermat and Pascal made several errors before solving the problem, but you should be able to get it right the first time.)