Consider a game played in a series of
rounds, each worth a point. The winner of the game is the first
person to have a lead of 12 points, so the game is over when the score
is 12-0 or 13-1 or 14-2, etc. The score is usually kept with 12
stones which begin in the middle of the board. When a player wins
a point, a stone moves toward that player, either from the middle of the
board to the player's pile if the opponent has no stones, or from the
opponent's pile to the middle of the board if the opponent has at least
one stone in his pile. At most one player can have stones in his
or her pile, since the pile signifies the amount by which one player
leads another.
Let us say a game, which is being played for money, has to be
adjourned in the middle, and one player has a lead; is there a
mathematical way to decide what is a fair payment? For example, if
the game is being played for a dollar, and Player 1 has an 8 point lead
when time runs out, what percentage of the dollar should Player 2 pay
Player 1? This is the Problem of Points which the Chevalier de
Méré proposed to Pascal in 1654; the game had been around
for a long time, and other mathematicians, including Tartaglia in the previous century, tried to
solve it but did not make any progress.
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