68

126

wins a dollar from the other and the chances
are perfectly even. The dollar is not actually
paid over until one of the players retires
temporarily from the table, and no
player does retire until he has netted a
gain during the sitting. Now the doctrine
of chances shows that at a perfectly even
game the probability that a player whose cash and credit
amount to c dollars, will net a gain of
n dollars before he is ruined will be c/c+n.
At this game the credit of the players is unlimited,
and thus the probability will be infinity
divided by infinity plus one, which fraction is strictly
equal to l. That is the probability that
a player will net a gain is 1, or certainty.