wrote a draft version of Van Rekeningh in Spelen van Geluck,a treatise about 15
pages long based on what he heard about the correspondence of French scientist and
religious philosopher Blaise Pascal (1623–1662) and French mathematician Pierre de
Fermat (1601–1665) the previous year. Of the fourteen problems he presents, the last
five became known as the “gambler’s ruin.”
In particular, Huygens (and others) wanted to find the probability of a gambler’s
ruin. A common way of expressing the idea is by a game that has two players, with the
game giving a probability qof winning one dollar and a probability (1 q) of losing
one dollar. In the problem, if a player begins with 10 dollars and intends to play the
game repeatedly until he either goes broke or increases his holdings to 20 dollars, the
question asked is: “What is his probability of going broke?” The answer involves quite
a bit of probability computation. (For more information about the gambler’s ruin, see
“Recreational Math.”)
What are permutations, combinations,and repeatables?
In order to perform certain probability problems, specific counting techniques need to
be used, including determining the number of permutations, combinations, or repeat-
ables. The following explains each term; the examples are based on a set of five cats on
a shelf—a, b, c, d, and e, for convenience. (Note: The cats can be arranged in 120 ways,
expressed as 5 4 3 2 1 5! [“5 factorial”] 120). 253
APPLIED MATHEMATICS
Dutch mathematician and astronomer Christiaan
Huygens devised the notion of the “gambler’s ruin.”
Library of Congress.
Galileo Galilei, best known for his work as an
astronomer, had already discovered the ideas of
probability later restated as the “gambler’ ruin” by
Christiaan Huygens. Library of Congress.