Craps

A game played with two Dice. If the total is 7 or 11 (a ``natural''), the thrower wins and retains the Dice for another throw. If the total is 2, 3, or 12 (``craps''), the thrower loses but retains the Dice. If the total is any other number (called the thrower's ``point''), the thrower must continue throwing and roll the ``point'' value again before throwing a 7. If he succeeds, he wins and retains the Dice, but if a 7 appears first, the player loses and passes the dice. The probability of winning is $244/495\approx 0.493$ (Kraitchik 1942).

References

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 12-13, 1951.

Kraitchik, M. ``Craps.'' §6.5 in Mathematical Recreations. New York: W. W. Norton, pp. 123-126, 1942.