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GeezerVison is showing mathworld.wolfram.com — Craps -- from Wolfram MathWorld 
CrapsCraps is 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 following table summarizes the probabilities of winning on a roll-by-roll basis, where
Summing The rolls in craps are sometimes gives special names, as summarized in the following table (Gardner 1978, p. 256; Mosteller 1987, p. 3).
See alsoBig Dick,, Boxcars, Dice, Eighter from Decatur, Little Joe, Snake EyesExplore with Wolfram|Alpha
More things to try: ReferencesGardner, M. Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, 1978.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.Mosteller, F. "Craps." Problem 9 in Fifty Challenging Problems in Probability with Solutions. New York: Dover, pp. 2-3 and 24-26, 1987.Saroyan, W. "Two Days Wasted in Kansas City." In Inhale & Exhale. New York: Random House, pp. 69-73, 1936.Referenced on Wolfram|AlphaCrapsCite this as:Weisstein, Eric W. "Craps." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Craps.html Subject classifications | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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is the probability of rolling a
point 
.
will be rolled first is found from
from 
to 12 then gives the probability of winning as 
(Kraitchik 1942; Mosteller 1987, p. 26),
just under 50%. Two and 12 are the hardest sums to roll, since each can be made in
only one way (probability 1/36), but neither 2 nor 12 can be a point. Three and 11
come next, with probabilities of 2/36, or 1/18, each, but 3 is a crap and 11 a natural
and so neither of them can be a point either. The hardest points to make are therefore
)