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 following table summarizes the probabilities of winning on a roll-by-roll basis, where is the probability of rolling a point . For rolls that are not naturals (W) or craps (L), the probability that the point will be rolled first is found from

			(1)
			(2)

		W/L
2		L	0
3		L	0
4
5
6
7		W	1
8
9
10
11		W	1
12		L	0

Summing 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 little Joe (4) and big Dick (10). Since each can be made in three ways, the probability of throwing each is 3/36, or 1/12 (Gardner 1978, p. 256).

The rolls in craps are sometimes gives special names, as summarized in the following table (Gardner 1978, p. 256; Mosteller 1987, p. 3).

roll	name
2	snake eyes
4	little Joe, little Joe from Kokomo
4 the hard way ()	little Joe on Viagra
8	eighter from Decatur
10	big Dick
12	boxcars