By Samuel Gugliotta
For Variety

BY “craps” I mean that famous, or infamous North American variation of the game of hazard which consists in rolling two dice and counting the face-up pips showing. According to “Scarne’s New Complete Guide to Gambling,” Craps is the most popular gambling game in the United States. Over 40 million Americans play the game every year, and wager over $70 billion on the outcomes of those random rolling hexahedrons.
The word, “craps” in the context of gambling does not have the same etymological root as its scatological homonym. Rather, it is thought to have evolved from the English “crabs” applied to the roll of two one’s, on the analogy of “crabs eyes,” which is a loosing throw. Other names for this loosing throw are “snake eyes” and “dogs.”
Let’s look at some of the grammar and vocabulary of standard “bank” or “open” craps. There are, of course, two dice, with the numbers one through six distributed over its six sides. The person who rolls the dice is called the “shooter.” The shooter’s first roll is called the “come-out” and there are 36 possible outcomes of any roll, resulting in 11 possible sums, from 2 to 12.
If the come-out results in a 7 or 11, the throw is called a “natural” which is a winning throw. The probability of a natural is 8/36 or about a 22 percent chance. Thus the odds against a natural is 7 to 2.
Throwing a natural is called a “pass.” But if the come-out results in a 2, 3, or 12 (boxcars), the result is a crap or loosing decision, also called a “miss-out.” The probability that the shooter’s come-out is a miss-out is 4/36, or about an 11 percent chance of happening. The odds against this happening are 8 to 1.
Thus the shooter is more likely to throw a natural than to miss-out on her come-out. But even more likely than a natural, is that the first throw is neither a win or a loss. That is, the come-out is a 4, 5, 6, 8, 9, or 10. The probability of this happening is 24/36, or about 67 percent chance. The odds that this will happen are 2 to 1.
Accordingly, 2/3 of the time the shooter will throw a 4, 5, 6, 8, 9, or 10. The resulting sum is called the shooter’s “point,” and she will continue to roll until she makes that point, in which case the result is a pass or win, or else rolls a 7, which is a loss or miss-out.
Using the inexorable laws of chance, the general probability of passing (winning) when your come-out is a point is 0.27071, or about a 27 percent chance that you will make your point before you roll a seven. If we add this to the probability of a natural, we see that the probability of winning in craps is approximately 0. 49293, or about a 49 percent chance that you will pass before missing-out.
Theoretically, this means that your chances of coming out ahead in craps are slightly better if you bet against the shooter. You bet on the “don’t pass” option, which has a probability of 0.50707 or about a 51 percent chance of happening. However, this is not what happens in the casino.
In casino craps, the rules are slightly altered. For example, the double six or box cars on the come-out is not counted as a win for the “don’t pass” choice. The result is that the probability is the same for the win or loose bet, that is, about 49 percent, which gives the house an edge of 1.41 percent on every dollar spent playing the game. So you can expect in the long run to loose about 14 cents on every $10 bet.
This House edge may not seem like much, but as one mathematician put it: “The stock of General Motors is selling at 71, and their dividend for the year is $2, or about 2.8 percent. So per two plays at craps your loss is at a rate equal to the yearly dividend payout by America’s largest corporation.”
Even so, the “house edge” of 1.4 percent is less by a factor of 4 than the house edge for roulette. Consequently, among the “smart” casino gamblers, the dice tables are more popular than roulette.
The game of craps is more complex than what I have indicated above. John Scarne lists no less than 15 types of bets which may be made at the tables. All the mathematician may say, which should be enough, is, like all casino games, in the long run you are bound to loose.
Life itself is the same sort of game. The Gods, they say, are playing dice. Under these conditions, when we go against the odds, it would certainly pay to obtain all the knowledge we can. At least we may become articulate losers as opposed to naive victims. In this regard, I highly recommend Scarne’s gambling guide. Know the ropes before you walk the line.
Puzzles
1. Suppose a drunken person is standing next to a cliff. He is going to take purely random steps either towards or away from the edge. If the probability is 1/3 that he steps forward, and 2/3 that he steps away, do you think that in the long run he is more or less likely to fall over the cliff’s edge?
2. Suppose that TAA-TAA-TAA = (T - 1)(CHA-CHA-CHA). Can you find digits for the letters to make this is true statement?
3. Suppose there are three utility companies, say CUC, MTC, and MTV. They have three important customers which they all must serve. Is it possible to connect the lines to the customers in such a way that none of the utility companies cross their lines?
Answers to Last Week’s Puzzles
1. Let x = 121/10 and y = 11/10. Then the difference equal the quotient.
2. Let H = 0, A = 2, B = 1. Then AHHA/A = BHHB; 2002/2 = 1001. There are an infinity of solutions. This is one.
3. The first book was published in 1911.