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Craps Countdown
A New Idea
by Lawrence W. Hill

The ancient and hallowed game of craps is played everywhere from city back alleys to the poshest of casinos. Craps offers a wide variety of bets on its various aspects, but at the core of it all it’s relatively simple: The shooter rolls a pair of dice, and if they come up with a total of seven or eleven, he wins; if they come up two or three or twelve, he loses; if they come up any other total (four, five, six, eight, nine or ten), then that number becomes his “point,” and he continues rolling the dice until he either equals that point number and wins or rolls a seven and loses. The probability mathematics of craps is fairly straightforward to work out and it shows that the shooter wins about 49.29% of the time.

In a casino’s intense competition for players and profits, it is always amenable to exploring innovative new ways to liven up the “action” in their games. Anybody who has ever hung out over a craps table knows that craps is already about as lively as a game can be, but here as an exercise in probability mathematics, we’ll offer a little “gilding of the lily” by looking into a possible new betting angle in craps.

Here it is, the “Countdown:” if the shooter’s first roll is a five or a nine, the shooter and all others who have bet on him have the option of doubling their original bets. Of course, because the odds are 6 to 4 against winning with a point of five or nine (six sevens lose, to only four fives or nines that win), no experienced player in that situation would ever take such an option to increase his bet—unless there was some other offsetting “plus” advantage in it for him. That plus here is that if the shooter goes ten more rolls without a normal win or lose outcome, then he automatically wins, or if the shooter does win by making his point number on exactly his tenth attempt, then he wins ten times his already doubled bet amount! Interesting, eh?

Here is how the probability mathematics of this new betting option described works out. First of all, normally with a five or nine point, the shooter expects to win 40% of the time (four dice combinations making his winning point number, six combinations making losing sevens), and for each $1.00 bet, that’s an average loss of 20 cents. With the new option for five and nine points, 94.65% of the time the issue will be decided anyway within the first nine additional rolls, the shooter making his point for a $2.00 win (after having doubled his original bet) 37.86% of the time, or rolling a seven for a $2.00 loss 56.79% of the time. But then the 5.35% of the times reaching the decisive tenth roll, the shooter would still be facing the six dice combinations for losing sevens, but now the 26 combinations that are neither sevens nor his point number would win for him; and best of all, he would have chances for his four combinations making his point number that now would win $20.00—twenty times each $1.00 originally bet.

How would these possibilities from this new betting option affect the average 20-cents-per-$1.00 loss for a shooter with a five or nine point under normal craps rules? Not much—increasing to only slightly 20.04 cents. But just imagine the “buzz” around craps table whenever the point is five or nine, and the steadily increasing excitement of anticipation with the “Countdown” toward the climactic tenth roll! Good luck!

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