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# How Often Can You Expect to Win

5 September 2000

Flat bets on Pass, Come, Don't Pass, and Don't Come at craps are expected to win as close to half the time as any even-money wagers in the casino. In terms of house advantage, they're improved by taking or laying odds after a point is established. Still, embellishments aside, they're about the most favorable strictly 1-to-1 propositions solid citizens are likely to find.

It's relatively easy to see how often you can expect to win with any of these craps bets. Just consider the statistically correct results of 1,980 come-out cycles, based on the number of ways a pair of dice can form various totals.

Don't Pass and Don't Come bets win during come-out rolls when the dice total two or three. They lose on seven or 11 and push on 12. On other totals, the bets move behind the point for a later decision -- winning or losing depending on whether the seven appears or the number repeats first. The following list indicates how the 1,980 come-out cycles will be theoretically resolved. Ignoring the pushes, the figures show that the chance of winning is 949/(949+976) or 49.2987 percent. The chance of losing is the complementary 50.7013 percent.

 Resolution of 1,980 come-out cycleson Don't Pass and Don't Come Result Probability Wins Losses Win on come-out 3/36 165 Lose on come-out 8/36 440 Push on come-out 1/36 Point is six or eight 10/36 Win on point (10/36)(6/11) 300 Lose on point (10/36)(5/11) 250 Point is five or nine 8/36 Win on point (8/36)(6/10) 264 Lose on point (8/36)(4/10) 176 Point is four or 10 6/36 Win on point (6/36)(6/9) 220 Lose on point (6/36)(3/9) 110 TOTAL 949 976

Pass and Come bets win during the come-out roll on totals of seven or 11. They lose on two, three, or 12. On other totals, the bets move to the point for a later decision -- winning or losing depending on whether the number repeats or the seven appears first. The following list indicates how the 1,980 come-out cycles will be theoretically resolved. The figures show that the chance of winning is 976/(976+1004) or 49.2929 percent. The chance of losing is the other 50.7071 percent.

 Resolution of 1,980 come-out cycleson Pass and Come Result Probability Wins Losses Win on come-out 836 440 Lose on come-out 4/36 220 Point is six or eight 10/36 Win on point (10/36)(5/11) 250 Lose on point (10/36)(6/11) 300 Point is five or nine 8/36 Win on point (8/36)(4/10) 176 Lose on point (8/36)(6/10) 264 Point is four or 10 6/36 Win on point (6/36)(3/9) 110 Lose on point (6/36)(6/9) 220 TOTAL 976 1004

Some craps players think that "Don't" bets win more often than their "Do" counterparts. These breakdowns confirm this belief. But, clearly, the difference is negligible. The greater vulnerability of the "Don't" bets during the come-out roll offsets their elevated strength after the point is established.

More tellingly, compare both wagers with other even-money bets. In single-zero roulette, for instance, you expect to win on red, black, odd, even, high, or low an average of 18 times in every 37 spins. The chance of winning is therefore 18/37, which equals 48.6486 percent. Flat "Do" and "Don't" bets at craps are over half a percent more likely to win. And that leaves out the bonus dice devotees earn in the form of license to hoot and holler in the heat of the action, without the casino sending goons from the decorum department to mark demerits on their rating slips.

As the celebrated Sumner A Ingmark apprised parsimonious punters:

A frugal bettor gets