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How Often Can You Expect to Win

5 September 2000

By Alan Krigman

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 cycles
on 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 cycles
on 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
Advances being thrifty,
With even money bets
At chances fifty-fifty.

Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns were focused on those interested in gambling probability and statistics. He passed away in October, 2013.