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Best of Alan Krigman
Don't Downplay the Importance of the Come-Out Roll in Craps5 August 2003
Almost everybody starts each round with one of two wagers: Pass or Don't Pass. These are duplex bets. The initial phase is the come-out; it can result in a win, loss, push in the case of Don't Pass, or establishment of a "point." The second phase occurs when the come-out yields a point; here, bets win or lose depending on the point repeating before a seven appears, or conversely.
Whether or not the round proceeds, the come-out lasts for just one
throw. Point rolls, however, can be lengthy. Further, solid citizens who
take or lay odds have more riding on the resolution of the point than
they did on the original Do or Don't during the come-out. Auxiliary
wagers raise what's at risk in the course of point rolls even higher.
Many dice devotees therefore underrate the relative impact on the game
of decisions during the come-out.
Pass bets are decided on the come-out if the shooter throws a two, three, seven, 11, or 12. Likewise for Don't Pass, except that 12 is a push. These combinations comprise 12 out of the 36 ways the dice can land, so an average of 12 out of 36 (33.3 percent) coups never reach the second phase.
On the come-out roll, considering only wagers actually resolved, Pass bets have a favorable eight ways out of 12 to win (66.7 percent), with the opposite four out of 12 to lose (33.3 percent). Because of the push on the 12, Don't Pass bets involve one less possibility and have an adverse three ways out of 11 to win (27.3 percent) with the remaining eight out of 11 (72.7 percent) to lose.
After a point is established, the specific probabilities at the moment of truth hinge on the number in question. For instance, with four or 10, the chance of winning a Pass bet is a paltry one out of three (33.3 percent) while that of scoring on Don't Pass is an attractive two out of three (66.7 percent). The respective figures for fives or nines are four out of 10 (40 percent) for Pass and six out of 10 (60 percent) for Don't Pass. Sixes and eights are looking at shots of five out of 11 (45.5 percent) for Pass and six out of 11 (54.5 percent) for Don't Pass.
Bettors can't pick their own points for Pass and Don't Pass. The dice do it. So, the real issue for the point roll is the overall outlook for either bet to succeed or fail, rather than for a particular number to hit or miss. This prospect combines the probabilities of being on or behind and winning or losing each point, then merges the values for all six box numbers. When the dust settles on the abacus, the likelihoods of joy turn out to be 40.6 percent on Pass, and the inverse 59.4 percent on Don't Pass.
The broad disparity between chances of cheer on Pass and Don't Pass during the point roll, 40.6 versus 59.4 percent, is offset by the contrary situation during the come-out. Were the come-out as inconsequential as many craps enthusiasts seem to think, Pass would be the mother of all sucker bets and Don't Pass would be the road to riches. But experience shows what the math predicts. The bets are essentially equivalent, statistically.
Or, as all true patrons of punting poetry recall, here's how the beloved bettors' bard, Sumner A Ingmark, sized up the situation:
Knowing your chances meticulously,
Best of Alan Krigman