Long Rolls Happen at Craps... But, Can You Wait?

27 June 1994

By Alan Krigman

Craps offers players the perennial promise of the long roll. The series that has pit bosses checking dice and calling for chip refills. The shooter who pulls you out of the deepest hole.

How frequently can you expect a long roll? The laws of probability give an easy answer. Especially if you'll grant the simplification that the length of a roll is the number of throws before a seven appears. True, a roll's not over if a shooter throws seven while coming out after a pass. But this complicates the math without significantly illuminating the aftermath.

The accompanying list gives expected percentages of rolls having the indicated number of throws before seven rears its ugly head:

roll length	probability (%)
1	13.89
2	11.57
3	9.64
4	8.04
5	6.70
6	5.58
7	4.65
8	3.88
9	3.23
10	2.69
11	2.24
12	1.87
13	1.56
14	1.30
15	1.08
16	0.90
17	0.75
18	0.63
19	0.52
20	0.43

The figures show chances diminish as rolls lengthen. The likelihood of 15 throws before a seven is about one out of a hundred; expect 20 throws before a seven with slightly more than four out of a thousand shooters. And, adding up the percentages shows that half of all rolls will comprise five or fewer throws and three-quarters will be shorter than thirteen.

For another perspective, I simulated a thousand make-believe four-hour craps games on my computer. This would be one long session a day for almost three years. Here are some key results:

o	The longest roll I got was 55 throws, followed by 53 and 49. These represent about an hour's shooting each. A player who couldn't make a mint in these games belongs in an institution other than a casino.
o	One game had five rolls exceeding 20 throws, 14 games had 4 longer rolls, and 54 games had three longer. We're talking big buck situations.
o	212 games had two rolls topping 20 throws and 424 games had one longer roll each. These account for over half the four-hour sessions, suggesting the importance of strategies that keep you in action for the good rolls that eventually come along.
o	295 games had no rolls greater than 20 throws. A right bettor who could endure four such hours either has the patience of Job and bankroll of Midas, or is closely related to the sap who didn't make anything on the 55-throw shooter.

So, long rolls in craps have low probability, but do occur during the course of normal play. If you step up to the right table at the right instant, you can make a bundle starting with a bantam bankroll and betting any amount anywhere on the layout. That's luck. More likely, you'll have to sweat it out with low-edge bets sized so expected downswings don't break you before a hot shooter puts you over the top. That's playing it smart. As Sumner A Ingmark, the bettors' bard, so vividly versified:

All right bettors share one goal,
Be there for that endless roll.