Short Rolls in Craps: Probability or Conspiracy?

raps players are always griping that even the best shooters get distracted and toss those ugly sevens smack in the middle of their hottest rolls. If an unscrupulous pit boss doesn't cause the problem by deliberately taking the dice out of action for an inspection and thereby letting them cool off, then it's something like a box man saying slow 'em down, a stick man sliding them over showing other than the complement of the point, a solid citizen betting on "don't come", or some Bezonian with hands hung over the table or chips stacked just where they block the throw.

Between you, me, and the cash machine in the lobby, these and other things that cause the seven to appear when you want it least are what spoil every system ever guaranteed to beat the house. Not to mention the many that haven't been devised yet.

But, let's make believe for a minute you don't believe in conspiracy theories about why professional craps players keep their day jobs. You've still probably been wondering why craps shooters in actual casinos hold the dice for less time, having much shorter rolls, than they do in the movies and in your reveries. Is it reality or your fantasy that's out of synch with the forces of nature certain scientists think govern the galaxy?

I'll let you decide that for yourself, using some figures indicating what the mathematics of the game say you should expect. Rather than obfuscate the issue with arcana such as decimal points and percents, not to mention means and standard deviations, I'll tell you what ought to happen when the limelight along with everybody's hopes fall on 1,000 shooters' shoulders.

To begin, the 1,000 shooters are going to have 2,520 come-out rolls. These will include the initial throws when shooters first get the dice, repeats when craps (2, 3, or 12) or naturals (7 or 11) yield one-roll decisions, and new come-outs after passes when points are made. Bettors on Pass will win 560 and lose 280 of these come-outs; bettors on Don't Pass will win 210, lose 560, and push 70. In the other 1,680 come-outs, the 1,000 shooters will set up points -- making 680 and missing-out on 1,000.

The average length of a roll after a point is established, before a repeat or a seven settles the bet, is just over two and a half throws. That's 2.57 for those who insist on authenticity but confuse truth with precision.

Players interested in earning money will be more interested in knowing how many numbers (4, 5, 6, 8, 9, or 10) -- as opposed to craps and 11s -- they should expect while the shooter is trying for the point. The average is just under two. That's 1.97 if you need a statistic to impress your friends.

These averages reveal the extent to which short rolls are the rule rather than the exception. To show this more sharply, I have to revert to a few dreaded decimals and percents in the following list. This gives the chance of throwing multiple intervening numbers before a decision is made on a point. You can see, as an example, that shooters can be expected not to hit any numbers after establishing a point and before passing or missing out in 33.8 percent of all cases. And their chances of hitting over 12 numbers in a round is a mere 0.7 percent -- seven out of 1,000.

intervening numbers	probability (%)
0	33.8
1	22.4
2	14.9
3	9.6
4	6.5
5	4.2
6	2.8
7	1.9
8	1.2
9	0.8
10	0.6
11	0.4
12	0.2
over 12	0.7

Well, go ahead if you want to believe that shooters' spouses walking over to nag them about going to the all-you-can-eat buffet affect the length of a roll. That's why they invented faith. I prefer to trust the math and bet accordingly, agreeing with Sumner A Ingmark, the bettors' Bobby Burns, who wrote:

If you, the laws of chance exalt,
Then fruitless search for blame now halt,
And look for remedy, not fault.