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Best of Alan Krigman

Gaming Guru

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Long Rolls in Craps Are Great, But Can You Wait Long Enough

10 April 1995

othing else in a casino even comes near the exhilaration of a long roll at craps. Players "lock-up" enough money on the first few hits to ensure a profit on the shooter, then use the proceeds to "press" their wagers upward while also covering more numbers. The excitement and noise level build. Solid citizens snowball their winnings into ever larger payoffs as numbers keep popping. If players manage their money wisely, raising bets without giving back the store when a seven eventually wipes out what's on the table, this is how big bucks and legends are made in craps.

Other casino games have "runs." Long series of wins for Banker Player at baccarat. One busted hand after another for the dealer at blackjack. Roulette wheels you could swear lure the ball toward a certain group of numbers. Video poker machines that forget how to deal anything less than two pair.

In these other games, every payoff ends a betting cycle and a new wager must be made to start again. A single throw of the dice also represents a complete cycle for some craps bets. But, owing to the strong role of pass line bets "contracts" extending as many throws as needed for a "point" to repeat or a seven to appear craps players view a betting cycle as including all the action between successive "come-outs." Payoffs other than on the "point" seem like intermediate rather than final decisions. If a shooter is hot, the most natural thing in the world is to pump up place, come, hardways, and proposition bets after every hit.

How often do hall of fame rolls occur? Some veteran craps players are still waiting for that first really spectacular roll. Of course, the worst cry-babies don't know an avalanche when they're in its path. They either hold back too long or bet so aggressively they leave all the profits on the table when the seven finally shows. Then they look at you and whimper, "one more, and I'd have been over the hump!"

The laws of mathematics can predict the chances that a shooter will throw the dice any given number of times before hitting a seven. Old hands know this isn't quite the same as the length of a roll, but it offers a good sense of what happens in real play.

The first of the accompanying tables gives the percent of shooters expected to throw the dice more than the indicated number of times before a seven appears. For instance, just over 2 percent of all shooters will have rolls longer than twenty throws. If you think in terms of holding the dice for a certain length of time, assume an average of one throw a minute, so tossing the dice twenty times means holding them for twenty minutes.

The second table illustrates chances of encountering a long roll. It shows that as you continue to play, the likelihood increases of at least one shooter having a roll longer than either 20 or 30 throws. These lengths are arbitrary. But a bettor who can't make money when a shooter throws 20 or 30 non-sevens in a row ought to be trying tiddly-winks at a kindergarten, not craps at a casino.

Here's an example of interpreting this table. Say you play long enough for 30 shooters to toss the dice. You've got more than a 48 percent chance of running into a roll longer than 20 throws. Wait for 60 shooters and the probability is over 73 percent. You can also use the table to see how longer rolls are tougher to find. Play through 50 shooters. Your chances of at least one roll of length 20 exceed 66 percent, while the probability of at least one 30-throw roll is only about 16 percent.

These figures demonstrate that you can't expect long rolls every time you belly-up to a craps table. Still, they happen. Sometimes, within your first few minutes of play, making you an easy big winner from the getgo. Sometimes, after hours of enduring a stream of shooters missing out in short order, saving your bacon but making you sweat for it. And sometimes, of course, right after you color-up and leave the table. As Sumner A Ingmark, creative craps chronicler, craftily commented:

In craps it takes just one good roll,
To put you o'er your wildest goal,
Or pull you from your deepest hole.

TABLE
Number of Throws
Before a Seven
Percent of Shooters
Expected to Have Rolls
Exceeding this Length
0 83.33
5 33.49
10 13.46
15 5.41
20 2.17
25 0.87
30 0.35
35 0.14
40 0.05
45 0.02
50 0.01

TABLE

Number of
Shooters
Probability of
Shooter Having
at Least One
a Roll exceeding:
20 Throws 30 throws
10 19.73% 3.46%
20 35.57 6.79
30 48.28 10.01
40 58.48 13.12
50 66.67 16.12
60 73.25 19.02
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 focused on gambling probability and statistics. He passed away in October, 2013.
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 focused on gambling probability and statistics. He passed away in October, 2013.