Are Controlled Throws at Craps Fact or Fiction?

Some craps buffs are certain it's possible to set and toss dice in a manner that changes the odds of the game, giving bettors an advantage. Others are sure this is drivel. Either way, more than a few practice their throws or look for "good" shooters. And almost all casinos are assiduous about ensuring that the dice bounce off the bumpy back wall of the table to randomize the rolls. Still, considering the money to be made or lost, it's surprising how superficially this issue has been investigated.

Compare dice control with card counting at blackjack, the latter having been examined in exacting detail by players and casinos alike. Ultimately, both could give solid citizens the clout. In each case, slight changes in prospects could translate into big bucks. And the presumed advantage in craps is available on every roll, while that in card counting arises only intermittently.

Card counters, except for the occasional artiste, pretty much only determine the proportion of high and low cards remaining to be drawn. They're cherry, and pounce, when the shoe becomes rich in high cards. How heavy does the ratio have to be to turn the tide? Not very. Assume, for instance, that 150 cards remain out of eight decks - 70 from two through seven and 80 from nine through ace, rather than 75 each. Chances are 46.7 and 53.3 percent for low and high, respectively, instead of 50 percent each. This small difference gives players an edge of about 1.3 percent. With a 20-card offset when 150 are still in the shoe, 65 lows and 85 highs, players have roughly 3 percent edge.

Consider how little bias would be needed to get this much or more over the casino at craps. A slight tendency in one direction or another would do the job. It takes nothing near the skill to roll a specific combination with enough consistency to be noticed.

Picture a bet on the 12 as an example. The probability of winning should be one out of 36; the 30-to-1 payoff then gives the house a huge 13.9 percent edge. Say you could average two 12s in 37 throws, the distribution of other totals being irrelevant. The dealers would be snickering at your "sucker bets," yet you'd have a casino-busting 67.6 percent wrecking ball. Far less bias would still put you in the catbird seat. At six boxcars in 181 throws rather than the nominal five in 180, you'd have 2.8 percent edge.

Alternately, pretend you had a facility with nines. Place bets on nine pay 7-to-5 and normally have four ways to win versus six to lose, bestowing the house with a 4 percent leg-up. Were you to average 22 and not 20 nines in 180 trials, while maintaining the chance of 30 sevens, perhaps by cutting down on sixes or eights, your juice would be 1.5 percent. Even better if you could trade nines for sevens. Averaging 21 nines and 29 sevens in 180 throws, you'd have a modest but respectable 0.8 percent edge. At 22 nines and 28 sevens in 180 throws, you'd have a 5.6 percent hammer.

In principle, data could be collected and analyzed to confirm or refute the effectiveness of setting the dice and controlling the throw at craps. In practice, the task is so formidable that nobody's done it - not properly, anyway. Unlike card counting, which can be analyzed on a computer without need for "live" data, dice control studies would necessitate recording results of huge numbers of throws by different shooters under a variety of actual playing conditions. Information gathered would have to include all manner of possible influences to ensure that outcomes attributed to setting and throwing weren't actually caused by other factors. Everything would have to be taken into account - from the size of the table, the placement of bets in the area where the dice land, the fuzziness of the felt, and whether the shooter was a bimbo, to the condition of the dice - fresh with sharp edges or rounded after several hours' use.

So, is controlled shooting fact or fiction? Nobody really knows. The anecdotal evidence is worthless. And statistically valid analyses haven't been done. Still, even if you doubt it helps, it may not hurt to try. As the poet, Sumner A Ingmark, observed:

When laws of math and science seem up-ended,
All facts may not be known or comprehended.