How Likely Are the Best Craps Players' Worst Dreams to Come True?

25 May 2005

By Alan Krigman

Craps buffs who prefer the "do" to the "don't" side of the game, and want the lowest possible house edge, bet strictly on Pass and Come. Players who don't "take Odds" on these wagers give the house only 1.4 percent edge. Passes and Comes augmented with Odds pay the casinos less juice as a fraction of the total at risk. The benefit increases as the ratio of Odds to flat money rises.

Lots of factors can inform the decision of how many Come bets to make. For instance, solid citizens may weigh the damage to which their bankrolls are exposed on any throw of the dice, against the desire to cover enough numbers so they're fairly confident of earning a profit on a roll of even middling duration. Enlightened joints with high Odds multiples also offer a choice between fewer Come bets each with more Odds, and the converse. Tending toward the former lowers the house advantage while raising the volatility a plus or a minus depending on how a person views the large downswings that are the complement of large upswings and reducing the likelihood that any particular throw will yield a return. More bets with less odds have the opposite effect.

Many players find that two Come bets are a good all-around compromise. But who among the initiated hasn't experienced the exasperation and expense of watching a shooter start a hand by throwing three different numbers, setting up the Pass and two Comes, then having the dreaded seven pop before anything repeats and pays off? Perhaps more cogently, how often can you expect this sort of nightmare to occur?

A computer simulation yielded the figures in the accompanying table, which can help answer this question. The data show the chances of a player whose strategy involves a Pass and two Come bets being frustrated by the appearance of a seven immediately after one, two, and three wagers are up on the numbers, as well as following additional throws but before any repeats. For reference, the values also include the overall probabilities of no hits and of at least one hit before the bets disappear.

Chances of a player adhering to a Pass and two Come
bet strategy losing at various points without a hit

Condition	Probability
Seven out with a Pass only	20%
Seven out with a Pass and one Come	13.2%
Seven out immediately after establishing a Pass and 2 Comes	5.8%
Seven out at some point after establishing a Pass and 2 Comes but no repeats	5.6%
Seven out with no hits, overall	44.6%
Seven out after at least one hit	55.4%

The good news is that 55.4 percent over half of all players using this strategy will be paid on at least one number before crashing with a seven. Some such hands will be lucrative; others will be losses. The amount in any case will depend on what numbers are rolled and in what order. Ignoring wins or losses while bets are coming out and assuming the flat portions of the wagers are constant, on hands that lose without a hit, the penalty could be as low as the Odds taken on the Pass bet or as high as the total of the three flat bets and their associated Odds. The first of these situations, according to the data in the table, can be expected to occur in 20 percent of all hands; the second, 5.8 plus 5.6 or 11.4 percent of the time.

Talk to a bunch of Come bettors and you're apt to find that they all vividly remember sessions in which the dice moved around the entire table, while they lined up three numbers on every shooter then hit the soup before anything repeated. Perhaps you recollect playing games like that yourself.

Or, perhaps the game is one your memory is playing on you. The chance of 12 shooters in a row being this unlucky is 11.4 percent multiplied by itself 12 times. And this is roughly one out of 200 billion. You may have played a load of craps in your gambling career. But not that big a load. Evoking this enlightenment from the erudite epigrammist, Sumner A Ingmark, who rhymingly wrote:

When events that get you aggravated
Are retold, they get exaggerated.