Can you make money converting the 12 at craps into a lay bet?

By the usual standard, house advantage, the 12 at craps is a sucker bet. It's a 35-to-1 shot paying only 30-to-1. The house edge is just under 14 percent. So the bosses figure every dollar dropped on boxcars puts almost $0.14 into their pockets.

Can money be made on the 12 anyway? Can people get rich on the lottery? Big lottery wins are well publicized. But the chances it'll happen to anyone in particular are minuscule. Scoring on a 12 at craps is less remunerative but more likely. And individuals can control their own chances, within some bounds, of course.

At a 30-to-1 payoff, a 12 would be lucrative or break even if it were bet for the same amount on successive throws of the dice and hit within 31 tries. How often have you played craps and not seen a 12 within 31 throws? A 12 seems to pop much more frequently than that when you have money on the Pass line during come-out rolls and this result causes you to lose. Or, does it?

The laws of probability -- and, if you don't trust the math, computer simulations -- say you've got slightly over 50-50 chance of the dice showing a 12 within 25 throws. And the likelihood of this outcome within 31 attempts is about 58 percent.

More precisely, pretend a million players start with $31 and bet $1 per throw on the 12, quitting when it hits or they bust out. Overall, 570,497 are expected to earn a profit, 11,931 to break even, and 417,572 to go belly-up. Further, more of the wins should be $30 than any other amount -- 27,778 are projected to finish at this level, with the tally decreasing gradually until it reaches 12,271 who win $1 and the 11,931 who break even.

To be sure, casino games are contrived to make money for the house. But they're also designed to send a fair share of folks out the door as winners. Gamblers, especially of the recreational as opposed to the inveterate ilk, don't live on promises and comps alone. They need encouragement and reinforcement or they'd get disheartened and stay home watching "Deal or No Deal." On the average, however, over enough trials, the gross lost must exceed the total won or the joints couldn't remain in business.

Although more players are predicted to win than lose making the repeated bets on the 12, this isn't the bottom line. Numbers of winners and losers alone don't matter. It's the combination of those numbers and the associated amounts.

The total projected payout to the fraction of a million hopefuls who win $30, $29, $28 and so forth is $10,032,609. The aggregate taken from those who lose $31 is $12,944,746. The casino nets $2,912,137, an average just over $2.91 per player.

Wagers that offer greater prospects of winning than losing, but pay less than the money at risk, are "lay bets." Isolated wagers on the 12 are high-return longshots. They become lays when made in sets as described. Gamblers who understand this type of bet don't mistake favorable odds of winning for edge on the action.

Many players avoid lay bets and, in fact, prefer precisely the opposite kind of gambling. They want small wagers that bring large rewards, albeit with low probability. For bettors who enjoy winning frequently, even if earnings are low, and who are disciplined enough to cut their losses when those inevitable cold sessions come along, lays are certainly worth considering.

Is it reasonable to conclude that repeating bets on the 12 is a good gambling strategy despite the exorbitant edge? The $2.91 is an average, not a sum anybody actually loses. Further, the odds are 60-to-40 that players will finish ahead or even rather than behind. Admittedly, at $1 per throw, bettors must be willing to risk up to $31 to win $30 or -- in the vast majority of cases when the approach proves successful -- less.

As usual in gambling, there's no absolute right or wrong. It's a matter of personal preference. As the pedagogical poet, Sumner A Ingmark, pedantically preached:

The size of a profit is pleasant to measure, But sometimes just winning is great enough pleasure.