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Should You Lay Odds When Betting "Don't Pass" at Craps?14 April 2000
By Alan Krigman
Dice devotees who bet against the shooter -- on Don't Pass or Don't Come -- often hesitate to lay odds after the point is set. Solid citizens experiencing these collywobbles know that gurus say laying odds shaves house advantage. Still, some feel queasy about putting the extra cash at risk. And, others balk because the flat portion of the wager pays even money while every $3 in odds only returns $1.50, $2, or $2.50 depending on whether the point is four or 10, five or nine, or six or eight, respectively.
Both issues can be resolved by looking beyond house advantage. Ultimately this factor is really meaningful only when millions of decisions are agglomerated and the law of large numbers prevails. Individual players with finite bankrolls are more concerned about their chances of surviving the downswings to be expected during sessions of reasonable duration and of reaching a target profit.
Make believe that when you were home and knew the value of money, you decided to play craps with a $1,000 stake. For simplicity, say you plan to have a single bet in action at any given time, on the Don't Pass, and won't vary the amount during the session. You wonder how much you should put down on the come-out roll, whether you should lay odds, and -- if so -- how much.
There's no one right answer. It depends on how long a session you think reasonable, how much profit would satisfy you enough to quit, and how sure you want to be of meeting your endurance and earnings goals. Representative criteria can provide guidelines, though, suggesting the kind of outcomes to anticipate using various approaches. For this purpose, consider the following benchmarks: a) 90 percent confidence that a $1,000 stake will be adequate for a 400-round session, and b) a win goal of $500.
If you bet flat, with no odds, a fancy "risk of ruin" analysis shows you can be 90 percent sure you won't tap out before completing 400 cycles by dropping $26 on the Don't Pass line. This approach gives you 48 percent chance of earning $500 rather than going broke. Rounding off to a more convenient $25 bet, you can be 90 percent sure of lasting at least 438 cycles and have just over 47 percent chance of achieving your $500 goal.
In contrast, a $10 don't pass bet with double odds offers 90 percent certainty of being alive after 400 come-out cycles and a 61 percent chance of reaching the $500 profit target. The odds portion of your bet would be $40 to win $20 on the four and 10, $30 to win $20 on the five and nine, and $24 to win $20 on the six and eight. By laying double odds on a $10 bet, you're therefore much more apt to earn your day's pay and have slightly less chance of survival than with a $25 flat wager. And, don't think you're risking all that much more moolah by laying odds. Your effective exposure is only marginally higher because nearly a third of your wagers will be resolved during come-out rolls when only the flat portion is up for grabs. Betting $10 flat and laying double odds, you're averaging $30.57 on the table per cycle. And, when you have the most in jeopardy -- on points of four or 10 -- you have the best chance of winning.
What if you bet $5 flat and lay 5-times odds? You can be 90 percent sure your $1,000 bankroll will carry you through 410 come-out cycles. You also have 64 percent chance of earning $500. Your average exposure per cycle creeps up to $30.71, but your chances of outriding the normal downswings of the game and of reaching your target have improved.
Apportioning your bet with the minimum flat and the maximum on the odds has two shortcomings. First, you'll have to play at a lower limit table and may not feel like such a big shot. Second, the casino bosses won't have as great an edge over you; their theoretical earnings will accordingly be less, and they won't comp you as readily and certainly not as generously. If these things are important to you, go hog wild on the line and forget the odds. If profits and longevity are more your reasons to gamble, skimp on the line and go bonkers on the odds. As Sumner A Ingmark wrote in one of his distinguished ditties about dice:
Those who think that shooting craps is purely random,