PLAYING IT SMART by ALAN KRIGMAN

Is 32-Across a good (bad) bet at craps?

Any Bezonian can bet on a particular outcome at craps. On Pass, Come, Don't Pass, or Don't Come, for instance; maybe on a lucky number -- a box or a proposition; even on the Field. But, say you want to impress the dealers, other people at the table, or the Plenty O'Tooles looking over your shoulder. For that, those in the know often rely on combination bets. The Horn is an example. Horn High Aces, High-Low, Three-Way Craps, and C&E are others.

A particularly elegant choice of combination bets among true craps aficionados is 32-Across. Or maybe 64-Across, 160-Across, and so on depending on a person's bankroll and the table minimum. The 32-Across bet -- multiply up for the others -- is $5 each on the four, five, nine, and 10, plus $6 each on the six and eight.

The best feature of 32-Across is that it's a strong favorite to hit. Out of the 36 possible ways the dice can land, 24 are winners (the box numbers) and six are losers (the seven). Nothing happens -- you push -- on two, three, 11, or 12. So the chance of winning is 24 out of 30, or 80 percent. Of course, as every good gambler is aware, the payoff falls as the probability of success rises. And, when wagers are more likely to win than lose, the potential profit per decision is less than the money at risk. With 32-Across, a four or 10 (six ways in all) brings $9 while a five, six, eight, or nine (18 ways in all) gains $7. A seven (six ways) sends $32 to the casino's coffers.

Every once in a while, some nattering numero-noodnik calculates the house's edge on 32-Across. Lo and behold, it's below that on any of the boxes evaluated independently. Indeed, the edge on 32-Across is 1.25 percent. The individual figures for four-10, five-nine, and six-eight are 6.7, 4.0, and 1.5 percent, respectively.

The comparison turns out to be of apples and oranges, however. This, because the percentages are fractions of different numbers of decisions. Picture 36 statistically-correct throws. Fours and 10s get nine decisions each (three wins, six losses), fives and nines have 10 decisions each (four wins, six losses), sixes and eights yield 11 decisions each (five wins, six losses), and 32-across sees 30 decisions all told (24 wins, six losses).

More critical in the broader context of house advantage is how much the bosses expect to "take" from a dollar in action for the 36 theoretical throws. It's 60.0¢ on the four or 10, 40.0¢ on the five or nine, 16.7¢ on the six or eight, and 37.5¢ on 32-Across.

More relevant yet to solid citizens are the chances of earning a target profit starting with a given bankroll, and of a specified stake sufficing to stay afloat for a session of desired duration. For this purpose, pretend you start with $200. And, admittedly artificially, imagine a $30 box or 32-Across is your only wager.

Make believe your goal for the profit criterion is to earn $200 before losing $200, no matter how long it requires. Here are your prospects of joy, from best to worst. Placing the six or eight, 46 percent. Buying the four or 10, 45 percent. Placing the five or nine, 41 percent. And 32-Across, 35 percent.

For the endurance criterion, suppose you want $200 to last for at least three hours, roughly 300 throws. Here are your chances of achieving this objective, from brightest to dimmest. Betting 32-Across (250 decisions), 44 percent. Placing the six or eight (92 decisions), 41 percent. Buying the four or 10 (75 decisions) or Placing the five or nine (83 decisions), 34 percent.

You be the judge. Is 32-Across good or bad compared with a like sum on any of the boxes separately? As always, it hinges on personal preference. And this is aside from the good or bad news that you can make out like a bandit on bets designed strictly for suckers, or lose your shirt on those the joints hope don't become too popular. For, as the punters' poet, Sumner A Ingmark penned:

The math is done, the trade-offs weighed,
Advice of gurus you've obeyed,
But still, in every session played,
It's fate that ruled if you got paid

(c) 2008, ICON/Information Concepts Inc

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