When to buy numbers at craps?

Among the dozens of betting options at the craps table, among the most commonly played are the place bets. They're wagers that the shooter will roll the number of your choice before rolling a 7.

You're paid at 7-6 odds on winners if your number is 6 or 8, 7-5 if you bet on 5 or 9, and 9-5 if you bet on 4 or 10. Payoffs are lower than the true odds of 6-5 on 6 or 8, 3-2 on 5 or 9, and 2-1 on 4 or 10. That's how casinos make a living, by paying less than true odds on winners.

One of the first things players who delve into the odds of the game learn is that it doesn't pay to make place bets on 4 or 10, or on 5 or 9. A house edge of 1.52% makes placing 6 or 8 is among the better bets in the casino, but the house claims a 4% edge on 5 or 9, and a 6.67% edge on 4 or 10.

Some players learn that you can "buy" numbers instead of placing them, paying a 5% commission in exchange for having winners paid at true odds. That doesn't help on wagers where the house edge already is lower than 5%, but it does reduce the house edge to 4.76% on 4 or 10.

That house edge remains too high for my taste, and if that's all there was to it, buy bets would be planted firmly on my "do not make" list. But there are a couple of wrinkles that make it possible to get a house edge on buying 4 or 10 that's even lower than the 1.52% for placing 6 or 8.

The starting point is to find out if the house collects a commission on all buy bets, or just on the winners. If you're paying the 5% every time you buy a number, then you're stuck with the too-high house edge. But at casinos that collect the commission only when you win, the house edge is reduced dramatically. Buying the 5 or 9 becomes a feasible bet, with a house edge of 2%, and buying the 4 or 10 drops all the way to 1.67%.

Instead of an average loss of $6.67 per $100 wagered when you place 4 or 10, or $4.76 when you pay a commission each time you buy those numbers, your average loss falls to $1.67 per $100.

That's still not as low as placing 6 or 8, but there's one more step available to those who wager more than $20. If you buy 4 or 10 for $20, your commission is 5 percent of $20, and that comes to a flat $1. But what if you want to buy for $25 instead? Five percent of $25 is $1.25, and some casinos don't want to mess with the loose change. They'll round down and just collect a $1 commission on your $25 winner instead.

Under those conditions, the house edge for buying 4 or 10 falls to 1.32%.

Here's how that works. When you bet on 4, there are only nine rolls that matter -- the three ways to make 4 and the six ways to make 7. If any other number is rolled, your bet remains in action. You bet $25 on each of the nine decision rolls, for a total of $225, and you pay the house an extra $1 on each of the three winners. That means you have a total of $228 invested.

Each of the three winners is paid at 2-1 odds. On each, you keep your $25 bet and collect $50 in winnings, for a total of $75. With three wins, you have a total of $225 remaining after an average nine trials. The house keeps $3 of the $228 you've invested. Divide $3 by $228, then multiply by 100 to convert to percent, and you have a house edge of 1.32%.

That's lower than the 1.52% on placing 6 or 8. It's not the best bet at the table. Pass or come plus free odds, or don't pass or don't come while laying the odds, where the house edge is measured in tenths of a percent dependent on the odds multiple permitted, remain better percentage plays.

Mind you, I'm not recommending that a low-bankrolled player push wagers to $25. Betting only what you can afford remains rule No. 1 of gambling. But for those who already bet at that level, buying the 4 or 10 for $25 at casinos that collect a commission only on winners becomes a viable play.