Decreasing the House Edge on the 4 and 10 in Craps

At the most basic level, place numbers offer craps only a couple of reasonable opportunities. Place bets on 6 or 8, with house edges of 1.52 percent, are among the better bets at the table. But bets on 5 or 9, with house edges of 4 percent, and on 4 or 10, with house edges of 6.67 percent, are wagers to avoid.

There's a way to improve your odds on 4 or 10, and that's by buying the numbers instead of placing them. You pay the house a 5 percent commission, and in return you're paid true odds if your bet wins. That lowers the house edge to 4.76--a bit too high for my taste.

But my old friend Frank Scoblete, author of Beat the Craps out of the Casinos and Forever Craps, always has a play up his sleeve that's far from basic. In the August 2002 edition of Casino Player magazine, he notes that Treasure Island casino in Las Vegas charges players a $1 commission only on WINNING $25 buy bets on 4 or 10. That, he says, lowers the house edge all the way to 1.3 percent, making the 4 and 10 playable numbers.

How does that lower the house edge all the way to 1.3 percent from the typical 4.76 percent when buying the 4 or 10? There are two parts to this little puzzle. First, buy bets on 4 or 10 will win an average of 1 in 3 times they're made, so when Treasure Island charges the commission only on winning bets, it means the player pays the extra only one-third of the time. Second, since the casino is accepting the buys in multiples of $25, it means a $1 commission is only 4 percent of the wager, instead of the basic 5 percent.

Let's walk through how all this works, starting with the place bets on 4 or 10.

The house pays winning place bets on 4 or 10 at 9-5 odds--bet $5, win $9. Let's say we place $5 on the 4 in an average three trials in which we win once and lose twice. We risk a total of $15. The one time the shooter rolls a 4, we win $9 and keep our $5 wager for a total of $14. So at the end of the trial we have $14 and the house has kept $1. Divide that $1 by the $15 risked, then multiply by 100 to convert to percent, and you get the 6.67 percent house edge.

Now let's say we buy the 4 for $20. Five percent of $20 is $1, so for each of our three trials, we have to put up $21 for a total risk of $63. The house pays winning bets at the true odds of 2-1 instead of the 9-5 we get on the place bets. So the one time we win, we're paid 2-1 on our $20, for $40 in winnings. We also keep our $20 wager, while the house keeps the commission. At the end of three trials, the house has kept $3 of the $63 we put up. Divide $3 by $63 and multiply by 100, and you get a house edge of 4.76 percent.

What if the house collects the commission only on winning bets? Using the same $20 wagers so that $1 is an even 5 percent commission, at the end of three trials we still have a total of $60--$40 in winnings plus the one winning $20 wager. But we've put up only $61, since the house has collected only one commission. The house edge is the $1 we've lost divided by the $61 we've put up. Multiply by 100, and we get a house edge of 1.64 percent.

Treasure Island goes one step further in allowing us to raise our bet to $25 without increasing the commission.

Now, in our average three trials, we have bets of $25 on the table, and since we win once, we pay the house $1 in commission. Our total outlay is $76. The one time we win, we collect $50 in winnings and keep our $25 wager for a total of $75. The house edge is the $1 commission on that winning bet divided by our $76 outlay. Multiplied by 100, that's a house edge of 1.32 percent.

Few casinos charge the commission only on winning bets. And not all will let you push that $1 commission to bets higher than $20. If you're in a house that's a real stickler, you might pay a $1 commission on a $20 bet, and find the casino wants to push it up to $2 on a $21 wager. On the other hand, Scoblete says he's been allowed to bet as much as $38 with a $1 commission. It doesn't hurt to ask.

Does lowering the house edge to 1.32 percent, as on the $25 wagers at Treasure Island, make buying the 4 or 10 bets worth making? That depends. At that level, the house edge is even lower than the edge on placing the 6 or 8. In fact, it's even lower than the 1.41 percent edge on pass or the 1.4 percent on don't pass.

However, place and buy bets are decided in fewer rolls than pass/don't pass wagers because there is no need to determine the point with a comeout roll. If you're placing or buying, the house edge has more chances per hour to work against you than if you're betting pass or don't pass.

Not only that. You can't back place or buy bets with free odds as you can pass and don't pass wagers. The free odds are among the few bets in the casino that have no house edge. Backing a pass bet with single odds drops the house edge on the pass-odds combination to 0.8 percent, and it sinks lower when more odds are permitted. Given my druthers and $25 to bet, I'd rather have $5 on pass and $20 in odds than a buy bet on 4--even with the edge lowered to 1.32 percent.