Playing it smart - Should you Buy, rather than Place, the four or 10 at craps?

Players who wager on the four or 10 at craps make "Place" bets at the $5, $10, and $15 levels, but generally "Buy" the numbers at $20 and above. They know that buying is supposed to be a break for players who bet bigger. But, few solid citizens understand the why and how. Or more importantly, the best way to take advantage of whatever benefits the opportunity offers.

It's not in chances of winning. Fours or 10s win with three dice combinations (1-3, 2-2, or 3-1 for a four; 6-4, 5-5, or 4-6 for a 10). Either number loses with the six combinations that total seven (1-6, 2-5, 3-4, 4-3, 5-2, or 1-6). So players must overcome odds of 6-to-3, which reduces to 2-to-1, whether they bet Place or Buy. The difference is in the payoffs for winners.

Place bets pay 9-to-5. Risk $5 to earn $9, $10 to win $18, and $15 to gain $27. For every dollar a bankroll is depleted on a miss, it's bolstered by $1.80 on a hit. If you're thinking this is good, you haven't read the fine print. When you must overcome odds of 2-to-1 to succeed, a "fair" reward would be in the same proportion. So $5 would get $10, $10 would bring $20, and $15 would yield $30. The difference, $0.20 on the dollar, is the source of the casino's edge or advantage on the action.

Payouts on Buy bets have a different structure altogether. In most cases, the casino takes a commission the "vigorish" or "vig" up front. You pay the dealer 5 percent of your bet, rounded down to the nearest whole dollar, when you make the wager. The bet is paid at the nominal 2-to-1. The vig is not part of the bet, however, and house keeps it whatever the outcome.

Make believe you want to go for $20 on the four. You drop the dealer $20 for the bet. You also fork over 5 percent of $20 or $1 for the vig. If the seven pops, you're out the whole $21. On a four, you get back your $20 along with a $40 payout. You started with $21 and finish with $60 so the profit is $39. Bottom line, $21 gets you $39. That's $39/$21 or just under $1.86 per dollar. It beats $1.80 for a Place bet. But it's still $0.14 per dollar less than the $2.00 a fair bet would be worth.

The vigorish stays at $1 because of the "round-off" until your wager gets to $40. This, because 5 percent of $39 is $1.95 while 5 percent of $40 is $2. If you go to $40, you therefore have to start by taking $42 from your rack. You recover $40 plus $80 on a win, so your net gain is $120 - $42 = $78. And $78/$42 is, as with the $20 Buy, a profit of just under $1.86 on the dollar.

Instead, say you make a $39 Buy. Now you give the dealer $40. Your wager is $39. It pays $39 x 2 = $78. So a successful coup begins with $39 + $1 or $40 and ends with $39 + $78 = $117. Your net gain is $117 - $40 or $77 on a $40 outlay. The rate of return is now $77/$40, which exceeds $1.92 on the dollar.

This is the best you can do. At $59, the most you can bet with a $2 vig, you lay out $61 and get back your $59 plus a profit of $59 x 2 = $118 for a total of $177. Net gain is $177 - $61 = $116 and rate of return is $116/$61 or slightly over $1.90 per dollar.

You'll occasionally find a casino that charges vig only on winning Buy bets. At the $20 level, you'd therefore take $20 from your rack to make the wager. A win would recover your $20, along with earnings of $39 ($40 minus 5 percent of $20 for the vig). In all, $20 nets you $39, a return rate of $39/$20 or $1.95 on the dollar. At the top of this range, you risk $39 for a net gain of $78 - $1 = $77; the return is $77/$39, somewhat over $1.97 per dollar. Again, you can't do better. Bet $59 to win $118 - $2 = $116 for a return of $116/$59, a bit under $1.97 on the dollar.

Assuming you're going to bet on the four or 10 anyway, is it reasonable to raise or lower the amount you might otherwise have in mind to get the most bang for your buck? That's between you and your financial advisor, someone you shouldn't confuse with your casino host, notwithstanding the trust you may have in one or both. For, as the poet Sumner A. Ingmark penned:

Discretionary money doesn't mean a session,
Ought to be conducted in the absence of discretion.