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# Playing it smart - Buying the four or ten at craps

9 July 2007

Solid citizens betting \$20 or more on fours or 10s at craps "Buy" rather than "Place" the numbers. The benefit is that edge is less Buying than Placing, so earnings per dollar up for grabs are more. The reason is not that odds against winning change. They're 2-to-1 either way. It's the payout structures that differ.

Place bets on fours and 10s are identical and uniform no matter where you play. You risk multiples of \$5 and earn corresponding multiples of \$9. So, \$5 gets you \$9, \$10 gets you \$18, and so forth. You're up to win \$1.80 for every \$1 you might lose.

Buy bets on these numbers pay 2-to-1. That is, \$20 gets you \$40, \$50 gets you \$100, and so on. The fly in the ointment is the "vigorish" or "vig" a fee you pay to make the wager. It's normally 5 percent of the bet, rounded down to the nearest whole dollar. Most casinos assess the charge when they book the action, and keep it whether you win or lose.

Say you Buy the four for \$20. You squeeze \$21 from your rack, the \$20 bet plus \$1 vig. A seven therefore costs you \$21. A four gets you back your \$20 and a \$40 payoff. You begin with \$21 and end with \$60. Net profit on \$21 is \$39, nearly \$1.86 on the dollar.

As a consequence of rounding down, relative profit rises and edge falls as bets increase toward higher integral multiples of \$20. As an example, pretend you Buy the four for \$39. A 5 percent commission on \$39 would be \$1.95. But the vig is rounded down to \$1. You put out \$39 + \$1 or \$40. Winning gets back your \$39 and a payoff of \$78. You start with \$40 and finish with \$117, a profit of \$77. That's over \$1.92 gain for every \$1 you can lose.

Had you bet \$40 instead of \$39, the vig would have been 5 percent of \$40 or \$2. You'd drop the dealer \$42. A win would recover your \$40 plus an \$80 payoff. You'd have started with \$42 and ended with \$120, a \$78 profit. That's back to a \$1.86 net per dollar.

Betting integral multiples of \$20 on four or 10 when you pay the vig up-front, you earn \$0.06 per dollar more on a win than risking the same total on a Place bet. You can improve on this with wagers just under each \$20 plateau. At \$39, you gain \$0.12 per dollar taken from your rack. You'll continue to benefit being just below each \$20 plateau as wagers get larger, but the effect weakens. Bet \$99 and pay \$4 vig for an outlay of \$103. A win gets back your \$99 plus \$198. You begin with \$103 and end with \$297, a \$194 net. That's \$1.88 on the dollar, \$0.08 over the Place bet.

At \$1,000, the vig is \$50 and your win is just under \$1.86 on the dollar. Instead, bet \$1,019. The vig is still \$50. You lay out \$1,069. On a win you get \$1,019 + \$2,038 or \$3,057 for the \$1,069 you took from your rack. That rounds off to \$1.86 on the dollar, but is a fraction of a cent per dollar better than at \$1,000.

A few enlightened establishments charge for vig only when a Buy bet wins. So, to Buy the four for \$20, you lay out \$20. A seven costs you the \$20. A four gets paid at 2-to-1 minus a vig equal to 5 percent of your bet rounded down to the next lower dollar. You accordingly pick up a \$39 profit, earning you \$1.95 on the dollar. Bet \$39 and you get back your \$39 plus \$78 minus \$1 for a \$77 net. That's \$77/\$39, or better than \$1.97 on the dollar.

In terms of edge, all Place bets on the four or 10 give the casino 6.667 percent. When the house collects the vig on Buy bets win or lose, edge drops to 4.762 percent at the \$20 plateaus. The edge is minimum at \$39 2.500 percent. In games that charge the vig only when you win, the edge at the \$20 plateaus is 1.667 percent and the best you can do is 0.855 percent at \$39.

It makes no economic sense to boost your bets on four or 10 to \$20, playing for stakes you can't afford simply to trim edge. If you're comfortable betting \$40, though, you may find it's a good idea to drop back to \$39. By settling for \$1 less profit, you're risking \$2 less on a proposition that's 2-to-1 against you. A prospect the poet, Sumner A. Ingmark presaged when he penned:

Examine where you'll start and finish,
To find points where returns diminish.

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Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.