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Playing it smart - Buying the six or eight at craps

23 July 2007

If you want to risk \$20 or more on a number at craps, Buy bets may offer some opportunities to reduce the house advantage relative to their Place counterparts. Buying doesn't affect the chance of winning a coup. The benefit accrues because it raises the return on a win relative to how much you go down on a loss.

Given the \$20 floor, Buying is always superior to Placing on fours or 10s. On fives or nines, it's preferable when casinos charge the vig up-front for bets of \$26 to \$38, \$50 to \$58, \$74 to \$78, or \$98. In joints that collect the vig only when you win, Buys beat Place bets for all wagers of \$20 or more on fives or nines, trimming edge from 4 to between one and two percent.

This leaves the question of Buy bets on the six or eight.

To Place either of these numbers, you must bet a multiple of \$6 and can win a corresponding multiple of \$7. Regardless of the precise sum involved, you earn \$1.167 for every dollar at risk. And the house's edge is 1.515 percent.

To Buy either of these numbers, you'd bet a multiple of \$5 and receive the corresponding multiple of \$6 as your payoff. When the house collects the vig up-front, though, you'd also have to give the dealer 5 percent of the nominal bet rounded down to the nearest whole dollar. This would increase the dent your bankroll would suffer on a seven and since you don't get the vig back decrease what you clear when the number pops.

As an example, say you want to bet \$35. The vig would be \$1 (5 percent of \$35 is \$1.75, rounded down to \$1). So, a win would net you \$42 minus \$1 or \$41, versus a possible loss of \$35 plus \$1 or \$36. This is \$41/\$36 or \$1.139 per dollar at risk, with an edge that works out to 2.778 percent. This size bet, \$35, is the best you can do. And it's not as good, percentage-wise, as Placing the box for \$36 to win \$42 or any other amount, for that matter.

When the casino collects the vig only if your six or eight wins, a \$35 Buy bet would entail a \$35 outlay. On a win, you'd collect \$42 minus \$1, but the base of your possible deficit on a loss would be \$35 rather than \$36. The return is therefore \$41/\$35 or \$1.171 per dollar at risk and the edge would be 1.299 percent. This is a respectable, albeit modest, gain over the Place bet.

Unhappily, even in a casino that collects 5 percent vig only on winning bets, \$35 is the sole Buy on six or eight that surpasses its Place alternative. Betting \$30, return on the dollar and edge are the same as for Place bets. And at all other levels, they're worse. As illustrations, at integral multiples of \$20, the return is \$1.150 on the dollar and the edge is 2.273 percent. At \$55, the figures are \$1.164 on the dollar and 1.653 percent.

In days of yore, Binion's Horseshoe in downtown Las Vegas featured 4 rather than 5 percent vig on winning Banker bets at baccarat. What if a casino were to book Buys for minimum bets of \$25 on the six or eight at craps for 4 percent, collected only on wins? How would these wagers then stack up against Place bets?

Breakpoints for the rounded-down 4 percent vig are at integral multiples of \$25. At these tiers, win per dollar at risk is \$1.160 and house advantage is 1.818 percent. This is less desirable than Place bets. Wagers for which the Buys are actually the more profitable choice are \$35 to \$45, \$65 and \$70, and \$95. The best possible situation, a \$45 Buy bet, returns \$1.178 on the dollar and has 1.010 percent edge.

Of course, solid citizens who can afford at least \$20 on a single number, and want to trim the house advantage at craps to the bone, won't make either Buy or Place bets. They'll put their pelf on Pass and Come, dividing the dough so that the smallest possible portion of the total is on the flat component and the largest on the Odds. But that's another argument for another time. For, as the beloved bard, Sumner A Ingmark, believed:

The person who on fatuity acts,
Refuses to consider the facts.

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Best of Alan Krigman
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.