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Best of Alan Krigman

Gaming Guru

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Would You Bet the Props at Craps if the Payoffs Were Higher?

29 March 2004

Among the great allures of craps to cognoscenti is the chance to make bets with low house edges. So low, that casino bigwigs tell themselves the game is dying to avoid having to admit why they're really scrambling to replace dice tables with slot machines. A sophisticated player betting, say, $10 on Pass or Come and taking $30 in Odds pays the casino only $0.14 in theoretical fees on the $40 total. Slot machines with what's deemed a "loose" 95 percent return would earn the joint an average of $2.00 on a total of $40 bet. At 90 percent return, you're talking $4.00. If you've been wondering why they're pushing the slots these days, now you know.

Craps, however, doesn't force folks to be any wiser in the wagering world than they are on the street. So dice devotees can always make bets with usurious house advantages instead of, or in addition to, those on which the casinos earn next to nothing. Placing the five for $40 has a covert cost of $1.60 and Buying the four for the same amount has an up front charge of $2.00, as examples. Contrast these with the $0.14 for the $10/$30 Come bet.

The worst edges in the game are on the one-roll "propositions" or "props" -- the Field, Hops, Any Seven, Craps numbers (two, three, and 12), and the 11, along with the multi-roll Hardways (two-two, three-three, four-four, and 10-10). All credible gaming goorahs, and some who aren't as credible as others, caution against these bets. Some solid citizens make them anyway. Perhaps they don't realize how much edge they're wasting, or they covet the payoffs, or they think of the bets as auxiliary longshots "for only a buck or two" so it doesn't matter, or they've doped out what they're sure is a brilliant hedge and aren't about to let anything as droll as facts and figures defile their fantasies.

What would happen if a casino tried to make its craps tables more attractive by raising payouts on the propositions, essentially taking less per dollar bet in the hopes of generating more action? Consider the possibilities in terms of the two, 12, or paired hops. Each is a 35-to-1 shot which normally pays 30-to-1 and hands the house close to 14 percent edge. If winners earned 35-to-1, they'd be "fair" bets with no advantage for either the players or the bosses. The accompanying table gives the edge in terms of the casino's theoretical profit per dollar bet, over the range between the present standard payoff and the fair situation.

House advantage on the two, 12, or any paired hop
in terms of theoretical cost per dollar bet
for alternate payoffs

payoff
edge
35-to-1 $ 0.000
34-to-1 $ 0.028
33-to-1 $ 0.056
32-to-1 $ 0.083
31-to-1 $ 0.111
30-to-1 $ 0.139

The situation for the three, 11, or a non-paired hop is similar. These are 17-to-1 longshots that normally pay 15-to-1 and squeeze over 11 percent, $0.11 on the dollar, from the money bet. They'd be fair bets at 17-to-1. The intermediate payoff, 16-to-1, would cost players $0.056 on the dollar -- half the standard amount.

The Field also offers casinos opportunities to tempt patrons with richer returns. Standard Field bets pay even money on the three, four, nine, 10, and 11, and 2-to-1 on the two and 12. The edge is 5.6 percent. Some casinos spike the punch with 3-to-1 on either the two or 12, dropping the edge to 2.8 percent. The bet would be fair at 3-to-1 on both the two and the 12. Another possibility would be to pay 6-to-5 across the board with no bonus on two or 12, in which case the edge would be 2.2 percent.

Higher payouts on the one-roll bets and Hardways might make for meaty marketing pitches that draw the unwary from yesterday's favorite casino to today's. They could likewise induce a few bezonians to put money on the peripheries rather than the substance of the game. But the changes most apt to be implemented still don't spin flax into gold. The insightful inkslinger, Sumner A Ingmark, intimated as much when he skillfully scribbled:

It's oft a sorry spirit who misunderstood,
That making something better didn't make it good.

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.