Simultaneous opposing bets in craps: what price moderation?

Some craps aficionados relish opportunities in the game to bet on multiple propositions simultaneously. The usual incentive is to have wins on one or more offset losses on others.

The approach most often takes the form of hedging. That is, using small, low-probability, high-payoff auxiliary bets as insurance to avoid or mitigate losses on larger primary wagers.

An illustration is a $1 on Any Craps along with $5 on Pass during come-out rolls. The $1 wins $7 on a two, three, or 12 and loses otherwise. The $5 wins even money on a seven or 11; loses on a two, three, or 12; and becomes the bet for subsequent rolls on anything else. The hedge changes a possible $5 loss to a $2 win on the come-out. But it also trims the ultimate win on the come-out and point phases of the hand from $5 to $4 while raising the overall loss from $5 to $6 if a shooter sevens-out on the point.

Less commonly, players may bet equal amounts on Pass and Don't Pass, or Come and Don't Come, simultaneously. During the come-out, these pairs of wagers can push (on a two, three, seven, or 11 push because one wins and the other loses), lose one unit (on a 12 because one loses while the other gets no action), or go to either side of the point. During the point phase of a hand, the combination always pushes -- one winning and the other losing.

Players who follow this strategy do it so they can take or lay Odds on one side of the pair or the other, usually Pass or Come, without risking the flat portion of the bet. They reason that since the house has no edge on the Odds, they're getting a free ride. What about the loss when a 12 pops during the come-out? They argue that this happens rarely enough to be neglected.

Another opposing bet ploy some solid citizens use is to bet $6, for example, on Don't Pass or Don't Come. Coming-out has three ways to win $6 (1-1, 1-2, 2-1), eight to lose $6 (1-6, 2-5, 3-4, 4-3, 5-2, 6-1, 5-6, 6-5), one to get no action (6-6), and the other 24 to finish with $6 bet against the point. After the come-out, they Place the point -- $6 for a six or eight, $5 otherwise. On point rolls, they can win or push but not lose. On a six or eight, a seven loses $6 and wins $6 for a push while the number loses $6 and wins $7 for $1 profit. On a five or nine, a seven loses $5 and wins $6 while the point loses $6 and wins $7 to earn $1 either way. On a four or 10, a seven loses $5 and wins $6 for $1 profit while the four or 10 loses $6 and wins $9 for $3 gain.

The weakness of all opposing bet strategies is that wins and losses subtract and yield a net, while the money the house averages from edge is the sum of its revenues on the separate parts. For $1 any craps, the bosses chalk up $0.111; for $5 on Pass, the casino earns a theoretical $0.07. The two together add up to $0.181. Concurrent $5 Pass and Don't Pass or Come and Don't Come bets give the joint $0.07 for each -- $0.14 total. Not by coincidence, the expected value of a 1/36 chance of losing $5 is $5/36, which also equals $0.14. With the Don't Pass or Don't Come plus Place approach, the casino's theoretical revenue depends on the points involved. For instance, with $6 on Don't Pass it's $0.084 and for $5 on the point it's $0.20 -- $0.284 in total.

Craps mavens who hold edge as supreme would bet only on Pass, Come, Don't Pass, or Don't Come then take or lay the maximum allowable Odds. To show the effect, $5 flat on Pass and $25 Odds on a point of 10 give the house $0.07 while bettors put up $30 to win $55. In contrast, with $5 on both sides and $25 Odds on Pass, the house earns $0.14 while players risk $25 to win $50.

Good gambling is not governed by edge alone, however. In sessions or visits of reasonable duration, the impact of edge on players is virtually imperceptible compared with that of volatility. And use of multiple opposing bets tends to moderate volatility, reducing the extremes of bankroll swings. Is it a wise trade-off? Individual players must decide for themselves. As the prodigy of punting poetry, Sumner A Ingmark, insightfully intoned: