Side bets at table games: high edge, but surely tempting

Folks who go to casinos nowadays often look for games in which small wagers can pay big bucks. Slot machines have traditionally afforded this possibility, and it's one reason for their immense popularity. Some table action now offers similar opportunities with side or bonus bets.

To understand the allure of bonus bets, make believe a craps player drops $10 on Pass and backs it up with $50 Odds when a point is established. Say the person also makes a $1 side bet.

From the casino's viewpoint, cash flows caused by wins or losses on individual coups don't matter. Profits depend on averages over many bets, made by legions of solid citizens during extended time periods. Edge on the flat portion of a Pass bet is 1.4 percent and on the Odds is zero; for $10 with $50 odds, the house therefore figures it earns $0.14. Say the side bet in question has 42 percent edge, which may seem excessive but is actually at the low end for such a wager; at $1, this is worth a theoretical $0.42 to the house -- triple that of the larger principal bet.

Unlike the house, players tend to think in terms of short-term bankroll ups and downs -- the volatility -- and are generally oblivious to the erosive effect of edge. The primary bet in this example represents a possible win of $10 on the come-out and -- subsequently -- $110, $85, or $70 when the point is four or 10, five or nine, or six or eight, respectively; possible losses are $10 on the come-out and $60 during the point phase of a roll. A $1 blown side bet tends to look like chump change next to the $10 and $50 on and behind the Pass line. Further, the payoff if the secondary bet wins, at least on the jackpot when there's a sliding scale dependent on the particulars of the proposition, may be substantially more than the returns in the basic game.

Maybe you think this is all just pie-in-the-sky speculation. It's not. Consider Application 11/835,358 now being examined by the US Patent Office. Entitled "Bonus Craps Gaming," this involves a bet on the number of successful passes a shooter will make.

The patent application lists seven alternate pay schedules as models of what a casino may actually implement. On one of these (the inventors label it "Version E") the bet loses if the shooter makes five or fewer passes; it wins 5-to-1 for six or seven successive hits, 15-to-1 for eight or nine, 30-to-1 for 10 or 11, 75-to-1 for 12 or 13, 250-to-1 for 14, 1,000-to-1 for 15 through 19, and 5,000-to-1 for 20 or more.

The payoffs are attractive. But how good are the chances of winning? And how much is the edge?

The answers hinge on what determines when a series of successive passes ends. There's wiggle room about this issue in the patent application. The document states that the count may terminate upon "the occurrence of one or more consecutive pass outcomes immediately followed by the outcome of the number 7 ... or the occurrence of one of the numbers 2, 3, or 12 on a come out." Either situation can be regarded as failing to make a pass.

For illustrative purposes, assume the less favorable of the above options. Namely, that the tally resets after either a craps during a come-out or a seven during a point roll.

The chance of making a pass starting with the come-out is 49.29 percent. The probability of winning anything at all on the side bet with the Version E payoffs is only 1.43 percent, roughly one out of 70. As for those big bucks, the likelihood of earning 1,000-to-1 is one out of 41,788 and that of grabbing 5,000-to-1 is one out of 2,749,406. The edge is a usurious 82.9 percent; on the average, for every dollar booked, the casino keeps close to $0.83 -- almost six times the $0.14 on the $10 Pass bet.

Should you go for a bet like this since it costs so little? Or avoid giving the house so much advantage? Here's how the writer of rhymes about risk, Sumner A Ingmark, depicted the dilemma: