Not All Craps Hedges Deserve the Bad Rap the Genre Gets

A simple and common example might be a $10 bet on the Pass line with $1 on Any Craps during the come-out roll. If a seven or 11 pops, the $10 bet wins even money and the $1 goes to the bosses; the $9 net profit seems pretty good, not much of a come-down from the $10 which would have been paid absent the hedge. On a two, three, or 12, the $10 is lost but the hedge pays $7 so the net distress is only $3; far less painful than the $10 that would otherwise have disappeared. Anything else hitting becomes the point with no immediate monetary action on the $10 but a loss of the $1 Any Craps; this sacrifice seems like chump change, a small price to pay for protection against the full $10 damage.

Players who hedge regularly can point to situations where such a strategy saved their necks. They generally don't even notice the erosive effect of the 'protective' bets on trimming their profits or deepening their losses. And, qualitatively, the approach has an undeniable appeal. Especially when the utility principle comes to the fore and the $1 or so is dismissed as inconsequential while the $10 or whatever is considered serious money.

Most credible gambling gurus eschew hedges. They argue that the approach can significantly raise the effective edge the house has over the bettor. And this translates into fatter donations by the solid citizens to the casino mortgage satisfaction fund.

Here's how it works out for the Pass and Any Craps strategy. I'll skip the long, boring calculations and jump right to the bottom line. Betting $10 on Pass, by itself, costs players an average of 1.41 cents per dollar at risk -- 14.14 cents for a $10 wager. Hedging this with $1 Any Craps brings the figures to 2.30 cents per dollar at risk -- 25.25 cents for the $11 total on the table. For reference, betting the whole $11 on Pass would cost 1.41 per dollar at risk -- 15.55 cents for the $11 wager. Comparison shows the insurance provided by this hedge to be rather dear.

The idea of hedging isn't what makes a protective strategy expensive. The problem with this and other common hedges is twofold: 1) they put money on both sides of a single proposition; 2) the protective component has a usuriously high edge.

Here's an alternate approach to protection that doesn't have these shortcomings. Say you can afford to have $60 on the table. Bet it all on the nine and you have a 40 percent chance of winning $84 versus a 60 percent probability of losing $60. The average cost of this bet, a result of the edge, is 4.00 cents per dollar at risk or $2.40 for the $60 total. Instead, pretend you bet $30 on the nine and put $30 plus $1 vigorish on "no five." You have 28.6 percent chance of getting a nine and winning $42, 28.6 percent chance of seeing a five and losing $31, and 42.8 percent chance of finding a seven and losing a net of $30 - $20 + $1 or $11. The average cost of this bet is 3.61 cents per dollar at risk or $2.20 for the $61 sum squeezed from your rack.

Here, the protective no-five bet lowers rather than raises the penalty for the total on the table. The reasons are inverse to those for the previous example. The bets are for opposite effects -- a seven versus a number -- but are not a tug-of-war on the same result. And the no-five lay has a lower rather than a higher effective edge than the Place bet on the nine.

It may be fun to devise hedges proving you're smarter than the gurus. Were minimum edge the object, though, you'd bet Pass and Come or Don't Pass and Don't Come with maximum Odds. And you'd start with enough of a stake to outride the normal downswings and not depend on ultimately expensive means of tempering them. It evokes this poetic proverb by the pundit, Sumner A Ingmark:

Weak's the gambler who esteems,
Labyrinthine betting schemes.