Are Hedges in Craps as Bad as the Experts Say, or Can They Work?

Perhaps the most common example involves "protecting" something like $10 on the Pass line with $1 on Any Craps during come-out rolls. The idea is that if the dice show a two, three, or 12 on these throws, the main bets lose but the hedges win $7 -- reducing the hurt from $10 to $3. The $1 loss on Any Craps when anything else appears? Well, hey, it's chump change. Or, is it?

If the Any Craps hedge seems sublime, others can be ridiculous. One in this category is equal bets on Pass and Don't Pass. Supposedly, these offset each other so players who take or lay Odds give the house no edge. What about losses on Pass not matched by wins on Don't Pass when 12s pop during the come-out? The rationale is that 12s are rare enough to be ignored. This, of course, ignores the subtle fact that the one out of 36 chance of a 12 is equivalent to the edge on the sum of the two bets.

On paper and over the "long run," the premium the casino squeezes from the edge on the hedge is money out of the player's fanny pack. Still, these wagers seem brilliant when they work. And, as a result, many solid citizens not only mock the math but pooh-pooh the pundits who propound it.

Fortunately, gamblers and other folks who make life's important decisions have computers at their behest. And computers can be programmed to simulate the real world such that lots of events can be executed and documented automatically in a brief time.

Accordingly, as yet another in a long string of services to humanity, I wrote a program simulating two individuals playing identical games -- one betting $11 flat on the Pass line and the other dropping $10 on Pass and $1 on Any Craps. Totals of $11 were put at risk in both modes. Simulated sessions were of moderate duration, and only the indicated wagers were made. Other hedges, differing amounts, or bells and whistles such as taking Odds would alter the details somewhat but not the general conclusions leaping out of the results.

One set of sessions was simulated for 10,000 games of 100 decisions each, about an hour at the rail. Data were gathered for only the wagers indicated -- no Odds, no auxiliary bets, no pressing or regressing. In a typical series, both the straight $11 Pass bettors and the $10 Pass plus $1 Any Craps players finished even or ahead in 3,957 sessions and lost in 4,993; the no-hedge approach won and the hedging strategy lost in 918 while the converse held in the remaining 132. Perhaps more tellingly, the no-hedge players did better than their hedging counterparts in 6,277 sessions, worse in 3,477, and the same in the other 246.

Repeating these simulations yields figures that differ, but not by much. Overall, players appear twice as likely to win less or lose more by hedging. However, the hedge helped often enough to reinforce the notion that it's good insurance for those who want to believe it is. Can a simulation be written that offers clues to predict conditions under which hedging will succeed? Only if a prophet happens to hold a day job as a programmer. So, until such an oracle steps forward, we'll just have to muddle through with this maxim by the immortal Sumner A Ingmark:

Gamblers whose fanny packs grow fatter,
Learned just what does and doesn't matter.