It’s Black Friday, and you are entering the battlefield: a mall parking lot. You’re determined to nail that doorbuster deal, and quantities are limited. The field is already full of other combatants. You must find the perfect parking spot.

Do you grab the first one you see, or drive as close to the mall as you can and hover? Or, do you choose a tactic that lies somewhere between?

Parking at the mall has long frustrated drivers and taxed the minds of traffic engineers—but after working on the problem for three years, physicists Sidney Redner of the Santa Fe Institute and Paul Krapivsky of Boston University have gotten closer to a winning strategy. “There are lots of studies of parking lots, but it’s just that they’re so complicated, you don’t get any insight into what’s actually happening,” Redner tells Mental Floss.

Redner and Krapivsky, whose work employs statistical physics to make sense of large systems, simplified the messy dynamics of a parking lot by modeling it with a one-dimensional grid of cells, each representing a parking space. They tested three simple, yet realistic, parking strategies using basic probability theory. Their model tested the following strategies to see which one resulted in least time spent walking and driving in the parking lot:

Meek Strategy: Meek drivers park in the first open space they see, however distant it is from the mall. As a result, they often spend the most time walking to and from the mall.

Prudent Strategy: Prudent drivers look for the first open spot but then keep driving toward the mall. They continue to drive until they see a parked car and then park in the best open spot between that first open spot and that first parked car. There may be a block of open spaces between the first open space and the first parked car. From that block of open spaces, they choose the one closest to the mall.

Optimistic Strategy: Optimistic drivers drive as close to the mall as possible and look for a parking space close to the entrance. If they see one, they grab it. If there are none, they backtrack and choose the first open space they see. Optimistic drivers probably spend the most time driving and the least time walking. In the worst-case scenario, they end up parking back where a meek driver would have parked.

Naturally cautious drivers are more likely to default to the meek mode, while aggressive drivers often use the optimistic strategy, well, aggressively. And most drivers have tried something like the prudent method.

So, which is your best bet in a crowded mall parking lot this holiday season?

In the experiments, the prudent strategy fared best, followed closely by the optimistic strategy. The meek strategy finished a distant third (“It’s hard to comprehend just how bad it is,” says Krapivsky, a self-described meek driver).

And even better: The more crowded the lot, the better the prudent strategy works, he adds.

One clear takeaway from the study is that meek drivers may want to ramp up their parking skills before going to the mall. “You don't want to park on the very outskirts of the lot, like a mile away from the stores. You want to go to the first place there’s an open spot and park somewhere in that first open area,” Redner says. They published their findings in the Journal of Statistical Mechanics [PDF].

The researchers say this is the best of the strategies they tested, but it has its limitations. It does not take into consideration competition among a sea of drivers all looking for parking spaces at the same time, and it doesn’t include (perhaps optimistically) the psychological aspects of operating a vehicle. “We are not rational when we are driving,” Krapivsky tells Mental Floss.

The researchers’ one-dimensional grid model also assumed that there would be one car at a time entering the lot through one entrance, unlike messier lots in the real world, where many cars enter from a multitude of entrances.

The optimal parking strategy, one that would best all others every time, has yet to be found. In their research, though, Redner and Krapivsky are homing in on one that integrates the more complicated aspects of parking.

For now, science says prudence is a virtue in the parking lot. And while the meek might inherit the Earth, they certainly won’t find the best parking space at the mall.