When golfers play as partners, either in four-ball matches (as in the recent Solheim Cup and upcoming Presidents Cup) or in scrambles, they commonly follow a strategy in which the first partner to play hits a “safe” shot—maybe a layup on a long par 5, or a tee shot to the center of the green on a par 3—and then, if the safe shot has been successful, the next partner hits an aggressive shot, right at the flag.

This sounds sensible—guarantee the par, then go for the birdie—but mathematically it makes no sense. A better strategy is for the stronger player to play the aggressive shot first. Then, if it’s successful, the second player can hit an aggressive shot, too, thereby increasing the chance of ending up with a spectacular result. And even if the first shot doesn’t work perfectly the result may be good enough to serve as the equivalent of a safe shot—as with a favorite play of mine, the Accidental Lay-up, in which I swing so hard in my effort to reach the green in two that I top my ball and end up pretty much exactly where I would have if I’d sensibly wedged it just short of the water.