The basketball shootout: Strategy and winning probabilities (Q1082257)

The Continental Basketball Association staged a shootout in which each contestant attempted one shot from a distance of his/her choice. The player scoring from the greatest distance won a large prize. The order of shooters was determined by a lottery and each player knew from where previous contestants had shot and whether they were successful. We derive a simple formula for the optimal strategy assuming equal abilities. The shooting order is shown to have a large influence on the winning probability.