Under the rules of NCAA Hockey and USA hockey, when a penalty shot is awarded, the nonoffending team has the choice of taking the penalty shot or having a minor penalty assessed to the offending team. Since the chance of scoring on a penalty shot normally exceeds the chance of scoring during the minor penalty, most teams will accept the penalty shot. We show, however, that there are times when selecting the minor penalty in lieu of the penalty shot is optimal. We show that when the nonoffending team is ahead near the end of the game, the optimal choice is the minor penalty.
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