The well-loved Grateful Dead tune "Lady with a Fan" presents the listener with a scenario: A beautiful lady throws a fan into a lion's den, and challenges two suitors to retrieve the fan in order to gain her affections. The solider refuses; the sailor takes the challenge and wins the lady's heart. Which made the right decision? Can Stephen Dillingham use Bayesian decision theory to tell us the answer? (Hint: happiness can be measured in units called roses.)