You are the chief guest at an auction, where an unknown number of horses will be revealed and auctioned, one after the other, randomly permuted. You are a connoiseur of horses, and can judge whether one horse is 'better' than another. Being the chief guest, you have a one-time privilege of selecting a horse, after it is revealed, but before it gets auctioned off. You get to keep this horse for yourself. Your objective is to maximize the probability of selecting the best horse. One strategy is to pick the first horse. Can you do any better?