Problem: You are the chief guest at an auction, where some number of horses will be auctioned, one after the other, randomly permuted. You are a connoisseur 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?
Source: Fifty Challenging Problems in Probability with Solutions by F Mosteller
Disclaimer/Hint: If you are even half like me, you would love attempting this puzzle. Just do it using basic math and you will hit it right. The solution would even imply "Birthday Paradox" beautifully. :)
Update: (22/12/09) Solution posted by Giridhar in comments.