One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt
Paul Wilmott dresses the wisdom of Sky Masterson up in academic garb:
Paul Wilmott's Blog: Magicians And Mathematicians: We've learned the hard way how important it is to measure and manage risk. Despite the thousands of mathematics and science PhDs working in risk management nowadays we seem to be at greater financial and economic risk than ever before. To show you one important side of banking I'd like you to follow me in an exercise with parallels in risk management.
You are in the audience at a small, intimate theatre, watching a magic show. The magician hands a pack of cards to a random member of the audience, asks him to check that it's an ordinary pack, and would he please give it a shuffle. The magician turns to another member of the audience and asks her to name a card at random. "Ace of Hearts," she says. The magician covers his eyes, reaches out to the pack of cards, and after some fumbling around he pulls out a card. The question to you is what is the probability of the card being the Ace of Hearts?... [Y]ou already have an answer? What is that, one in fifty two, you say? On the grounds that there are 52 cards in an ordinary pack. It certainly is one answer. But aren't you missing something, possibly crucial, in the question? Ponder a bit more....
You have another answer for me already? You'd forgotten that it was a magician pulling out the card. Well, yes, I can see that might make a difference. So your answer is now that it will be almost 100% that the card will be the Ace of Hearts, the magician is hardly going to get this trick wrong. Are you right? Well, think just a while longer....
Are those the only two possible answers? Either one in 52 or 100%? Suppose that you had billions of dollars of hedge fund money riding on the outcome of this magic trick would you feel so confident in your answers? When I ask this question of finance people I usually get either the one in 52 answer or the 100%. Some will completely ignore the word 'magician,' hence the first answer. Some will say "I'm supposed to give the maths answer, aren't I? But because he's a magician he will certainly pick the Ace of Hearts." This is usually accompanied by an aren't-I-clever smile! Rather frighteningly, some people trained in the higher mathematics of risk management still don't see the second answer even after being told....
[W]hen I first heard this question an obvious answer to me was zero. There is no chance that the card is the Ace of Hearts. This trick is too simple for any professional magician. Maybe the trick is a small part of a larger effect, getting this part 'wrong' is designed to make a later feat more impressive... the Ace of Hearts is later found inside someone's pocket. Or maybe on the card are written the winning lottery numbers that are drawn randomly 15 minutes later on live TV. Or maybe the magician was Tommy Cooper. Or it was all the magician's performance-anxiety dream the night before....
A member of wilmott.com didn't believe me when I said how many people get stuck on the one in 52 answer, and can't see the 100% answer, never mind the more interesting answers. He wrote "I can't believe anyone (who has a masters/phd anyway) would actually say 1/52, and not consider that this is not...a random pick?" So he asked some of his colleagues the question, and his experience was the same as mine. He wrote "Ok I tried this question in the office (a maths postgraduate dept), the first guy took a fair bit of convincing that it wasn't 1/52!, then the next person (a hardcore pure mathematician) declared it an un-interesting problem, once he realised that there was essentially a human element to the problem! Maybe you have a point!" Does that not send shivers down your spine? It does mine...
