The oddness of odds
Stuart Wheeler
CHANCE by Amir D. Aczel High Stakes Publishing, £12, pp. 192, ISBN 1843440229 ✆ £9.60 (plus £2.45 p&p) 0870 429 6655 Ido find this an extraordinary book. Distinguished as the author is, ‘an internationally known mathematician with a BA in mathematics and Master of Sciences degree from the University of California ’, he nevertheless has no instinct for his subject: i.e. chance, or probability. This he presumably would not dispute, for we find him saying, ‘No one really has an intuition for such things,’ and ‘These results never cease to amaze me,’ and ‘This result is surprising.’ The fact is, though, that a lot of people do have a good intuition or instinct for these matters, but, curiously enough, they are not usually statisticians.
The book has a lot of amusing stuff in it. You may not have thought that mathematicians could tell you how many blind dates you should go on before deciding on your mate but they can, they really can! Also, why is it that, according to the author, who grew up in Israel, that country has many chain-smoking, pot-bellied men, and yet it is second only to Japan in the longevity of its men? Once you think of it, the answer is pretty obvious, but can you see it? When the book deals with this kind of thing it is all good stuff and very readable as long as, most of the time, you skip the attempts at explanation. Another example: how many people do you need in a room for there to be an even chance that two of them have the same birthday? If you do not know it already, the answer, 23, may indeed surprise you if you are not a gambler.
Although much of the book is certainly entertaining you get some rather long winded explanations with tiresome formulae, for propositions which common sense and logic tell you are obviously true. Take this example. A house has three apartments, one containing two men, one two women and one a married couple. You want the married couple. Obviously you have a one-in-three chance of knocking on the right door. You knock on one. A woman answers. What is now the chance that that is the right door? The book gives a rather long and certainly tedious explanation involving a tricky formula, before coming out with the answer that the chance is still one-in-three. But it should have been obvious that it made no difference whether a man or a woman answered. You were no further forward. Obviously the chance still remained one-in-three.
The book contains a number of errors, and the tendency to err has been caught by the author’s colleague who wrote the appendix. He is discussing poker when he writes, ‘Say you hold a full house and your opponent has a four-flush in five-card draw. If he draws one card, he has a 19 per cent chance of making the flush and beating your full house.’ More learned stuff follows, but it is all rather spoilt by the fact that, as any poker player knows, a full house beats a flush anyway!
None of these points really detracts much from the book. There is good advice about a variety of matters. Suppose you have $20,000 and you are in a Las Vegas casino, expecting to be visited by the Mafia at dawn when your fate will be too horrible to describe unless you can produce $40,000? You are going to have to gamble at, say, roulette. Should you be bold and put $20,000 on red or black, thus losing everything or reaching $40,000 in one fell swoop, or should you be ‘cautious’, making a series of $1,000 bets? The answer here is right and, while I hope you do not actually find yourself in this position, the advice will be important if you do!
If you skip the turgid bits, I think you will enjoy this short book.
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