IT gleamed ominously up at me. Aghh! It鈥檚 a 拢1 coin! Last week I gave every coin in my possession to charity. It wasn鈥檛 altruism, it鈥檚 just that coins scare me out of my wits. Even though I know they鈥檙e still out there, I feel safer if I鈥檓 not carrying any. From now on, it鈥檚 notes or flexible friends for me.
I guess I should start at the beginning. A few weeks ago, one of our graduate students put a press cutting on the departmental noticeboard. It was a piece by Roger Anderson, The Sunday Times鈥檚 鈥渙wn consumer champion鈥�. 鈥淚 have come to the conclusion,鈥� it began, 鈥渢hat the one indisputable thing about probability theory is that many of the people who are obsessed with it are very rude鈥� (5 March 1995).
It transpired that in a previous article Anderson had rather unwisely suggested that you can improve your chances of winning the National Lottery if you choose the same numbers every week. Not surprisingly, he had been deluged with letters pointing out that since the chances of any set of numbers coming up are exactly the same, this strategy neither improves nor worsens the probability of winning. Presumably, many of these letters had been less than polite.
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To be fair, Anderson had merely been quoting a 鈥渟cientist鈥�, who had said much the same thing even though he should have known better. But it was the two other statements that Anderson made in his defence that got to me. The first was that probability 鈥渋s just a theory based on some pretty big assumptions鈥�. The second: 鈥淢oreover, probability theory suggests that there will be an equal distribution of heads and tails in any 100 tosses of an evenly balanced coin, but what I find hard to swallow is that it does not then allow any greater chance of tails coming up in the final 25 tosses if heads have come up more frequently in the first 75.鈥�
The lottery is one thing, but these two attacks on the very foundations of probability really set me thinking. There were two possibilities. One was that Anderson is indeed ignorant, since having been informed of his error he then repeated it 鈥� and his correspondents were justified in telling him so. That, it seemed to me, was so unlikely as to be beyond reasonable contemplation. After all, he is an important man, unlike all those ridiculous probability theorists. His job is to tell the nation about money matters, and nobody could perform such a crucial job if they were innumerate.
That left only the second possibility: that Anderson was right. In vain might the probability theorists point out that their views were not 鈥渙nly a theory鈥�, but had been subjected to literally billions of stringent experiments (many of them at the racetrack or casino). Nor would it improve matters to explain that probability theory doesn鈥檛 predict an even distribution on every sequence of 100 coin tosses, but only in the long run. Previous imbalances are not wiped out by being cancelled by imbalances the other way, but are simply swamped by the huge numbers of tosses that occur after them, so that their distorting effect becomes negligible.
No, forget all that. Anderson knew something that the probability theorists didn鈥檛. He must have done, or he wouldn鈥檛 have gone to such lengths to make so many statisticians 鈥� normally pleasant quiet people 鈥� so angry and rude. I could work out what it was from the hints he had given, and that鈥檚 when I began to suspect the awful truth.
Imagine our stalwart cricket captain Michael Atherton walking out for the toss at the start of a test match. The umpire pulls a coin from his pocket, and throws it in the air. You or I might naively imagine that it has the same chance of coming down heads as tails, but Atherton knows what Anderson has discovered. It all depends on what the coin has done before. If in previous tosses it has come down heads more often than 50 per cent, then it is more likely to come down tails, and vice versa. For several days Atherton has been sorely tempted to sneak into the umpire鈥檚 room while he鈥檚 asleep, remove his coins, and subject them to stringent statistical tests to find out which coins are biased in which direction.
It鈥檚 so sneaky. You can look at the coin till you鈥檙e blue in the face and never notice the difference, but every coin in the umpire鈥檚 pocket carries an invisible stamp of history. If it鈥檚 been tossed before, it鈥檚 biased. Worse, all the West Indies captain has to do is toss a coin repeatedly until it notches up more heads than tails. From that moment on it鈥檚 a dead cert for tails, a statistical time bomb. Slip it into the umpire鈥檚 pocket and Atherton had better watchout.
And imagine all those numbered plastic ping-pong balls used in the lottery. You can stir them around in their bag before putting them into the machine and it makes not the slightest difference to their statistical properties. But once they know they鈥檙e taking part in a real lottery draw, suddenly they become susceptible to their own past history. Even if some of them have been damaged and replaced by others, the memory has been passed on. Not only that, those balls know what numbers every single one of us chose last week because they鈥檙e going to make sure that our chances are improved today if we didn鈥檛 win last time. Provided we don鈥檛 ruin it all by-changing our choices.
So now the big secret is out. Coins are telepathic entities, able to sense human intentions and distort the laws of dynamics accordingly. Now do you see why I can鈥檛 bear to have the things near me? For all I know my once-revered 50p coin could decide to break the law of gravity (which is only a theory) and dump me into orbit without a spacesuit. Coins in my pocket? I shudder at the thought. Nasty sneaky underhanded things. Thank you, Anderson, for opening my eyes.