## The Law of Averages

Just a couple of weeks ago I found myself bemoaning my bad luck in the following terms

A few months have passed since I last won a dictionary as a prize in the Independent Crossword competition. That’s nothing remarkable in itself, but since my average rate of dictionary accumulation has been about one a month over the last few years, it seems a bit of a lull. Have I forgotten how to do crosswords and keep sending in wrong solutions? Is the Royal Mail intercepting my post? Has the number of correct entries per week suddenly increased, reducing my odds of winning? Have the competition organizers turned against me?

In fact, statistically speaking, there’s nothing significant in this gap. Even if my grids are all correct, the number of correct grids has remained constant, and the winner is pulled at random from those submitted (i.e. in such a way that all correct entries are equally likely to be drawn) , then a relatively long unsuccessful period such as I am experiencing at the moment is not at all improbable. The point is that such runs are far more likely in a truly random process than most people imagine, as indeed are runs of successes. Chance coincidence happen more often than you think.

Well, as I suspected would happen soon my run of ill fortune came to an end today with the arrival of this splendid item in the mail:

It’s the prize for winning Beelzebub 1303, the rather devilish prize cryptic in the *Independent on Sunday* Magazine. It’s nice to get back to winning ways. Now what’s the betting I’ll now get a run of successes?

P.S. I used the title “Law of Averages” just so I could point out in a footnote that there’s actually no such thing.

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