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Can Prediction Markets Help You to Win the Lottery?

November 22, 2011

Derren Brown, the magician, is no stranger to the use of the idea of the wisdom of crowds as part of his entertainment package. A couple of years ago, for example, he selected a group of people and asked them to estimate how many sweets were in a jar. All conventional ‘wisdom of crowds’ stuff, albeit wrapped as part of a magical mystery tour. His more recent venture into this world of apparent wisdom went down a rather singular avenue, however, as he explained how a group of 24 people could predict the Lotto numbers better than one. The idea in essence was that each of the 24 would make a guess about the number on each ball in turn and the average of each of these guesses would in each case converge on the correct chosen numbers. It appeared to work – but that is the thing about illusionists; they are good at producing illusions. I will not go into how he did generate the effect of predicting the lottery draw, because there is no point if you already know, and because it would spoil the fun if you don’t. What is sure, however, is that the musings of the crowd had nothing to do with it. But why not? After all, if the crowd can accurately guess the weight of an ox or the number of jelly beans in a jar, why not the numbers on the lottery balls? The simple answer, of course, is because the lottery balls are drawn randomly. And the thing about random events is that they are unpredictable. This is at the heart of what economists term ‘weak form market efficiency’, i.e. that future movements in share prices cannot be predicted from past movements. In this sense, the series has no memory. So what is likely to happen if you do get a group of friends around and ask each to guess the number that will appear on each of the Lotto balls drawn next Saturday? If you take the average of the guesses about each of the balls in turn, my best estimate is that you are likely to end up with a prediction for each ball that is about 30 or less. Why so? Partly this is because people tend to pick birthdays but it’s also because the averaging of a large number of guesses is likely to produce a number somewhere nearer the mid-point of the set of numbers than the extremes. But if you do use these numbers and just happen to win, you’re likely to be sharing your winnings with a lot of other people who’ve chosen birthdays. The better strategy is to populate your ticket with bigger numbers, which are likely to be less popular. This strategy won’t alter your chance of winning but it will increase how much you can expect to win if you do win. And that is no illusion!

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