The lottery insight

A while ago I mentioned how those who criticize people who enter the National Lottery as stupid individuals that don't understand probability miss the point, because it's a relatively low investment you can forget about, in return for quite a lot of pleasure occasionally when you do win something.

We can also use the mechanism of a lottery to explore how human beings get their gratification.

One of the UK's National Lottery games is called Thunderball. The player has to choose 5 numbers between 1 and 39, and a sixth number between 1 and 14. The maximum prize for matching all six is £500,000, while you get £3 for just matching the Thunderball.

Imagine two strategies, both costing £14. One is to play the same set of numbers each week for 14 weeks. The other is to play 14 lines on a single night, using all the numbers between 1 and 39, shuffled, to populate the first 5 (you would have to do this nearly twice), and sequential numbers from 1 to 14 as the Thunderball.

Most people, I think would prefer to have 1 go a week for 14 weeks, rather than blow it all on one week. Yet the second strategy is the better of the two in terms of being certain to win. Both strategies have the same chance of winning the jackpot. But the second strategy ensures you win a minimum of £3, and that you are guaranteed to match at at least five of your numbers. The first strategy could go through the whole 14 weeks and never have a single match. (Admittedly, it's slightly more complicated than this, as in principle with the first strategy you could win 14 times, where with the second, your maximum number of wins is likely to be 3. But the fact remains that one is a certainty and the other isn't.)

What this shows, I think, is that the primary enjoyment value of the lottery is anticipation. The first strategy gives you 14 nights when you could be a winner. ('It could be you!' as the slogan goes.) The second strategy only gives you one night. So even though the chances of winning something are better, it will tend to be less attractive.


  1. And of course if you play the Wed/Sat game, you should choose some numbers over 31. Why? Well, it won't make any difference to whether you win, but if you get lucky, you should have to share your jackpot with a smaller group of fellow winners ... because of the practice of using birth dates to select numbers ...

  2. Quite right, Sue - in fact, good advice for any lottery entries.

  3. Actually only half the population can use their birth date in their lottery entry as in but only where yy is less than 49; when the yy is greater than that you're stuck with having to concoct the entry around the higher number as in (eg) 31.12.96 where we often use the 9 and 6 separately to generate a number.

    However even with my "random" number generator and the range of birth dates available I've still only won about £10 since the damn thing was launched! I wouldn't mind sharing a jackpot win with anyone, however many, even if they did have the same birthday....I'd probably double my winnings to date, wouldn't I?

  4. That advice came courtesy of my scientist son, who would rather microwave his head than waste money on the Lottery. He's interested in odds, not hope.

  5. @Laurasdad: 'Actually only half the population can use their birth date in their lottery entry' - I think you miss what they actually do, which is usually only to use the DD and MM parts of birthdays/anniversaries, not the YY part.


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