SurplusGamer's Thought Limbo

2nd November 2010

Post with 1 note

Fun With Lotteries

People have a counter-intuitively high expectation of how likely they are to win a standard lottery jackpot. Common things you hear are ‘Well someone’s got to win it,’ (unless of course it turns out to be a ‘rollover’) or ‘I’ve got as much of a chance as everyone else. These of course fail to take into account the fact that you and everyone else has a vanishingly small chance of winning, including the person who actually ends up winning. So far, so easy.  

People think of the best pick of random numbers to be a fairly even spread across whatever they happen to be choosing from, so a typical lottery ticket might be for example, 9, 15, 23, 31, 39, 45. True randomness is, of course, not so picky about keeping the spread even. Whatever number pops out of the machine next doesn’t depend on what popped out before, so a draw with lots of numbers bunched quite close together is as likely as one with a lot of spread. Look at the last handful:

2 22 32 33 37 45
3 5 11 16 41 48
2 3 14 29 35 42
14 30 31 36 44 47
6 30 34 38 45 48
18 19 24 26 27 44

Lots of clumps! Four results on that list have two adjacent numbers, and most have pockets of numbers closer together and further away. These kinds of results are what is to be expected from randomness.

Indeed, any result is equally likely, that’s what it means for it to be random. But try posing this:

“I’m going to make my lottery numbers 1, 2, 3, 4, 5, 6”

I’ll bet the answer will be something like:

“Why would you do that? Those numbers will never come up!”

And yet think about it: there is nothing about randomness that makes that series of numbers less likely than any other. It’s just that that particular 1-6 sequence appeals to our intuitions about what is and isn’t likely to come out of a machine at random. The faux-random set of numbers the average punter picks is just as unlikely, but in a way that is less intuitively obvious.

Something to think about, next time you pick up a ticket.  If you wouldn’t be happy betting on 1, 2, 3, 4, 5, 6 coming up, you shouldn’t be happy with whatever numbers you picked, either!