It's traditional for those with some grasp of probability to belittle those who enter the National Lottery. 'Clearly idiots,' they say. 'These people don't understand probability, or they wouldn't play.'
I must admit, I've taken this stance a little in the past. Imagine, I've said, that the lottery balls came out one Saturday as 1, 2, 3, 4, 5, 6. There would be questions in the House no doubt. A new scandal to rival phone hacking - how could the National Lottery draw be so obviously rigged? Last Saturday's draw numbers were 4, 9, 13, 15, 18, 40 (as the website kindly sorts them into numerical order, I don't know what order they were drawn in). But in drawn order, that sequence of numbers had exactly the same probability of coming up as 1, 2, 3, 4, 5, 6.
Our natural suspicion of the ordered set arises because it makes it more obvious just how unlikely it is that a particularly sequence will be drawn - yet the same goes for the numbers on your ticket. It is ridiculously unlikely that your numbers will be drawn. So why bother? It's a waste of money.
But here's the thing. I play the lottery. Every four weeks I allow myself £10 to play. No more - very tightly controlled. I don't enter the main Lotto draw, but rather the Thunderball draw, which has lower winnings (£500,000 for matching a full set) - but that would be enough to change my life, I don't want to be multi-millionaire, and the lower jackpot comes with better odds. Even so, it's an immense longshot. So why do I do it?
Essentially it's a kind of utility that conventional economics is not very good at reflecting. If the sum involved is so small that I can consider it negligable (we're talking a coffee and cake for two at Starbucks per month), then I can effectively mentally lose it and easily offset it against a very low chance of winning a rather exciting amount. To add to the benefit side of the equation, with this style of play I get a win about once every couple of months. This will inevitably be for between £3 and £10, but there are still a few minutes of delicious anticipation after getting the 'Check your account' email from the National Lottery when it could be oh so much better.
One of the important factors in making the decision to play rational to me is I totally forget about my entry unless I do get one of those emails. I don't anxiously check my numbers. I don't know what my numbers are. As far as I am concerned, once the payment has been made the money has gone, just as if I had spent it on those coffees. That way, any win is pure pleasure, because it has no cost attached to it. Let's face it, the only thing I'm likely to get the day after a visit to Starbucks is indigestion.*
All in all, then, I say pish and tush to those who put down lottery players. If it's done in the right frame of mind, and in a controlled fashion, why not? Of course you aren't going to win the jackpot. But is there anything wrong with having a dream? After all, one thing is certain. If you don't take part you will certainly never win anything.
* This is not casting aspersions on Starbucks, espresso-based coffee always gives me indigestion.