There is a persistent meme that lotteries are a tax on people who can’t do maths and are stupid. I don’t think I’m stupid^{1} and I’m OK^{2} at maths, and I play the lottery. This is why.

Basically, my desire for money is not linear, because I’m not *homo economicus*.^{3} My laws of desire for money are more Einsteinian than Newtonian: linear desire for money works at *small* amounts, but as they get higher it gets weird. I might desire £4 twice as much as £2, true enough; small amounts, Newton’s sensible laws. But I don’t desire £2 million twice as much as £1 million, because having a million would be enough and what would I do with the second million? I desire a million quite a lot more than a hundred times as much as £10,000, because a million quid is amazing and ten grand is a new car. The lottery gives me, for a negligible outlay, an outside chance of having a million quid, which would be radically life-changing (because I’d never have to work again).

There’s no other way I’ll get a million pounds. Sure, my chances of winning the lottery are at pretty adverse odds (roughly, 1 in 14 million chance of winning; when I win I get somewhere in between 2 and 6 million pounds). But having a million quid is a goal I’d like to hit. I can attempt that with almost no work.

Imagine that I wanted a million, and I started with a pound. Perhaps I should play roulette instead, which has a *much* more favourable edge than the lottery (although it’s still unfavourable; 5 ^{5}/_{19}% for the bank and against me). So I stick my quid on black 17, and it comes up; a chance of 1/38, and I get £36 back for a total of £37. I let that £37 ride, and black 17 comes up again, so I now have £1369. Ride again^{4} for £50653, and again for £1.8 million, which is retirement money and so I stop. The chances of that happening; 1 in 2 million or so. So playing roulette is very roughly equivalent to playing the lottery (chances of getting a million quid: one in some millions). And the lottery is a *lot* easier to do; you don’t have to put on a dinner jacket and walk to the casino, and you *can* play for a pound.^{5}

This is the point. I won’t miss the money, it’s very easy to do, and it *might* end up changing my life, so why not do it? If I were *actually* good at maths, maybe I’d plot a graph of some sort of quotient made up of “amount spent” vs “effort required” vs “amount won”. I bet the lottery looks quite a lot better than “working for a living”, on that graph.

I should note here that the second part of the meme which is often quoted alongside it is that lotteries are a tax on the poor; that is, people who *will* miss that hundred pounds a year. This is completely correct. I would not notice the half-a-pint a week that the lottery costs me; this is not the case for others, and lotteries being a tax on the poor is entirely correct.