By definition, the expected value of a one in five chance of winning $10 dollars is worth $2 ($10/5). But to human beings, with our finite life spans and our asymmetric financial needs, a one in a million chance of $1,000,000 is not necessarily worth $1, it might be worth more.
Lottery tickets cost far, far more than their expected value. The amount you would win times the probability of you winning is pretty close to zero. They are, as far as expected value goes, practically worthless.
But despite what Adam Smith says, buying lottery tickets is not necessarily a bad idea. They’re vastly overpriced, but unless I’m already rich the difference winning $1,000,000 would make to my life is worth far more than the extra $1 I’m getting charged for my ticket.
Given the choice between $2 and a one in a million chance of a million dollars, I know which choice is more exciting. The poorer I am the more enticing that is. (If I’m well off I have many more, and better, opportunities to make money.)
The injustice of lotteries is that they exploit the perfectly natural assumption that if buying one ticket is a good idea buying 20 is 20 times better. But Adam Smith is right again: buying all the tickets would guarantee that you won the lottery and lost a fortune.
Lotteries are not a tax on stupidity, they are a tax on poverty and lack of opportunity that exploits an almost universal miscalculation of the effects of scale on risk and value.
They are a lousy form of taxation. If you want more money for schools, roads or, cultural institutions, then raise taxes, or issue bonds. Don’t fund opera from lotteries, that way poor people pay for things they can’t afford to enjoy.
[...] needs, a 1 in 10 chance of winning $10 is not necessarily worth $1, but that’s another topic. The real question is the reliability of the ratings. How do I know that this company has a 0.1% [...]