We all know playing the lottery is a mug’s game, right?
If I have (say) a one in two million chance of winning a million, with one dollar ticket, then my expected return is 50c. I expect to get 50c, for my $1, only an idiot would take that. Lotteries are for mugs. It’s no wonder poor people play the lottery more than the wealthy. Clearly poor people are more stupid than the middle-classes.
If you don’t play the lottery, chances are you have some variant of that story. Perhaps without the bald-faced bigotry at the end, perhaps not (can you be honest enough with yourself to know?).
Of course it is rubbish. For a very simple reason. The value of money you control is not proportional with its quantity. If you have a billion dollars, you won’t feel 1000x times more wealthy than you will if you have a million. And with good reason: your standard of living won’t be 1000x times as high.
For those on low income, the value of a lottery jackpot is much higher than it is for you. So much higher that the expected value is greater than the cost. It is rational to play.
This isn’t novel or my idea, this has been analysed by many economists and is perfectly unremarkable.
What I was thinking about tonight, however, was Pascal’s Wager. Unlike the lottery, Pascal’s Wager is the opposite way round. It is always worth taking. The normal objections to it (how do you know if you’ve got the right God with the right arbitrary requirements, there is no good reason to believe in heaven or hell, etc) are merely ways to shorten the odds, but the reward is claimed to be so great, infinite even, that tiny chances of winning still give you a positive expected value. If salvation is infinitely great, no probability is small enough for you to pass.
But I suspect why Pascal’s Wager doesn’t work is for similar reasons to the naive lottery analysis. Our perception of value in eternal bliss tapers off, beyond a certain degree of bliss, it really is no more attractive to us than a slightly less blissful state. We accord an infinitely wonderful salvation with no more value than just a stupendously, but finitely, wonderful salvation. And so the small chance of getting the right God, of propitiating it in the right way, and of the afterlife being in any way as claimed, serves to make a lie-in on Sunday morning more rational than going to church.