Lottery rollover - fewer players, bigger prizes? Bad maths
I was sceptical of a claim on Free Exchange today: "...if there is no winner the prize is carried over to the following week. A smaller participant pool can then result in infrequent, higher jackpots." This struck me intuitively as unlikely. So I thought I would work it out. Probability theory has been unpopular among economists this year - everyone quotes Nicholas Taleb and slowly, loudly explains to us how the financial markets don't behave like a normal distribution after all, and we don't have enough historical data to give us a predictable distribution for the future. Insufferable. Fortunately lottery draws do obey standard probabilities and we do have enough data (and enough theory) to predict how they will behave. So we can use some standard results. Assume that a lottery has 10 million participants each paying $1, with a 50% payback. The prize fund in a typical week is $5 million. Let's say the odds of getting the right numbers are 1 in 14 million; then...