There is no mystery that under normal circumstances, homo oeconomicus does not play the lottery. Exceptions arise when there is enjoyment in playing the lottery (is this why slot machines a so popular in the US?) or when there are particular reasons. But casual observation indicates people play the lottery, and a lot. Maybe these circumstances mentioned above are met, maybe they are not rational economic agents.
Claus Bjørn Jørgensen, Sigrid Suetens and Jean-Robert Tyran would say lottery players, at least some of them, have a peculiar sense of probabilities. While many change their numbers, among those who change, many avoid numbers that have recently been drawn, as if the lottery were a drawing without replacement. But if a number is on a streak (drawn a few times in a row), then they choose it. If margins were not so high in lotteries, one could possibly make money by arbitraging against these people trying to predict the lottery numbers. But you can actually getting a positive return from lotteries by only buying tickets when large jackpots are at stake. The International Lottery Fund based in Australia is there to prove it.