I put "maybe once a year," though it is probably more like three times a year. I never played at all until about three years ago, then money got tight and I realized I couldn't afford NOT to play!
Plus, my kids love it. So every now and then, when they ask for it, I do. But what we actually usually play is not the lottery per se, but scratch-off cards. Do you have those, Chrissi? You scratch off the silver rubbery stuff, and underneath hope to find some certain pattern of numbers or symbols, like three of a kind or whatever, like you might get on a slot machine. The winning patterns are worth different amounts of money, usually also depending on the cost of the card itself. I've never won more than about $10, which I then invest in new cards until I lose everything.
Your mathematician's analogy is interesting, except for one thing. If a million cars went on that route, still nobody might ever hit the stick. However, people do occasionally hit the jackpot. Knowing that it's at least possible, and that for a small amount you can buy the chance that it will be you, is what keep people playing.