$1M ticket or not, the lottery is still a fool’s game

News broke this morning that a Sioux Falls store sold a metaphorically golden lottery ticket worth $1 million (minus taxes).

Whenever a local person wins the lottery, or when the PowerBall jackpot gets up into the stratosphere, a peculiar but predictable kind of mass mania tends to take over. People speculate longingly about what they would do if a million dollars or more dropped into their lap. Otherwise sensible and sober individuals go out and buy lottery tickets — sometimes a lot of them — driving the jackpot higher and higher in a feedback loop until someone, finally, cashes in on the big bucks.

This frenzy is no accident, of course. Lotteries are designed to excite our baser emotions, to fire up our greed until it overpowers our good sense.

That’s why it works. Buying a lottery tickets makes no sense if you make a decision based on good sense.

The math is pretty basic probability. The “expected value” of a gamble is based on the total jackpot times your chance of winning. So if you buy one of 10 raffle tickets, your odds of winning are one in ten. If the prize is $100, that’s your payout. The expected value of one raffle ticket is (1/10)*$100, or $10. If the ticket costs $10, then you’ll break even — imagine if you bought every single ticket, you’d spend $100, and win $100 back, for zero change.

But if each ticket cost $11, then the expected payout is below the cost of the ticket, and becomes a bad bet (so long as your chief goal is making money).

Lotteries, of course, like video lottery and casino games, are designed to have a negative payout. That’s how the governments running them make money — they’re not doing this as a charity. A few people will win big, and everyone else is out their money.

(Note: When the Powerball jackpot gets really large, the expected value can actually exceed the cost of the ticket — if you look at the pre-tax jackpot. Once you reduce the payout to account for taxes and the chances that you’ll split it with other people, the payout drops back to negative. It’s less stupid to buy a ticket for the big jackpots than it is for smaller jackpots. But it’s still stupid.)

That’s not even accounting for the fact that winning the lottery often ends up being a disaster for these “lucky” gamblers. A huge percentage of them end up going bankrupt, squandering their newfound¬†largess. Of course, you’d be different. You’d break the trend.

There’s only one way buying a lottery ticket makes sense: if you don’t need the money and don’t care about winning. If you view the lottery ticket as a form of entertainment rather than a financial investment — $2 spent for the ephemeral pleasures of participating in Lottery Fever, $2 that you might as well have put toward an ice cream cone, a cup of coffee or a song on iTunes — then knock yourself out. Even I will sometimes get in on an office pool when the jackpot gets big. I can spare a couple bucks as the cost of entry into a social ritual with my coworkers. If I were broke, though, I’d pass.

Buying one lottery ticket will hardly hurt, of course. It’s the people who play the lottery every week who are flushing serious money down the drain over time.

Sadly, millions of Americans take part in this fool’s game every year. And many or most of them probably aren’t going into it with clear heads. Congrats to the winners — 28 coworkers from Beal Distributing, who look like they’ll get about $26,000 each after taxes — but they’re the anomaly, not the rule.

(And if this little social ritual were to pay off for me with a jackpot? I’d take my winnings as a yearly payout, not the lump sum. Less money up front means less pressure to squander it. The taxman takes a smaller percentage of my money. And even the lesser payout of the annuity would still be more than enough to resolve my financial pressures and let me pursue whatever dreams I desired, while still saving up plenty for later in life.)