Sunday, March 24, 2013

A tax on people who can't do math? Maybe, maybe not.

My friend Clay used to regale us all with tales of the fantastic things he had planned for when he won the lottery.  One day someone pointed out the fact that Clay never bought a ticket, an observation which he scoffed at.  "All that does," he said, "is increase your odds an infinitesimal amount."  He was right, of course, while also overlooking (for comedic effect) the qualitative difference between no chance and even the smallest non-zero chance.

That qualitative difference, not the actual odds, is what keeps people playing the various lottery games that have sprung up around the country.  After all, if you're working a minimum wage job, you've never heard of anyone like you who ever got rich by working, but every week or two you see on the news someone like you who got rich by winning the lottery.  Just last night, someone in New Jersey won $338 million in a Powerball drawing.  And besides the fact that you see people who win the jackpot, there's also the fact that every now and then you'll win a smaller prize.  This intermittent reinforcement has been determined by scientists to be the best way to train an animal* to exhibit a certain behavior.

Recognizing this, the people who run the lotteries have devised a variety of different games, with a variety of different reinforcement schedules, in order to provide maximal appeal to the maximum number of players.  Besides the big weekly and biweekly draws, there are smaller daily draws that can be placed for a little as 50 cents.  For people who'd rather not even wait for a daily draw, there are scratch-off games.  For people who don't even have time to wait to buy a scratch-off ticket from a cashier, there are vending machines that sell scratch-off tickets.  And finally, for people who want to "invest" larger amounts of money in the lottery, scratch-off tickets are now offered in multi-dollar denominations**.

Financial planners, libertarians, and other true believers in the capitalist system generally say that people shouldn't play the lottery, but should instead save and invest that money.  They might be right, from a strictly mathematical point of view.  But, interestingly, they're not right by a sufficiently noticeable margin that they don't feel the need to pad their numbers.

The effect of compound interest on investments funded by cutting out small, "frivolous" purchases has been dubbed "The Latte Factor" by author David Bach.  Bach has made a career out of this one idea, and latte factor calculators have sprung up all over the web.  The one that I used in writing this post sells the idea by urging people "just input $5 daily for fancy coffee over a period of 40 years at 10% and see what happens."  What happens, as it turns out, is that by cutting out this coffee you'd save just over $73 thousand in foregone spending and earn just under $890 thousand by investing these savings.  Of course,  the most expensive coffee on Starbuck's menu is only $4.25 and Warren Buffett, the most successful investor in the world, says says investors should expect a 7% return.  Plugging these numbers into the calculator yields savings of $62 thousand and earnings of $277 thousand.  Still nothing to sneeze at, but noticeably less than the fanciful example touted by the calculator.

But let's go back to our hypothetical lottery player.  They're going to be spending less than someone buying the most expensive drink at Starbucks every day, and hence saving less when they cut out this spending.  While some lottery players spend more, a fairly typical amount - and what I'll be using for my example here - would be $2 per week (one entry for each of that week's Powerball drawings).  Likewise, they're not going to be able to afford to invest in a mutual fund in order to get higher returns.  Once they save enough to move beyond hiding their money in their mattress, they'll probably be putting it in a saving account earning 1% interest.  Using these numbers, over a period of 40 years, would yield savings of $4159 and interest of $954.  Even if they do the math on this, our hypothetical lottery player is likely to decide that given the lower amount of effort involved in investing that $2 a week in the lottery rather than a saving account, coupled with the potential (however unlikely) for higher returns through playing the lottery, that they're better off with the lottery.

*  People are animals, my friend.
**  The largest of which I've ever seen is a $30 scratch-off game.  I'd never play it, but apparently I'm not the target audience.


  1. Minor correction - Powerball tickets are now $2/draw, so $4/week.

    I buy Powerball tickets. I buy them for entertainment - I get my $4/week of fantasy out of them.

    1. I guess that goes to show how long it's been since I played Powerball.

      I definitely think you can get $4/week of fantasy out of Powerball. I look at it the same way I do when I go to a casino (which is also exceedingly rare): I plan before I go in how much I'm going to gamble and I consider that money as spent. If I ever did win the jackpot, I'd be thrilled, but more generally I consider the money I gamble as the cost of that evening's entertainment.