Wednesday, June 27, 2012

Because you care what I think about lotteries

A brief discussion with a friend who now lives in a lottery-enabled state (read: not Utah) got me thinking about lotteries in general. In the mind of the average taxpayer, the lottery is some kind of blessed magical fairy creature: the government gets revenue to provide services, and you don't have to pay for any of it. Yay!

But the reality is a lot uglier, more like a slimy cave troll: it raises the effective tax rate on people who are simultaneously poor, desperate, and mathematically challenged, while lowering tax rates for people who can better afford to pay. So it's inherently regressive. The fact that it's voluntary doesn't mitigate the ickiness much.

I went looking for an article that estimated the ROI for a lottery ticket. It's about fifty cents on the dollar once you account for income taxes and the fact that the cash payout is much lower than the advertised prize. Yes, the cash payout is the one to plug into the equation. Just roll with it.

But even that may be overstating the value. I'm sure people buy tickets for lots of reasons, but to simplify the discussion, let's assume that every person who buys a ticket does so to receive a small chance of never having to work another day in their life. It sounds fairly reasonable, but it entirely changes the effective value of a lottery ticket. To see why, we need to account for something called...

The Law of Diminishing Returns

The law of diminishing returns comes out of economics 101. It says that, the more you have of something, the less valuable another one of those things is. Take eyeballs. If you have no eyeballs, and someone fits you up with a working eyeball, that eyeball is very, very valuable. Now say that you have one eyeball, and someone fits you with a second eyeball. You might end up with a wider range of vision, but it's not nearly as dramatic a change in your life. Now say that someone hooks you up with a third, fourth, and fifth eyeball. You look at them with all your eyes, and think to yourself, "how are you being helpful?"

It works similarly for television sets, bottles of beer, cars, and laptops. In fact, most useful things become dramatically less useful as you get more of them. This includes money.

Say that your income rises from $0/month to $1000/month. Now, rather than starving in the street, you can suddenly afford food and a roof over your head. Maybe bus fare as well, if you're lucky. Now let's raise your income again, from $1000/month to $2000/month. Now you can afford slightly better food, a slightly classier roof over your head, a car instead of a bus, perhaps health insurance, and the occasional luxury item. Now let's raise your income again, to $3000/month. You use it to start buying organic food, a house of your own, a slightly nicer car, more comprehensive health insurance, and start saving for retirement.

I could go on like this all day, but the point is that, each time your income is raised, you use the new money to buy less value than the old money was buying. I'm 35, so let's assume I'll live another fifty years. How big a lottery jackpot would I need to give me $3000/month for the rest of my life? About $1.8M (pretending the jackpot doesn't accrue interest). A jackpot of $18M would give me $30K a month, which is more than I could imagine spending on myself.

So if your goal is a comfortable income, a $100M jackpot is barely more valuable than a $20M jackpot, which is only a fair amount more valuable than a $2M jackpot. In the astonishingly unlikely event that you win the lottery, most of the "return" comes in the form of a useless pile of money piled on top of the much smaller pile of money that you would actually miss if it disappeared.

What does this mean for you, gentle ticket-buyer?

  1. This cannot be stressed enough: DO NOT BUY LOTTERY TICKETS!!!
  2. It would be better for participants if lotteries were restructured so that, instead of having one $300M jackpot, it had 300 $1M jackpots (or perhaps even 3000 $100K jackpots). If people are dumb enough to buy these tickets in the hopes of gaining a better life, let's give them a slightly better shot at it.
  3. The law of diminishing returns can also apply to other forms of gambling, or any game where money is on the line. If you're playing "Deal or No Deal," it suggests that you should walk away way sooner than an ordinary ROI calculation would suggest. Remember that the ROI doesn't distinguish between a 100% chance at $500K and a 50% chance at $1M. But the latter will make a somewhat smaller impact on your life.

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