So, Why Is the Lottery Not a Good Investment?

Hotlinked photo of a Oregon Lottery Billboard form the Oregon Department of Forestry website. This image may disappear. It says

Do you see that “entertainment only” part? Yeah.

So, you can probably guess that playing the lottery (and most other forms of gambling) are poor ways to invest your money for the future, but do you know why? I comes from the idea of expected value.

Expected value is a statistics concept that gives us an expected outcome if we perform a random act an infinite number of times. Let’s use a fair coin toss as an example, one with 50/50 odds. Pretend that, every time heads comes up, you get a dollar. Every time tails comes up, you get nothing. Now, if we were to repeat this game just a few times, it’s possible to end up with nothing, or perhaps win every time. However, if we repeat this game millions upon millions of times, the average outcome for each game will be $0.50. So, the expected value of this game is $0.50.

This is a pretty good game, right? After all, you can either win a dollar or lose nothing. So it would make sense to play this game over and over again. What about the lottery? Does it make sense to play that game as much as you can? Let’s think about it for a minute.

First, every prize granted by the lottery must be paid from ticket sale revenues. Next, the lottery has to pay all the other costs of running the lottery from ticket revenues; things like lawyers, staff, and other distribution expenses. This means the output of the lottery in prizes must be less than the input in ticket sales. We don’t even have to know the exact numbers, we can surmise the expected value of any lottery game is going to be negative. Even if you played every lottery ticket, you’re going to come out behind, because the prizes will never exceed the cost of purchasing all the tickets.

Good investments are expected to have positive expected value over time. Lottery games have a negative expected value. The negative expected value is why the lottery (and gambling in general) is not a good investment.

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