I’m a bit behind the curve, but there’s a a coming change to the Mega Millions interstate lottery game. Of course, as a statistics nerd,^{1} I’ve talked about the lottery before. So when I got this on my Facebook page, I was all into it:

First, we need to take a look at the current game configuration. Right now, tickets cost a dollar and the jackpot starts at $15 million. Given the game configuration, we can estimate what the expected value of a ticket is. That is, if I spend a dollar, how much can I expect to get back.

Using the basic statistical data about the Mega Millions, we can build a quick spreadsheet to get the expected value. The statistical data comes from the April 24, 2017 Meeting Book of the New York State Gaming Commission. Page 34 contains the tables.

As we can see, the expected value of a lottery ticket is a loss of 77 cents. That means that given a single random Mega Millions ticket, of which there is an initial loss of $1 (to buy the ticket), we’ll get back 23 cents. In practice, the return realized is not quite so hot, much of the return comes from hitting the jackpot. And that’s highly unlikely.

After Halloween this year, we will see some changes to game. First, tickets will go to $2. Second, the odds will change, by changing the game configuration. The base prize has also gone up to $45 million and the lower prizes are also reconfigured. It’s not worth going into those details here, but we can see the new numbers back on page 34.

As we can see, for every $2 spent, we can expect to lose $1.63. That means a loss of 37 cents for every $2. It’s important to understand that these values are all premised on the jackpot having just reset to its baseline **and** there being only one jackpot winner. Parimutual splits, due to multiple jackpot hits, pushes the expected value even lower. Today, the Mega Millions is at $323 million. That leads to an expected value of 42 cents. Again, this assumes no splits.

Now, it turns out whether or not this is better is up to your own outlook. But, as it is, your chances of winning are still about the same as the snowball.

- If stats were a drug, I’d sell it by the gram. ↩