Science

# Don’t Just Look at the Odds: The Math Says You Should Buy a Mega Millions Ticket

The Mega Millions jackpot has reached a staggering \$1.6 billion, meaning Tuesday’s drawing will be the largest in U.S. history. The odds haven’t changed, with your chances of winning at 1 in 302 million, and so the value of a single \$2 ticket has only increased.

As we wrote when the jackpot was a mere \$970 million last week, you can do the math by multiplying the size of the winnings (very large) by the probability of you winning (very low) to get the value of your ticket. For this new \$1.6 billion jackpot, ignoring tax implications, the value of a ticket comes out to be \$5.53—a very good deal.

We wrote last week that the complications of tax brackets and the variability of state taxes meant that you were probably making a mathematically smart bet by buying a ticket. The conclusion was that, to be absolutely certain the expected value of your ticket was worth more than its cost, you’d have to do a bit of research into your own state’s tax and lottery rules. Well, that’s no longer true. There’s no way to slice the numbers where you don’t come out with a good deal.

Here is how we (with the help of some experts) did the math:

The value of a ticket, as laid out by Jordan Ellenberg, can be found by multiplying the probability of getting a certain prize by the value of the prize itself, repeating for all potential prizes, and then adding your results. If we consider just the jackpot, we multiply the incredibly large prize (\$1.6 billion) by the incredibly small odds of winning (1 in 302 million) and get an expected value of \$5.29—definitely a lot more than the \$2 cost of a ticket.

But you’re not just competing for a jackpot when you buy a ticket. There are other prizes for if you get some of the numbers but not all, ranging from \$1 million to just \$2. When you plug those numbers with their respective probabilities (you can see them here) into the equation, you get an even better value for your ticket: \$5.53. That’s a great deal.

And even when you factor in federal taxes at the highest tax bracket of 37 percent, which you’ll have to pay if you hit the jackpot, and state taxes at the highest level, you won’t come close to dipping down to that \$2 mark. With the highest federal tax rate and an 8 percent state tax, your ticket is still worth \$3.23.