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The Math of Mega Millions: How to Tilt the Odds in Your Favor

by | Jan 11, 2023

Lottery photo from Davidson website.


Editor’s update: The top prize for the Mega Millions lottery has now risen to an estimated $1.35 billion, with a cash option of $707.9 million, for the next drawing on Friday, Jan. 13.

But actually bringing home the big check is next to impossible. Mega Millions lists the odds of winning the grand prize at 1 in 302 million. So, yeah, it’s a longshot.

Tim Chartier, Joseph R. Morton Professor of Mathematics and Computer Science

But according to Math Professor Tim Chartier, there are some small actions that tip those long odds (slightly) in your favor. 

How unlikely is it to win a lottery like Mega Millions?

One way to visualize it: It’s equivalent to flipping heads on a coin 28 times in a row.

Does buying more tickets increase your odds? 

Yes. If you buy five tickets with different numbers, you are five times more likely to win than buying just one. But, keep in mind, this is like saying you need to flip heads 28 straight times. Try it. In fact, try it five times. Try it 100 times. You are amazingly unlikely to get it any single time. So, the odds are more likely but still very unlikely. 

Here is an app that lets you simulate flipping a coin 28 times. (Note, you need to select ‘Number’ to be 28.). You could do this yourself with 28 coins–toss them and see!  

You are almost 300 times more likely to get hit by lightning in your lifetime than win Mega Millions. If you bought 300 tickets, only then would you have the same chances as getting hit by lightning in your lifetime.

Why don’t lotteries like Mega Millions and Powerball produce winners more frequently? 

We will get a winner at some point, which is the exciting part. But, there is some math behind the growing jackpot.  

First, people can pick numbers–and they tend to pick numbers from a similar range. People frequently pick birthdays and ages which makes lower numbers more common.

Second, while someone will win, it simply can take time given how unlikely it is. The odds are made high enough to make the game compelling and get winners JUST enough that we have hope in the improbable and, frankly, it makes it fun. 

When the jackpot is this high what should we think about? 

Any time you play a lottery like Mega Millions or Powerball, the odds of winning stay the same. But, there are ways that you can make it more probable that you win ALL the money. 

In particular, pick random numbers. If you pick your favorite number or the day of your birthday like the 7th, which is the day of the next drawing, many people can be doing the same and that puts a lot of numbers between 1 and 31. Picking your own numbers doesn’t change the odds of winning. But, picking random numbers does increase the odds that if you win, no one else wins.  

The final number on the last draw was 13. Should we stay away from that number for the next drawing? 

The balls are random so you only have a 4% chance 13 will come up again. But, you only have a 4% (or 1 in 25) chance that any other ball is chosen, too.

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