Probability in Real Life > Mega Millions Odds
What is Mega Millions?
Mega Millions is a lottery game where you choose six numbers from two pools of numbers:
- Five numbers between 1 and 70 (“white balls”)
- One number from 1 to 25 (“gold Mega ball”)
In January 2021, the jackpot reached one billion dollars.
What are the Mega Millions Odds?
According to the official Mega Millions website, the odds of winning the jackpot in Mega Millions is 1 in 302.6 million—what CNBC [1] calls “staggering” odds. You’re over five hundred times more likely to die by falling off a ladder in the next year (1 in 583,019)[2] than winning that jackpot with a single ticket.
Mega Millions Odds and Prizes
Your overall odds of winning a prize is 1 in 24, but don’t get too excited: the prize with the best odds (1 in 37), is a mere two dollars. Here’s a rundown of the odds:
- Mega Ball only ($2): 37 to 1
- 1 number plus the Mega Ball ($4): 89 to 1
- 2 numbers plus the Mega Ball ($10): 693 to 1
- 2 numbers ($10): 606 to 1
- 3 numbers plus the Mega Ball ($200): 14,547 to 1
At this point, the odds are starting to get steep. To put this in perspective, you are much more likely to be nonfatally injured by a toilet (1 in 5,000) [3] than choose the correct 3 numbers plus the Mega ball.
- 4 numbers ($500): 38,792 to 1
- 4 numbers plus the Mega Ball ($10,000): 931,001 to 1
- 5 numbers ($1 million): 12,607,306 to 1
This is where the odds are so against you, it can be hard to visualize them. Imagine that you are in the largest stadium in the world which is filled to its capacity of 150,000. Now imagine there’s a raffle for one car. Your odds of winning: 1 in 500,000. To equal the odds of winning the Mega Millions jackpot, you would have to have 605 stadiums, side by side.
How are Mega Millions Odds Calculated?
The calculation of chances involves several elements:
- How many numbers you have to choose from (70).
- How many numbers you pick. For Mega Millions, that’s 5 (plus a Mega Ball, which we’ll look at in the next step).
- How many numbers you don’t pick. 70 – 5 = 65.
The number of correct matches between your pick and the numbers that the lottery machine draws (Hopefully, all 5!).
Plugging those numbers into the combinations formula, we get:
If you figure this out on a calculator, you get 12,103,104. Here are the steps (The ! is a factorial).
Finally, we have to multiply this by the number combinations of Mega Balls. There are 25 balls, and you only choose one, so:
12,103,014 * 25 = 302,575,350.
As you are only choosing one of these possible combinations, your odds are 302,575,349 to 1.
Can I improve my Mega Millions Odds?
Like all lottery games, you can improve your odds a hair (i.e., by not very much) by:
- Buying more than one ticket for the same game. You can increase your winnings on Mega Millions by spending an extra $1 on a “Megaplier”, but this does not increase your odds.
- Avoiding traditional lucky numbers: 7, 11, 13. Avoid choosing numbers 1 to 31, which are birthdays—meaning a lot of people will pick these “lucky” numbers. Exception: Do choose numbers 21 and 23; As stated in the previous article on lottery odds, these balls have more ink on them so are more likely to be chosen.
References
Powerball Billboard: Tony Webster from Minneapolis, Minnesota, United States, CC BY 2.0 via Wikimedia Commons
[1] CNBC: https://www.cnbc.com/2021/01/21/how-to-up-the-odds-of-winning-a-lottery-harvard-professor.html
[2] III Facts, Statistics, Mortality Risks.
[3] CDC: https://www.cdc.gov/mmwr/preview/mmwrhtml/mm6022a1.htm?s_cid=mm6022a1_w