A few weeks ago, Taylor Swift surprised the world by releasing a secret double album. If the world's biggest pop star can release a double album, one of New York City's biggest data newsletters can release a double newsletter (here’s yesterday's edition in case you missed it). Can you say 2x2xParked (or 4xParked)?
It is like you won the lottery.
Speaking of the lottery -- this is what we call a "transition" in the podcast world -- I am often asked a question from my adoring fans, 2xParkedies, "how can we use your statistics brain to win the lottery?"
With Friday's Mega Millions approaching $400M and ample locations in New York to buy a ticket, 2xParked will give you some good pointers.
Play to Win the Game
The bad news is the statistician in me will tell you the probability of winning the big bucks is almost 0%. The good news is the statistician in me will tell you that you improve your odds of winning infinitely just by playing. The best strategy, conditional that you want to win, is to play.
But What Numbers Should I Choose?
Assuming lottery numbers are randomly chosen -- of which I do not have any reason to think otherwise -- there are not a whole lot of strategies.
As a reminder, you choose 5 different numbers between 1 and 70 and 1 number between 1 and 25. To win it all, you have to correctly match your chosen numbers with the official numbers chosen at random.
I ran 1 million lottery simulations. Below is a distribution of frequency of each number, 1 to 70, being chosen. As you can see, it is perfectly random; every number has the same probability of being selected. This is a perfect example of a "discrete uniform distribution".
We do know the average winning number card will be around 35, with 50% of the winning cards having an average between 30 and 40. This is more a nature of the distribution as opposed to the strategy. You are not trying to pick the average number on your ticket.
Scientific American ran a survey of most common favorite numbers. These are numbers you might want to exclude from your card. Winning $400M would be amazing, but if you had to split it, is $200M really going to make a difference in your life? Some numbers you might want to avoid are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 27, 28, 37, 42, and 69. Around 79% of those surveyed said these were their favorite numbers between 1 and 1000.
Choosing numbers at random is a great strategy.
So Why Play at All
We can think about things in terms of a "utility." You have a 1.4% chance of making profit and a 4.2% chance of at least making your money back. This means you will likely be giving away your $2.
There is more to utility than money. As long as you don't habitually play and have the means to play, there is the utility value towards your emotional satisfaction. There has been some research which indicates that there is an increase of momentary happiness by playing the lottery. Although we know we will likely not win, there is the joy anticipating what we would do if we did win. That makes it worth the $2 for many.
So if You Play...
Here are some things to keep in mind if you are playing on Friday:
Choosing random numbers is a fine strategy.
Realize you will not win big, even if you purchase $100 worth of tickets. Budget how much you are willing to spend on a little moment of happiness. How much more does an extra ticket actually improve your joy? Is there a difference in your happiness between a $2 ticket or $20 of 10 losing tickets?
If you do win big, thank me. Thanks in the form of a Brooklyn brownstone would be appreciated. This one looks nice.