Powerball: Just the Odds

The Powerball is up to $337M.  A lot of people will pay $2 for a ticket this week for a chance to dream about what they’d do with the grand prize of hundreds of millions.  A quick scan of the Powerball odds show the mathematical probability of picking the grand prize correctly is 1 in 292,201,338.  

I suspect a lot of people dreaming about their potential windfall this week will overestimate what they are really up against.  The problem is we don’t have any context for rationalizing large numbers.

Below are a few scenarios to provide context on a few probability sets:   

1 in 2:  You and a friend are trying to determine who needs to take out the trash.  You decide to settle the decision based on a coin flip.  You pick heads.  Your friend tosses the coin up in the air and it lands with heads facing up.  You win and your friend takes out the trash.    

1 in 10:  You are among 9 other kids, sitting on a green lawn, with Billy circling around tapping everyone saying duck-duck-goose.  As Billy approaches you tense up in anticipation you are going to be the “goose.”  You are not, he picked Sally.

1 in 100:   Think about every weekend day for the last year (you can exclude Christmas and New Year’s weekend to make this a true 1 in 100).  You are told that someone has selected a random Saturday or Sunday and you have to guess which one they picked.  Your first instinct is the Saturday before 4th of July but then you remember it’s random so you try and pick a less obvious one.  You go with the third Sunday of February.  You were wrong, it was the second Saturday of October.

 1 in 1,000:   Imagine you are a very diligent college student who wants to complete a five-year program in four years.  You attend classes five days a week and takes summer and winter sessions so you are in school all year long.  As you receive diploma a stranger challenges you to guess a random college day of yours that they have written down on a piece of paper.  You guess Sophomore Year,  Fall Semester, 4th Week, Tuesday.  The stranger reveals he had written down Junior Year, Winter Session, 2nd week, Tuesday.

1 in 100,000:  You are sitting a rest home next to a 92-year-old, Bob, a 93-year-old, Hank, and a 94-year-old, Harold.  You are told that the envelope in your hand contains a single calendar day and year noted for one of three elderly men.  You are told to guess.  You ask if the current day is eligible to pick.  To make it easier on you, the moderator tells you that the current day is excluded.  You go with Hank, May 3, 1955.  You open the envelope and you find the correct answer was Bob, June 2, 1924.  You weren’t even close!

We will skip a few and jump straight to the final odds:

 1 in 292,201,338:   You are 56 years old and have had a very diverse career.  You’ve worked for seven different companies since you turned 21.  You started your career at McDonald's working the graveyard shift, then you moved to FedEx where you had very early mornings.  When you turned 30 you switched over to Ford and worked there for almost a decade with a more typical 9-to-5 schedule. Following Ford, you spent some time working at General Electric and then you transitioned over to Chevron. Your sixth company was IBM which lasted for five years and then led to your current role at Intel.  

The Envelope: The moderator tells you within the envelope there is a specific date written for one of your work days during your time at one of the seven companies.  With that backdrop you begin to think back on your career. You don’t like your chances.  

The moderator then informs you that in addition to picking the correct work day you also have to pick the correct work hour.  Before you can say that’s impossible the moderator adds you will need to also pick the correct minute of the day.  You laugh as you realize this guessing game is no longer possible. But wait, one more thing the moderator adds, you now have to pick the actual second of your workday.   Realizing this has turned absurd you look back and try and pick the exact one second period of your career.  You go with IBM, August 5th 2010, 11am hour,  26th minute, and 14th second.  

You open the envelope, FedEx : January 16th, 1991,  4am hour, 13th minute and 57th second.

You lose, but you don’t really care because you never had a chance!

 The moderator then tells you he has a 2nd envelope with another date and time period written (down to the second again).  This time he tells it will cost $2 to play but if you guess correctly you will win $337M.  What do you do?