A mathematical approach to the lottery
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As I sit here in my graduate economics class, we are currently reviewing decision making with expected value and decision trees. As the professor introduces a simple example to get the class comfortable with the initial material, I wonder if each person who played the lottery ever calculates the true value of their $1.00 investment decision.
It has been well published that playing the lottery is one of the worst financial decisions you can make, but that doesn’t seem to stop millions of people buying that ticket in hopes for the mega jackpot.
Before getting into the analysis, I will be using the PowerBall lottery rules as a basis for this post. If you are unfamiliar with the PowerBall, to win the grand prize you have to match 5 numbers and the “PowerBall”.
Here are the rules and prize distribution charts from the PowerBall site.
The below chart illustrates the last 5 years of PowerBall winners that took the cash prize and the grand prize amount. You will notice that the average grand prize is $45.6 Million, not bad for the $1.00 entry fee…
From there, let’s create the expected value calculation using a grand prize of $100 million. To start create a table with 3 columns. The first column will be the Prize amount for each winning option. The second column should include the odds of winning that prize. Please note that I was able to confirm these odds using the combination rule in statistics. The last column will include the result of the multiplication of the first two columns. Don’t forget to have 1/odds for the second column. By totaling up the 3rd column, you will have the expected value of the calculation. When comparing the EV of $0.27 to an entry fee of $1.00, you will notice that this is a bad decision to make. Losing your money 73% of the time doesn’t sound like a wise investment.
Looking at the above analysis: “So what would it take to have a favorable expected value against the $1.00 entry fee?” It will take $1.173 Billion as a grand prize for you to consider that decision, not even close to what the historical payouts have been.
So if you still decide to play the lottery, I wish you good luck and just say you purchased a dollar worth of hope versus saying you purchased a lottery ticket.
3 Comments on this post
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Benjamin said:
Great article!
I agree, the lottery is a tax on people who can’t do math!
On the other hand, I’ve been known to buy a dollar’s worth of hope on occasion!
June 29th, 2008 at 2:18 am -
Jonathan said:
So… the trick is to figure out how we can start our own lottery and make a 70% profit margin!
June 29th, 2008 at 8:43 pm -
Elias said:
Jonathan – That is the first thing that I thought of as well….
June 30th, 2008 at 4:36 am
