Like many, I purchased a Power Ball ticket today. I usually buy a single Quick-Pick ticket for every drawing for which the prize is greater than $100 million. I know the statistics are way against me, but for $2 I can fantasize for a while about what it would be like to be utterly, ridiculously wealthy.
I used to wait for it to go to $175 million, so I’d have a positive expected value. Then they changed the price of the Power Ball to $2, raising the expected value bar considerably higher. Then I realized that the expected value calculation is meaningless since I’m not immortal, and drawings don’t occur every nanosecond.
Part of the fantasy relies on the fact that the odds are so utterly, completely remote that human beings can’t possibly conceive them. So I tried a thought experiment to see if we can get the sheer incredible unlikelihood of winning into something I can comprehend.
Imagine you’re in a completely full football stadium, filled to the brim with 100,000 people. They announce a raffle, in which they’re going to randomly pick a ticket, and whoever is sitting in that seat wins. You’re one person in this football stadium. How do you like your chances? Not impossible, sure, but it’s not like you’re going to be the farm.
Now imagine that there are not one but ten, completely full to the rafters football stadiums, each filled with 100,000 people. And they’re still going to pick only one seat from only one of these ten stadiums to see who wins. Really try to imagine it… Ten football stadiums, filled utterly and completely with fans, all right next to each other. (Oy, the traffic when this contest is over!) How do you like your chances now?
Got that image in your head? Feeling the sheer remoteness of winning a contest with this one-seat-in-ten-football-stadiums scenario?
Now imagine 1,752 completely full football stadiums.