It's hard for me to fathom that much money. That's half a billion dollars, just for matching numbers. Incredible.
Now the odds for winning that prize are a little more than 1 in 175 million. This got me thinking, if the jackpot has a larger number than what the odds are, shouldn't every person have a reasonable positive expectation if they played the lottery? But, you can't really ever expect positive returns from a lottery, right?
As math is a fuzzy subject for me, I deferred to my buddy the math whiz (he wrote a post for me on the NBA lockout a few months ago). Here's what he had to say.
Great question. Some of the math of probability isn't super fresh in my mind (though I'd say it's one of my favorite areas of mathematics), but I'll offer what I can. First, I would say that what you said isn't wrong, but the situation is more complex.
It's important to remember that there are both helpful and harmful nuances to the system that affect the expected return on a lottery ticket. On the helpful side, you have opportunities to make money without hitting the jackpot (if you get x, y, or z numbers right). On the "harmful" side (as it relates to expected return), you could win the jackpot but end up having to split it with another winner, or two other winners, etc.
Let's pretend that those nuances weren't there. (You may know all of what follows in this paragraph, but I'll just cover the bases.) If you were to buy 175,000,001 lottery tickets for $1 each, you'd of course spend $175,000,001. Odds are, 175 million of those tickets would not hit the jackpot and thus would give you no money. The remaining ticket would hit the jackpot, which we'll pretend is $350 million (not far from the actual current situation, right?). That means your profit from buying all those tickets would be $175 million (rounded up $1).
The thing is, you're obviously not going to buy that many tickets, and that's where expected return comes in. To find the expected return on a ticket, I believe you would divide the profit by the cost in the above scenario (at least in this case, because the number of tickets purchased is equal to the $ spent). So, yes, you'd have a positive expected return of $1 for every ticket purchased (ie, a *profit* of $1 for every ticket purchased). However, the concept of expected return isn't very helpful on an all-or-nothing investment with incredibly long odds. The reality is that there is a very high chance of you winning absolutely nothing, and that only changes if you buy an incredible number of tickets.
Then, the math would be further complicated by the nuances mentioned above."
What do you think? Will you be trying to win Friday's prize? Let me know in the comments.
Photo by cpradi.