Mega Millions, Probability, and You

If you haven't heard, this Friday's Mega Millions lottery jackpot, which already has an estimated pay out of $500 million, will be the largest lottery prize ever won (assuming somebody hits all six numbers).

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.

"Hey Bry,

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.

Overvaluing Intangibles, Part 1

If you're anything like me, you watch Pawn Stars (because you're interested in historical items) and you watch Hardcore Pawn (because you're a horrible person).  One of the defining moments in both shows occurs when people walk into the pawn shops wanting to either sell or pawn items, and they inevitably think that their item is worth a ridiculous sum of money.

"So, all you'll give me for my seal is a
swift kick in the pants?
I guess I can do that."

Sometimes the object is worth as much as the people expect, but most of the time it isn't.  Even if it is worth money, because the pawn shop needs to make money when they resell it, the pawn shop gives the seller a necessarily lowball offer to ensure that money can be made.

In the first place, in this age of eBay and Amazon, why on earth do people still insist on selling to pawn shops?  If you have something of value that you want to sell, SELL IT YOURSELF TO MAKE MORE MONEY.  This is called the American Way.

In the second place, when something isn't as valuable, why do people assume that it is?  The answer to this lies in an object's intangibles.  This can also be known as sentimental value that we tend to place in items that is above and beyond what those items are actually worth.

As a point of comparison, consider Tim Tebow.  The guy is not your normal quarterback in that he can't throw two consecutive good passes to save his life.  Still, he was a first round pick in the NFL draft because scouts really talked up his intangibles.  He isn't a partyer.  He is a natural leader.  He says his prayers, minds his manners, and chews with his mouth closed.  Because of these things, certain coaches in the NFL ate him up and drafted him (arguably) much higher than he should have been.  He began starting as a quarterback last season, and he lead the Broncos into the playoffs even though nearly every person who comments on football considers the guy a sub-par quarterback.

Will Tebow's intangibles eventually translate to a Broncos Superbowl victory?  Only time will tell, but in my opinion, you'd be better off engaging in a land war in Asia or going against a Sicilian when death is on the line than betting the Tebow will lead the Broncos to a Superbowl.

Not Pictured: Wallace Shawn.

In a similar way, we overvalue objects that we've had with us our whole lives.  Sure, you've had that clock that your great-aunt Mildred passed down to you all your life (so it's worth a lot to you), but the truth is that it's not as much of a clock as it is a piece of plywood with (most of) the numbers between one and twelve painted on it.  Even though you may value this item intensely, from an objective standpoint, it's not worth a whole lot.

Make sure to come back later this week to see how this mindset costs you money (even if you're not a pawn shop regular).

Photo 1 from Thomas Shahan 3.
Photo 2 from Jerf Kern.

This post was featured in the Carnival of Personal Finance #350.

Why I'll Probably Never Buy Season Tickets Again

Even though my Chargers are looking quite a bit better than they did when I wrote this, they will still almost certainly not make the playoffs.  The biggest reason for this is Tim Tebow loves God, God loves Tim Tebow, and Tim Tebow is in the same division as the Chargers.

Seriously, if the game's close, the dude can't seem to lose.

Anyways, my point in all this is that the Chargers haven't had the great season that I (and many others) were pretty sure that they would.  Based on my belief that they would have a great season, I purchased a partial (4 game) season ticket package for several tickets under the hopes that I would be able to sell the extra tickets that I wasn't able to use.*

Had the Chargers had the tremendous season that I had expected, I probably could have made some money off of my extra tickets.  As it turns out, nobody wants to pay full-price to see a bad team play (and if that bad team is playing another bad team, as happened when the Chargers played the Chiefs, it gets really bad: I ended up selling some tickets with a face value of $70 for only $10 a piece).

I tried selling on Craigslist.  I tried selling on eBay.  I tried shaking down friends and acquantances, all to no avail.

While it makes me too sad to come up with a specific number, I easily lost several hundred dollars on my extra tickets.  And that is why, after my very expensive experiment in selling tickets, you can count me out of that particular game.  I'll be leaving the ticket-selling to the professionals, and I'll happily let some other sucker lose their money.

In short, if you are not absolutely certain that you will be able to use all the tickets you buy when you buy a season ticket, you probably shouldn't buy them.  I learned that the hard way.

*If you're wondering why I bought season tickets instead of just a single game ticket, here's the reason: my family really wanted to go to what turned out to be a super-expensive game if you bought the tickets in the secondary market (the Packers/Chargers game).  Because the Chargers organization knew that this was going to be a popular game, they didn't let people only buy tickets to that game; you could only buy tickets to this game as part of a package.

While I saved my family members money on this particular game by buying the season ticket package, I sure lost a heap of money on all the other games.  Oh well.  You live, you learn.