Post-Hoc Lottery Thoughts

[First: I don't like using footnotes in these posts because it's annoying and distracting to scroll down to find 'em.  I couldn't help it here, though.  I encourage you not to worry about the footnotes until the end; they usually just address technicalities that you're probably not concerned about anyways.]


The Mega Millions jackpot reached a record high a few days ago.  It was estimated to be worth $540 million, but with late-minute sales driving up the number, the final jackpot turned out to be $640 million.  (That's if you take an annuitized payment, of course.  If you take a lump-sum, you "only" receive $462 million.)  Your odds of winning are 175.7 million-to-one.  The price of a ticket is $1.  Therefore, it was +EV to play the lotto, right?

Well, that answer is a bit complicated.  I think the concept of EV gets oversimplified too often.  When you're playing a game like poker, it makes sense to do whatever's necessary (within the bounds of your own morality, of course) to maximize your winnings.  That's because the way you beat poker is by getting more money than your opponents.  As a result, every EV consideration begins and ends with a calculation of how much money you stand to win/lose over the long run with each available option (bet, call, raise, fold).  There are no other factors brought into the calculus.  Again, this is because the way to "win" poker is to make as much money as possible.

Is that really our goal for life, though--to win as much money as possible?  Of course not.  So, it logically follows that our EV calculation would take other factors besides the economic ones into consideration.  Here's an example:* you've just been hired out of college to start your first full-time job.  When discussing salary, your boss offers you a choice: you can take $60k a year, or you can choose to gamble.  You get to flip a coin--if it comes up heads, you get $120k a year.  If it's tails, you get $20k a year.**  Obviously, if you're only looking at economics, the flip is the +EV play.  Just as obviously, it almost certainly doesn't make sense for you to limit yourself to economic factors.  The difference between $60k and $20k is enormous--you'd almost have to move into the YMCA on $20k a year.  The difference between $120k and $60k, however, isn't as large.  You'd have a slightly nicer apartment and a slightly faster car.***  For many people, taking the guaranteed $60k is the +EV play.

So, back to the Mega Millions.  First, let's get the simpler question out of the way.  Even if your only goal is to maximize your money, playing the Mega Millions a few days back would have been -EV.  Here's a great article that explains why.  When taking subjective factors into play, however, maybe it would make sense.  It's almost impossible to make this calculation, though.  You'd have to assign numbers to concepts like happiness, frustration, etc.  That's not easy to do, despite what Jeremy Bentham would have you believe.  Also, people have trouble conceptualizing just how slim their odds are.  I'm guilty of this, too, sometimes.  "It could happen to anyone."  "Someone's gotta win."  Sound familiar?  There's a psych term for this, but I didn't take enough psych courses to learn/remember it.

I don't really have a neat way to wrap this all up, so enjoy this Simpsons clip instead.







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*This example comes from an economics textbook whose name and author I never learned.  I came across this hypo while shelving books at the NU bookstore.

**You're not allowed to quit, ask for a raise, etc., because you're signing a one-year contract.  Okay, technically, you could quit but then you could get sued for breach of contract and that'd be -EV.

***remember, in this example you're straight out of college.  If you're married with a large family to support, it's conceivable that the difference between $120k and $60k is indeed bigger than the difference between $60k and $20k.  Also, yes, I realize that some people who are straight out of college are married with a large family.  Sorry for my imprecision.