Power Ballin'

Behavioral Economics and the Largest Lottery

On Saturday, my neighbors handed me a lotto ticket as a birthday gift. Of course, this was no ordinary lottery ticket; the Powerball had reached the biggest pot ever at nearly one billion dollars. Later that night, I remembered that I had shoved the ticket in my pocket. I had fleeting a moment of joy, where all of a sudden the future seemed wide open. Anything was possible. 

Then, I checked the results. It turned out the only plausible thing occurred, I lost. So did everyone else, and pot for the next lotto increased to well over a billion dollars. Since that moment, I have been more than a little obsessed. 

Even understanding probability as I do, I found myself falling prey to many interesting behavioral phenomena.

Fear of Missing Out

An e-mail circulated amongst my team at work. We were starting a pool. Anyone who wanted could throw in ten dollars, and we would  buy as many tickets as we could afford. At two dollars a piece, we would get five times the number of participants. We agreed to split any winnings. 

I did some back of the envelope math (confirming a Marginal Revolution post) and found that despite the size of the pot, it was still a bad bet. The odds of winning are roughly 1 in 300 million. At two dollars a ticket, I would need to win $600 million to break even. Though $1.3 billion is greater than $600 million, that amount would be paid out over 30 years. I could either do some time discounting, or just  assume we take the lump sum pay out. The pay out is probably about half the jackpot total. At $650 million, now it's a border line proposition but still profitable.  But about 40 percent will go to taxes, and now I am down to 390 million.*  This is pretty clearly below the threshold where it is a profitable bet. On top of that, I am pretty risk averse. I'm out.

One co-worker, a recent immigrant, starts asking questions about the pool. I get snarky. I tell her, she could hand the person collecting money $10 for the incredible opportunity to never see it again. I suggest putting the money in her 401K or employee stock purchase program. Then, a coworker walks over and throws a ten into the pot with all the confidence in the world. Then, another does the same. To my surprise, I find myself opening my wallet and following along.

I  was experiencing FOMO: the fear of missing out. When my coworkers started participating, I had an image in my head of them winning. I could see them all quitting, going on great vacations, and once in a while meeting up for fancy dinners in San Francisco. I am the last man standing at work, coding alone in a sea of empty standing desk. As soon as they all joined, my framing of the lotto changed. Instead of experiencing my potential winnings as windfall, I started thinking about what I would be missing without the money; failing to win was now a loss. 

I was experiencing loss aversion, with the new reference point. The behavioral economic research suggests people dislike losses about twice as much as they like gains. Previously I was feeling like this was a chance to win my share of $390 million. But when I framed it as a loss, the pay out felt like my share of $780 million. If this is how I would experience the lotto, the bet is back above that $600 million threshold.

The first co-worker essentially created a race to the bottom. Once he created the FOMO, everyone hopped on board. As each marginal team member joined, the FOMO became even worse. This was some weird mixture of behavioral economics and a prisoners dilemma. Conditional on my irrational loss aversion, it was suddenly rational to play. 

Rationalizing My Decision

But as we started talking about this, we came to a rationalization. For a lotto this size, maybe in some weird way, it was actually rational to join the pool.  

Realistically, I am probably not all that sensitive to the size of the pot. Roughly 45 of us joined the lotto pool, so my share of the $390 million is about $9 million. In my head, I know that $390 million is a lot more than $9 million. $390 is more than I can burn through in a lifetime, even I tried. All my family would be set forever, and I could probably do some awesome things like set up a foundation. But,  $9 million covers everything I imagine when I think about being rich. I could by a nice house (well maybe, it is the bay area), my wife and I could travel for a year, and I know I can pay for college for my future kids. Taking some risks like a startup  (or better yet, opening that sandwich shop) become a real possibility. The point is, when I think about what the future looks like, I am pretty insensitive to the difference between $390 and $9 million. I have reach the point where my marginal utility of income is practically flat. 

So at $390 million vs. $9 million, it's pretty much "win" or "don't win". So by joining the pool, rather than buying my own ticket, I haven't cost myself all that much future happiness. But my cost for the opportunity to "win" has just dropped from two dollars to about 5 cents! My cost per ticket has dropped dramatically, but potential winnings (in terms of utility, not dollars) hasn't dropped all the much. It's a much better deal, at least than going in alone would be. 

This is really only possible with a pot this large. A smaller pot, split so many would be a point on my utility curve where I have higher marginal utility. For example, splitting $45 million with 45 others would "only" give me $1 million. Not that I would complain, but I'd pretty much have to stop the list of things I wanted to do after buying the house. Or I join a pool with five us to stay a 9 million, but then its 40 cents per ticket. Given the odds of winning, its probably not worth it.

If I sat down and did a bunch of math, I could draw a curve which plots the relationship between income and future happiness that fits this behavior.  I would never buy a lotto ticket on my own because of the negative expected value, but I would buy this ticket in a pool because of positive expected utility. Weird. It's like some strange inverse insurance scheme.

Because I fancy myself a rational economist with a solid foundation in statistics, I can safely pretend that joining the pool made perfect economic sense. It just revealed something about my marginal utility of consumption. But deep down, I know FOMO and loss aversion drove a poor decision.

* There is some probability of collisions, so the expected payout it decreases further. But there is also some probability of smaller pay outs, so it increases again. I just called it a wash, but I know there are others who have looked at this more closely