Wednesday, January 13, 2016

Ponderings on Powerball, Probability, and Poverty

Yes, there is. A mighty slim one, but still a chance.
So, have you bought your chance to be an instant member of the “one percent”, courtesy of Powerball and your fellow greedy, gullible Americans? I have. I’m worse than greedy and gullible — I know a little about probability math and finance, too. If I knew more, I’d be the worst: a trader in derivatives, the triumph of faith in mathematics overcoming common sense.

A friend of mine posted on Facebook, “I’m not a math person at all, but I was explaining to [her partner] that the odds of winning get lower as the powerball amount gets higher. What would I do if I won (assuming I bought a ticket)? Ruin my perfect life.” She explained:

Years ago I had an AA sponsor who told me that scarcity is a mindset characteristic of addiction. They have to grab as much as they can in case it dries up. They don’t trust that there is plenty. It doesn’t seem healthy for the whole country to be fantasizing about their epic dream binge. There’s bankruptcies, paycheck advance usury, blacks stuck in jail because they can’t pay traffic tickets, subprime car loans you need to get to work that doesn’t pay enough to cover the bills. And the shrinking middle class, of course [what comprises the “middle class”?]. I’m not good at the math, but I can see society is psychologically sick to get off on a game like powerball.

My friend’s wrong about the odds, precisely because she’s not a math person. As for the rest of it ... later we’ll talk.

Probability, I may have said before, is our best evidence that God has a sense of humor. At minimum, it’s His gentle reminder that we’re not as clever as we think we are; that we don’t know as much about the workings of the universe as we think we do; that, no matter how much we try to mathematize and regulate the workings of a determinist cosmos, we’re going to get our butts kicked by the unpredicted and the unpredictable; and that, while the impossible and the improbable may look similar to each other, they’re still very different things. After all, something must be possible in order to be improbable; if it’s impossible, then probability has nothing to say in the matter.

For those who aren’t mathematically inclined (and, believe me, I empathize with you): The odds of any particular number combination winning has nothing to do with the number of tickets sold, but rather depends on the number of combinations possible. In October of last year, Powerball went from 59 white balls and 35 red balls to 69 white and 26 red; this changed the number of combinations possible from 175,223,510 to 292,201,338.

However, the number of Powerball tickets sold affects not only the probability that someone in the population will pick a winning sequence, but also the probability that more than one person in the population will pick the winning sequence:


The numbers I used here were taken from the Jan. 9, 2016 Powerball drawing, where over 440 million tickets were sold. The number under it is the estimated number of adults over 18 in the US as of 2014; I use it to show how the probabilities change with a smaller number of tickets sold (1 per adult). It also gives an idea of just how much attention the jackpot has drawn. Nevertheless, even with the higher odds that more people will draw the winning combination, the current jackpot ensures that, even with ten winners, each winner would have an income placing him/herself well within the top 5%:


None of the above numbers reflect after-tax disposable income. Nevertheless, even if half the money goes to Uncle Sam, there’d still be more than enough left for a comfortable retirement (assuming one manages his winnings responsibly).

The point is that Powerball is designed so that, despite the absurdly high odds against any particular sequence winning, more players means a greater probability of someone winning — and more money to continue the game in the future. The game is designed to be won; therefore, some people do win.

I’m reminded of a man over twenty years ago who was reputed to be connected with the Boston Mafia. When he won the Connecticut lottery, his reaction as printed by Newsweek was, “No one’s ever gonna believe this.” But why not? Given that honest lotteries make winning just as improbable for a person of unimpeachable probity as for an unrepentant crook, our reaction should be merely amusement, not suspicion of rigging. Again, the difference is between the impossible and the merely improbable.

Impossible is the chance that a random tornado would assemble a pile of spare aviation parts into a working Boeing 747. Or the chance that any one of a million monkeys in a million years would pound out a single verse of one of Shakespeare’s couplets. But that’s not really what I want to talk about.

How does the lottery stack up as an investment? Honestly, unless you’re starving, it’s probably a better use for your two dollars than that hotdog on the rollers at QuikTrip. There are a few investment options geared to small change that you could investigate; there are other ways you can spend money that would have positive financial effects down the line, such as putting money in an emergency-fund account, or making extra payments on the principal of your home loan, credit card, or auto loan. But none of them have the same risk/reward ratio as does a lottery ticket.

Here’s what I mean: If you bought two Powerball tickets twice a week at $2/ticket over the next thirty years, the potential loss of $12,480 must be matched against the potential reward of $40 million or more. By contrast, if you walked into a casino once a year over that same period and placed a $416 bet on a one-time bet on the twelve, even if you won every time — a statistical improbability on the order of 1 in 4.887 x 1046 — the upside would at most be $374,400. Put that money twice a week in a savings account paying 1% annual interest, and in thirty years the final value would be $59,756.01 ... enough to buy a nice new car, but not enough to retire on. If you put that money in a quick-start investment account, you’d have to pound money in for months, even years, before the returns justify the fees and risks.

One other thing you could do with that $2 — give it to a needy person. And you will have treasure in heaven (cf. Matthew 19:21). But that’s not really what I want to talk about, either.

The fact is, most investment schemes that have any hope of providing a decent return are geared towards people who make much more in a year than they need to survive, requiring thousands and even tens of thousands of dollars just to get in the door. For most people in the bottom 40% of household incomes, whatever propensity they have to save has to be expressed in discounts, coupons, sales, deliberate choices of lesser-quality products, and self-denial; the cost of living takes almost all their disposable income. And deliberate policy choices by the Fed have rendered the most accessible financial instruments — savings and money-market accounts — helpless against the ravages of inflation. (One point eleven percent was the best rate I could find in researching this post ... and that required a hefty minimum deposit!)

Catch-22: You need some wealth to create more wealth.

As I say, a Powerball ticket is probably a better way to waste one’s $2 than on the hundreds and thousands of gewgaws, snack items, and tchotchkes we buy for no other reason than “it seemed like a good idea at the time”. As far as risks go, people have lost a lot more on investments that never promised as much of a return. If you’re “just making someone else rich”, that someone else is most likely another Joe Schmuckatelli like yourself; for a while, at least, you put one of your own in with the fatcats and CEOs at the top of the income tree. No, I don’t seriously advocate it as a solid investment; I certainly don’t advocate buying more than two or three tickets at a time. But a couple of bucks spent twice a week is relatively harmless; and hey! you might win after all.

As evidence of a sickness ....

While Powerball and other lotteries aren’t solving the many problems my friend listed, neither are they the cause of those problems, nor do they prevent said problems from being solved. In fact, I’ll go so far as to speculate that 99% of the problems listed — bankruptcies, paycheck-loan indebtness, incarceration for unpaid tickets, and so forth — are due to a combination of bad luck and bad choices that had nothing to do with Powerball, with the addition (in the case of the incarcerations) of corrupt municipal systems that prey on their residents through traffic fines.

The desire to be wealthy isn’t in itself a sickness, nor is it really evidence of the addictive mindset. Having plenty of money enables people to do a lot more, not only for themselves but for others; as I’ve said before, only the “haves” can take care of the “have-nots”. I have to admit some unease, though: lotteries don’t “create” wealth; they simply make one person wealthy. As I implied above, millions of people willingly pay to make someone else rich, their only reward a fleeting hope that the person who’ll be made rich is themselves. Say what you will about the morality of moneylending, at least you get something tangible out of it. Nevertheless, the desire to be wealthy only becomes a sickness and a sin when it becomes inordinate, when it’s tied to selfishness, when it begins to drive our behavior to the exclusion of all other human considerations.

Once you abstract the compulsive gamblers from the equation, is it really a perception of scarcity? That implies people perceive that there isn’t enough to go around, which I don’t think is the case. Many people want to be rich, not because there isn’t enough to go around, but because they don’t feel what they have is enough — whatever that may mean to them. And most people know that Powerball isn’t going to go away soon, that eventually there’ll be another insanely huge jackpot. But while the opportunity’s here ....

The logic of the imbalance between the risk and the reward is compelling in itself, especially when you’re talking about a ten-digit reward. As well, I think the vast majority of people, even those drawn by the enormity of the payout, realize their chance of winning is negligible, and consider it fun to fantasize about what they’d do with the money, like Tevye in Fiddler on the Roof.
Games of chance (card games, etc.) or wagers are not in themselves contrary to justice. They become morally unacceptable when they deprive someone of what is necessary to provide for his needs and those of others. The passion for gambling risks becoming an enslavement. Unfair wagers and cheating at games constitute grave matter, unless the damage inflicted is so slight that the one who suffers it cannot reasonably consider it significant. (Catechism of the Catholic Church 2413)

In sum, I can’t see a problem with Powerball that isn’t a problem with other forms of gambling, even the more socially useful kind called investing; after all, investments are by their nature wagers on outcomes, often without knowing the odds in advance. Like any other form of gambling, you should never spend more on Powerball than you can afford to lose.

But while I can’t blame anyone for thinking the odds against winning absurdly high, I can’t agree that purchasing a ticket is irrational or unreasonable, save in the way that Hope, if it’s any virtue at all, is irrational and unreasonable. Here’s hoping ....