Musings on Lotteries, Probability, and Wealth

dice, probability

So, have you recently bought a chance to be an instant member of the “one percent,” courtesy of the Powerball and Mega Millions lotteries and your greedy, gullible fellow Americans? I bought one Sunday while the Mega Millions jackpot was still at $654 million and another yesterday when it hit $900 million. 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. An above-average intelligence and education is a great aid to cognitive biases and wishful thinking.

“Society is Psychologically Sick”

In January 2016, as the Powerball jackpot climbed towards the dizzying record of $1.6 billion, 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 is the “shrinking 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, whether such rapt national attention paid to lotteries is sick … well, let’s meander a bit and see where we fetch up.

Lottery Math for the Mathematically Declined

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.

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 with the number of number combinations possible. For Powerball, 69 white balls and 26 red balls allow 292,201,338 different combinations of 5 white and 1 red; for Mega Millions, 70 white and 25 yellow balls allow 302,575,350 different combinations.

However, the more tickets that are sold, the higher the probability that at least one ticket will hold the winning combination. In fact, the more tickets that are sold, the higher the likelihood that more than one ticket will have that combination because no one is prevented from choosing the same sequence as someone else. When the number of tickets sold climbs past 500 million, it becomes more probable that 10 tickets will win than that none will win. And the higher the jackpot, the more likely that each individual winner will have an annualized income placing them within the top 1% (assuming the ticket doesn’t belong to a big office pool).

The point is that lotteries are 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 creators designed the game to be won; therefore, some people do win. 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 a million monkeys given a million years would pound out a single verse of one of Shakespeare’s sonnets.

Sickness or Despair?

While lotteries don’t solve the many problems my friend listed, neither are they the cause of those problems. In fact, I’ll go so far as to speculate that 99% of the problems listed—bankruptcies, paycheck-loan indebtedness, incarceration for unpaid tickets, and so forth—are due to combinations of bad luck and bad choices that had nothing to do with lotteries. (In the case of the incarcerations, we must add “corrupt municipal systems that prey on their residents through traffic fines,” like Ferguson, Missouri did prior to the 2014 riots.)

The logic of the imbalance between the financial risk and the financial reward is compelling in itself, especially when you’re talking about a nine- or 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 the milkman in Fiddler on the Roof. Honestly, unless you’re starving, it’s probably a better use for your two dollars than that hot dog on the rollers at QuikTrip.

If there is a sickness involved, though, I’d say it’s economic despair. Catch-22: You need some wealth to create more wealth. Lotteries don’t create wealth; they merely redistribute it. Wealth isn’t what you make; it’s what you keep. And more and more Americans can keep very little of what they make. There’s your scarcity, my friends.

Over the last 38 years, real wages for the lower 80% have stagnated, household debt has doubled, and personal savings have been cut in half. Almost four in five Americans making $100,000 or less per year report they’re living paycheck-to-paycheck; over half of Americans report they have less than $1,000 in savings. Sure, the marquee unemployment rate as of September was 3.7%, but the mean duration of unemployment was still 24 weeks, about 50% higher than it was prior to the last recession, and the labor force participation rate was at the lowest it has been in 40 years. Just creating jobs isn’t enough to stop the bleeding of the middle class’ wealth.

What Can It Hurt?

Lotteries, I submit, are a kind of psychic relief valve. We indulge in fantasies of wealth not because we’re greedy but because we want to be free of the stresses that having an insufficient income creates for us. We imagine retiring wealthy and young enough to enjoy it, rather than working in our “golden years” to eke out an anemic Social Security check. I’m reminded of the shtetl resident who sighed, “God, I know, will provide. I just wish He would provide until He provides.” Like Tevye, we wonder: Would it spoil some vast eternal plan if we were rich?

Perhaps not. But it more than likely will spoil us. Even people who are already wealthy when they win aren’t always prepared for everything that comes with having that much money dumped in your lap. Instant wealth can not only change you in ways you won’t like; it can also change the people around you (or the way you perceive them) in ways you’ll hate. As counterintuitive as it may seem, winning the lottery can ruin your life … even if it’s already less than perfect.

The Catholic Church teaches, with some qualification, that wagers and games of chance aren’t inherently sinful. But she also has plenty to say about detachment from riches and relying on God’s providence. “Let the proud, therefore, seek after and love the kingdoms of the earth,” said St. Augustine; ”but blessed are the poor in spirit, for theirs is the kingdom of heaven.” Maybe you’re better off buying that hot dog off the QuikTrip rollers and giving it to a vagabond. That way, you’re storing up heavenly wealth.


The key rule to any form of gambling, whether it’s penny-ante poker with your buddies or on the Dow Jones Industrial Average, is Never bet more than you can afford to lose. On its face value, buying a lottery ticket every now and again seems to fit. Underneath, though, we make a more crucial bet: that winning will make our lives much better. And I don’t know how many people—if any—have ever won that bet, or have ever been able to afford the loss.

So yeah, occasionally, when the jackpot size overwhelms my common sense, I buy a lottery ticket. It’s almost like buying a slider from Krystal or White Castle—as bad as it is, every now and again, you gotta have one. And I enjoy the fantasy of instant wealth because I don’t have a solution to the growing wealth gap or an answer to the spiraling costs of college and healthcare or a dozen other economic issues.

But I wonder if I would be so careless with the risk to the rest of my life if the probability of winning weren’t so small. And that’s a question we should all ask ourselves.

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3 thoughts on “Musings on Lotteries, Probability, and Wealth”

  1. Pingback: Immoderate Desires I: The Deadly Sin of Gluttony - Catholic Stand

  2. Nice article, Tony. Lot’s of us old folks do the net lotteries cause they’re free and don’t require much effort. My wife and do the HGTV ‘free home” ones that amount to about $700 k to $800 k winnings and require only about 20 seconds of typing in each day you enter. Winnings so far? zilch. Expected winnings? zilch. But it’s fun to fantasize. And, BTW, I’m most pleased that you didn’t mention Pascal’s Wager.

    1. Thanks. As I understand it, Pascal’s Wager really only becomes strong after you work through the rest of his Pensées, after he’s eliminated all other possibilities. Outside of that context, it’s the weakest of the arguments for God. In any event, not having read Pascal, I don’t feel confident in deploying it. I still believe St. Thomas Aquinas’ “Five Ways” are the most robust set of arguments.

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