As the Powerball pot climbs toward or past $800 million dollars, the start to this post may seem a tad esoteric, but bear with me.
François-Marie Arouet, the French philosopher better known as Voltaire, made his first fortune cornering the market on a lottery back in the 18th century, buying up all the “tickets” after a mathematician explained to him that the pot would pay far more than the total cost.
The same opportunity crops up occasionally in American lotteries when there’s no winner for weeks on end and the winning pot grows large enough.
So for example, with an expected pot of $800 million for a ticket that costs two bucks, then so long as your odds of winning are better than 1 in 400 million, they would seem to be in your favor.
Or, to put it more formally, the “expected value” of buying one ticket — or 50 — seems almost surely positive, given that the odds of winning Powerball are only 1 in 292 million-to-one, considerably less than 400 million-1. That is, 292 or so million tickets would cost you only $584 or so million dollars at $2 a ticket, yet you stand to win $800 million. (An astute Alabaman named Kyle Whitmire points out on AL.com that an economist would also factor in the cost of your time getting the ticket, but let’s assume you were going to the drugstore anyway.)
Now put yourself in Voltaire’s shoes. If you buy every possible combination — all the 292 million possible number choices of 6 numbers— you’re assured of winning. By spending $584 million dollars, two dollars for every combination. The mechanics of such a strategy being cumbersome at best, lottery pools have grown up to lower the transaction costs. They are all over the Internet.
So okay, maybe you’re not going to buy 292 million tickets. Still, why not pick up a ticket or two, or two thousand? Well, for one thing, the odds of winning may seem positive, but they remain minuscule. Say you bought those two thousand tickets. Your odds of winning? 292 thousand-to-one. As for the lottery pools, there may be frauds galore, for all I know, and of course the lottery poolers will take their own cut, just like the folks who run lotteries.
Next there’s the time value of money to consider. The grand prize winner tonight gets the whole pot, but only paid out as a pre-tax annuity over 29 years. Any inflation over that time, and the $800 million will come to you in dollars with diminished value, not 2016 dollars, as the cost of your ticket(s) is. In fact, the lump-sum payout, if you asked for it right away, is estimated at only $500 million or so in today’s dollars. And that, dear readers, is already less than the $584 million you’d have to lay out.
And there’s another wrinkle still: the taxman. You may remember him from George Harrison’s song for the Beatles, written to protest high marginal taxes in England for high earners under the Labour government of Harold Wilson:
If you drive a car, I’ll tax the street
If you try to sit, I’ll tax your seat
If you get too cold, I’ll tax the heat
If you take a walk, I’ll tax your feet
In this case, the taxman would simply tax your winnings at the highest marginal federal rate: 39.6 percent for anything over about $450,000 in household income, plus state and even city taxes if you live in New York, say.
So what are we down to now? The $500 million lump sum can be no more than $300 million, after taxes, even in a no-tax state — which is considerably less than the $584 million you would have to spend.
And sad to say, even then, should someone else also have the winning numbers — or worse still, several someones — you would have to split the now-meager pot with them.
Yes, there are other prizes. But let’s face it, except for the million and maybe the $50,000, the secondary prizes are chump change. And so the personal finance advice from here at Making Sen$e, then: wait till next week at least. I suspect that’s what Voltaire would do.