Preying on suckers

With nobody hitting the jackpot for the multistate Powerball lottery this weekend, the prize rolls over and may be as high as $210 million for Wednesday night's drawing.

I'll take this opportunity to revisit my earlier calculations (aided by my actuary brother) regarding whether or not Powerball constitutes a "fair game."

The idea of a fair game is that a good bet is one in which the odds of winning are roughly equivalent to the potential payoff.

Take for example the daily "pick three" games promoted by many state lotteries. The odds in such a game are obvious — 1,000 to 1. If such a game offered a $1,000 prize for a $1 ticket, it would be a fair game. These games, of course, typically pay out far less than that — usually only a few hundred dollars — and are thus, obviously, a sucker's bet. They're like betting on a 50-to-1 horse, but with the winnings being no better than for the 2-to-1 favorite.

(My dad had a friend back in Jersey who was a gambler, like some character out of Mamet. He couldn't resist the lure of the daily number, so he played every day by sticking a dollar in an old pickle jar. Whenever his number hit, he emptied the jar. He said he always "won" more than he would have it he'd actually bought a ticket.)

Another way of looking at the idea of a fair bet is to ask what would happen if one had enough money to "invest" in enough tickets to guarantee a win. With the pick three games, this would mean spending $1,000 on tickets for every possible combination of numbers. Doing so would guarantee you hit the winner, taking home a prize of, say, $400. You would, in other words, be throwing away $600. That's a sucker's bet.

In the case of Powerball, the odds of hitting the winning combination are 120,526,770 to 1. This would seem, at first glance, to mean that once the jackpot exceeds $121 million — as it did this weekend — the game would become a fair bet.

So why aren't people like Bill Gates and Warren Buffett lining up to buy every possible combination of Powerball numbers for Wednesday's $210+ million drawing? If they can guarantee a win by "investing" only $120,526,770, wouldn't this be a rational investment?

Well, no.

First of all, there's taxes. Despite Grover Norquists best efforts, these still exist and they will take a hefty chunk out of that jackpot.

Then there's the possibility of multiple winners. If both Gates and Buffett try to game the system, they will both "win" — meaning that jackpot will be split in half, with each of the billionaires losing some $15 million even before taxes.

Finally, there's the fact that the jackpot isn't really as high as it's advertised. That's an annuity value — the total if you accept it paid out in pieces over several decades. If you want the prize in a single lump sum — which the term "jackpot" conventionally means — you'll have to settle for considerably less.

Taking these three factors into consideration, I've estimated that Powerball does not become a fair game until the advertised jackpot exceeds $278 million.

Those folks lining up for Wednesday's drawing, in other words, are suckers, rubes, hayseeds, fools.

Somebody eventually has to win, of course, and the happy proles will get their picture in the paper. Not pictured will be the millions of others whose cumulative losses vastly exceed whatever the taxman allows the winner to keep.