Last night’s Powerball payoff was $1.6 billion.
Even at Powerball’s ridiculous odds – 1 chance in 250 million of winning – that’s a good bet statistically, right?
Let’s go thru some math.
In econ-speak, the nominal expected value of the payoff is $1.6 divided by 250 million … about $6.
Since each PB ticket costs $2 … and $6 is way greater than $2 … that’s a good bet, right?
As Mr. Miyagi would tell the Karate Kid: “Not so fast, Grasshopper”
First, the $1.6 billion is the sum of payments stretched over 30 years.
Remember the old ‘time value of money’?
The immediate cash payout is about $900 million … in MBA-talk: that’s the net present value.
OK, $900 million divided by 250 million (odds of winning) is almost $4 … and, $4 is double $2 … so, it’s still a good bet, right?
Again, not so fast.
Remember the the old tax the rich bromide?
Nail those 1 percenters with high taxes!
Well, welcome to the 1% club, Mr. Powerball winner.
Combined, Fed & state income taxes will be about 50%.
So, the $900 gets slashed to $450 … which, divided by 250 million, is less than the $2 cost of a PB ticket.
Oops … suddenly the good bet turns bad.
And, oh yeah, defying the odds, there were 3 winners.
So, divide the $450 by 3 and you get $150 million … which divided by 250 million odds … gives a win of 60 cents.
Subtracting the $2 ticket cost, and the net is a $1.40 loss per ticket.
A very bad bet, even with a headlined $1.6 billion payout.
The real winners
Obviously, the big winners are the states and the Feds.
The states rake off the top – they don’t payout the full amount collected … and, they collect income taxes on the backend from the winners.
The Feds collect high-bracket income taxes from the winners
First, all the folks who bought tickets … save for the 3 who won … and those who got $2 worth of entertainment value from playing the game.
Empirical studies have shown that the vast majority of players are low and very low income folks dreaming of a score … the folks who can least afford to pour money down a rat hole.
In other words, PB is a truly regressive tax.
Other losers: all of us tax payers.
To the extent that poor players are, in effect, using money that comes out of, say, subsidized food budgets … the real players and losers are all of the folks who pay taxes that fund the subsidies.
Think about that for a moment.
The entire “system” makes Bernie Madoff look pretty clean.