Tomorrow night we may see the largest Powerball jackpot in history, and the 2nd largest US lottery payout ever. But we can say one thing for certain: we won’t win it, because we aren’t playing. But why not? It is a bet with an asymmetric payoff – the chance at an outlier gain, the kind of long gamma-type strategy managed futures are known for… You would think we would be all over it.
So why don’t we like the lottery?
As with most things, it’s the math that gets in the way – those very small winning percentages. You see, while hitting the outlier trade in managed futures is far from a certainty, it’s definitely more likely than your chance of winning the big payout in Powerball. So, while an outlier trade in managed futures would only be a factor of 10 or maybe 20 above the invested amount, the odds of it happening are well within the realm of possibility. But with the Powerball, where the outlier is several hundred million times the investment, the odds are almost as bad at just 1 in 175 million (essentially 0%).
All that said, there is one thing that makes this drawing special. As Walter Hickey points out over at Business Insider, the jackpot has grown so large as to make the expected value of a ticket higher than its purchase price. In other words, if you could purchase every single Powerball ticket combination, you could make more than the cost of your total purchase (assuming you didn’t split the prize with anyone else… or take the lump sum payment… or pay taxes).
But short of such an undertaking, it still probably isn’t worth your money. To give a better sense of your odds, there’s a nifty little tool which can simulate the results of buying Powerball tickets thousands of times.
We ran a simulation playing 10,000 times (or the equivalent of two $2 tickets per week for 96.2 years), which gives an expected return of -$18,488, having purchased $20,000 in tickets, and “won” a whopping $1,512 over the years (by hitting the Powerball alone, or getting just a few numbers correct). As one commenter said, you have a better chance of being eaten alive by a shark and a tiger on the same day than winning the lottery (although that may be somewhat of an exaggeration).
And what would happen if you saved that $16 per month instead? Even at the current ultra low rate of 1%, saving the $16 per month for 96.2 years and compounding it monthly at a paltry 1% annual rate (and it would be something if rates stayed there for the next 96 years…) would result in a final balance of just over $31,000. You’d have made more than $12,500 in addition to keeping your money – definitely preferable to losing more than -$18,000.
You never know, you could get really lucky. But you’re almost certainly losing yourself real money by playing the lottery week after week, year after year.
November 28, 2012
Hello again! Thanks for the link to the simulator. The problem with this analysis is that it is not universally true in the sense that it is rejected by the winners, even posteriori. For them it made sense to play the lottery, posteriori. If we can find a black swan then the rule that all swans are white does not hold. Similarly, since there are already winners, the rule that it makes no sense to play the lottery does not hold. The rule could hold only if there were no winners yet. How will you convince a guy who is driving a Bentley that his 1$ bet was no good? It just fails verification. What do you think?