Why Playing the Mega Millions Isn't Stupid (Even If You Lost)
I’m not a gambler, but this week I played the Mega Millions. I obviously didn’t win the $640 million, or I wouldn’t be writing this. Someone in Maryland won. Did I ever stand a chance, or was I, as my sister likes to say, simply paying a “tax on stupid people”?
I’m not stupid, and here’s why. Mathematical arguments that the lottery is a losing proposition are based on fallacies of mathematics. Such arguments usually go something like this: The price of a ticket is $1, the prize is $1 million, the odds of winning are 1 in 2 million, therefore the value of the ticket is ($1 million) divided by (2 million), or $0.50. The rationale is the law of averages. If you play many games, the argument goes, over time your winnings will be smoothed out, and on average you’ll earn $0.50 for each $1 you spend.
These mathematics explain small lotteries, but not big ones like the Mega Millions. Suppose you and nine friends chip in $1 each for a 1/10 shot at the $10 prize, and you do this regularly. Here, the law of averages holds, because you actually will play many games, and when you add up your winnings at the end of the year, it will come out to just about $1 per ticket. In other words, the law of averages holds when the number of games played is large relative to the frequency of winning. This is why casino blackjack is safe but boring – you’re sure to win, and often, but the amount will never be very much.
In contrast, Mega Millions carries odds of 1 in 172 million (or so). It’s drawn twice a week, so to guarantee a win you’d have to play for 1.6 million years straight, and you’d obviously spend $172 million (not accounting for 1.6 million years’ worth of inflation). The law of averages is reversed – the number of games in between wins is far larger than the number of games you’ll ever play. You’ll never play Mega Millions enough times to actually smooth your winnings into an average income stream. If God played Mega Millions, maybe He could assign a ticket an average value of $0.76 or $1.39 – but to me, a mere mortal, it’s all-or-nothing.
We call this a quantum phenomenon. There is a world in which you win and one in which you lose, and the two can never co-exist. This is unlike your $10 lottery with your roommates, a game which you can win and lose multiple times in the same week. Compared to the enormity of Mega Millions, your puny ticket is an atom that exists in one quantum state or another, but not both and not some average. It’s Schrodinger’s cat – it’s either alive or it’s dead, but it cannot be some average of alive-and-dead.
Borrowing more vocabulary, you might call this a black swan event – like, say, a global financial crisis or an unprecedented tsunami. Some people planned for a global crisis and shorted the rest of us. Before the black swan event actually happened, we thought they were crazy; now they seem prescient. Conversely, when the Fukushima Daiichi planners did not account for massive catastrophes like last year’s earthquake-tsunami-flood combo, no one faulted them, but in retrospect their mathematics look flawed. It would have made no sense for Fukushima Daiichi to calculate the average price-per-share of a highly unlikely event that destroys the entire company value (and maybe that of Japan’s whole nuclear sector). Similarly, presenting the average per-ticket value of the Mega Millions as $1.09 (or whatever) is utterly meaningless. You don’t get nine cents – either your life is changed massively and forever, or it isn’t.
Finally, the lotto doesn’t cost very much. If I play a ticket every single drawing, that’s only $100 a year, not a burdensome sum for most Americans, and far less than I already spend on totally stupid shit. Black swan events do happen – as some lucky bastard in Maryland is learning right now. To summarize, therefore, the logic behind choosing to play the Mega Millions is this:
- - Spend nearly $0 to have a small but nonzero chance to completely transform your life,
- Or
- - Give up any chance whatsoever of that life-changing event, and get nothing in return.
When framed that way, the small fortune I spent this week feels slightly less stupid.



