Over at the Washington Post, Brad Plumer looks into the question of whether a wealthy person could guarantee himself a win by buying every possible ticket in the Mega Millions lottery, and discovers that the answer is no:
Of course, another strategy would simply be to buy up every single ticket combination. That would cost $176 million. But you’d be guaranteed to win about $293 million after taxes. Good deal, right? But there’s one big hitch: “First, if it takes five seconds to fill out each card, you’d need almost 28 years just to mark the bubbles on the game tickets. You’d also use up the national supply of special lottery paper and lottery-machine printing ink well before all your tickets could be printed out.” (Also, if just one other person picked the winning number, you’d end up losing $30 million all told.)
It’s true that you can’t guarantee a win in this Mega Millions game, because it’s too likely that you’ll have to split the jackpot. If 300 million tickets sell, the average jackpot winner ends up with only 48 percent of the jackpot. If 600 million sell, you’ll only get 28 percent on average.
But it is not true, as a general proposition, that a lottery can never be cornered. In 1992, an Australian investor syndicate succeeded in cornering the Virginia Lottery. At the time, the odds of hitting that lottery were about 1 in 7 million, and the jackpot had grown to $27 million dollars. The Australians bought about 5 million tickets (logistics prevented them from buying every combination) and won the jackpot.
There were a handful of key differences between the Virginia situation and Mega Millions. The most important is that there was not a similar frenzy over the jackpot: even though playing the lottery had become a positive-expectation endeavor, there was not a similar rush to buy tickets, so the Australians could feel better about their odds of winning the jackpot alone.
The Australians also figured out the logistics of buying tons of lottery tickets. Plumer talks about how you would never have the time to fill out all the Scantron forms you would need to buy every lotto combination. But the Australians didn’t have to fill out any Scantron forms—they paid retailers to sell them blocks of lottery tickets in bulk. At least one retailer closed its lottery terminal to the public in order to constantly produce tickets for the syndicate.
Even so, the Australians only managed to purchase five million lottery tickets. And after their win, Virginia and some other states instituted rules to make it more difficult to buy lottery tickets in bulk. So, their feat would be difficult to replicate.
Virginia isn’t the only place where a lottery game has reached positive expectation. When I was in college, the jackpot on Mass Millions (then the big jackpot game of the Massachusetts Lottery) reached over $42 million, with win odds of about 1 in 13 million. This is because nobody hit the jackpot for nearly two years. Yet, there was very little attention focused on the huge jackpot—probably because lotto players were drawn to Mega Millions, which featured bigger jackpots with much longer odds of winning.
During this time, I bought a few Mass Millions tickets, and if I hadn’t been a capital-constrained college student, I probably would have bought more. But why didn’t somebody with lots of cash come in and do what happened in Virginia? The answer is probably that logistics made it too difficult to buy the 13 million tickets you would have needed to guarantee a win.
Buying 176 million tickets to guarantee a Mega Millions win would be even more difficult, and you would have less time to do it, since the game is drawn twice a week, unlike most states’ once-weekly big jackpot games.
So, cornering a positive-expectation lottery is difficult, and it probably will never be possible with Mega Millions. But with state-level games, if you have a few tens of millions of dollars to throw around and are in a place with the right rules about ticket sales, you might find an occasional opportunity.