# Can you "invest" in the lottery?March 31, 2012 9:07 AM   Subscribe

The recent Mega Millions lottery got me thinking: why don't wealthy individuals/corporations ever attempt to buy out the lottery?

The recent \$640 million jackpot, according to the AP: "amounts to a \$462 million lump sum and around \$347 million after federal tax withholding. With the jackpot odds at 1 in 176 million, it would cost \$176 million to buy up every combination. Under that scenario, the strategy would win \$171 million less if your state also withholds taxes."

So seriously, why is this never tried? I realize that \$176 million is a lot of money, but for those that do have it, you're talking about a pretty great return on investment.
posted by lobbyist to Grab Bag (18 answers total) 2 users marked this as a favorite

Well... usually when the jackpot gets this big, there are so many tickets bought that multiple winners are practically guaranteed. Split the pot with just one other person and you're already down what, \$5 million?
posted by jabes at 9:08 AM on March 31, 2012

Because you have to split the money with anyone else who has the same combination. The chances of being the sole winner are much smaller.
posted by supercres at 9:09 AM on March 31, 2012

In 1992 someone tried this.
posted by GuyZero at 9:10 AM on March 31, 2012 [4 favorites]

More than one ticket can be purchased with the same numbers. So if two entities bought all the numbers, the winnings would be halved, and so on.
posted by ssg at 9:10 AM on March 31, 2012

There also might not even be enough time to buy all those tickets, even if you had the form filled out in advance. Say the cashier can run each one through in 5 seconds. She's got 35.2 million forms to run through (5 combinations per form)! Unless my math is totally jacked, in one day working non-stop she can only run through 17,280 forms, which means you've gotta have 2,037 cashiers working non-stop in one day to get all the numbers out. And considering there's only a 3-4 day turnaround between drawings, you're gonna have to totally monopolize the lottery sellers throughout a major city even to get them all printed.
posted by jabes at 9:20 AM on March 31, 2012 [2 favorites]

This is sort of like the birthday problem with 175,711,536 birthdays. If only 25,000 quick pick tickets are bought, the probability that two of them are the same is about 83%. So, when millions of folks all over the country are buying quick pick tickets, it is practically certain that two of them will be the same.
posted by King Bee at 9:28 AM on March 31, 2012 [1 favorite]

What everybody else said, but applying it to the current real life situation: There were three winners last night. After federal tax, they'll get about \$116 million apiece. So if one of them used this strategy, he or she has lost fifty million dollars.
posted by Flunkie at 9:35 AM on March 31, 2012 [6 favorites]

In theory, for a game where you pick your own numbers, there's a winning strategy in which you determine which number combinations are least likely to be played and then invest only in those numbers when the jackpot is high enough to make it worthwhile.

It would only work if some numbers are drastically less popular than others. (Though I think that is the case for most games. For instance, I'd bet that any number that can be read as a date is more likely to be played than a number that can't be read that way.) It would have to be a real long-term strategy — you'd need to wait for really unbelievably huge pots and not merely large ones, and even then you might lose a few times before you won big.

But the worst part is that, to make it work, you'd need to be the only one with access to information about how often different combinations are played. If other players started using the same strategy, based on information that was as good as or better than yours, then they'd wipe out your advantage pretty quickly. Think of it like the difference between insider trading and honest trading based on public information. If you know something about the market that nobody else knows, you can earn yourself a huge profit very easily. If enough other traders have access to that information, then it becomes very hard to reliably outperform the market as a whole. In this case, "the market as a whole" is losing money — the expected return on a lotto ticket is negative — so the only way to turn a reliable profit is through insider trading.

I don't think it would be practical to try to use inside information on a public lottery like this. Anyone who works at a store that sells lotto tickets has some information on which numbers are popular. To have even a theoretical shot at outperforming them, you'd need essentially perfect information. And you can't have perfect information on the subject unless you work for the lotto or break into their records. Either strategy would be illegal, and neither strategy would let you keep the information away from your competitors. For instance, if there's a computer vulnerability that lets you get at the information about ticket-buying patterns, you can never be sure that you're the only one who's noticed that vulnerability.

Anyway, if you can break into the lotto commission's computers, there are probably some easier, more profitable, lower-profile ways you could be spending your time.
posted by nebulawindphone at 9:51 AM on March 31, 2012 [1 favorite]

It has been reported that 1.6 billion tickets were sold for the \$640 million dollar jackpot last night. And, even with that, only 3 winning tickets were bought. So, in terms of investment, there are more profitable ways to make money.
posted by Stynxno at 9:58 AM on March 31, 2012

It has been reported that 1.6 billion tickets were sold for the \$640 million dollar jackpot last night. And, even with that, only 3 winning tickets were bought. So, in terms of investment, there are more profitable ways to make money.

But only 600 million in the most recent drawing - the 1.6 billion is for all the previous drawings that had no winner, plus the most recent week.
posted by RustyBrooks at 11:00 AM on March 31, 2012

I remember seeing a segment on some TV show where someone did that (probably the same group linked above) and one of the things that made it possible was that the lottery rules allowed for cards to be filled out mechanically. They was the only way that they would have enough time to fill out all of the cards and they still didn't get tickets for every possible number. Then they spread people out to have cashiers issue the tickets (which is the other time problem as pointed out above). As I recall, most lotteries today require the cards to be filled out by hand so if you get together enough people to fill out all of the cards, the payoff (even assuming just one winner) won't be very big on a per person basis.
posted by VTX at 11:45 AM on March 31, 2012

Also was done in Ireland in the same year.
posted by w0mbat at 11:46 AM on March 31, 2012

Sometimes you can.

Because of a quirk in the rules [of the Massachusetts Cash WinFall game], when the jackpot reaches roughly \$2 million and no one wins, payoffs for smaller prizes swell dramatically, which statisticians say practically assures a profit to anyone who buys at least \$100,000 worth of tickets.

This was reported in July 2011, one hopes they've altered the rules since then. But then again, this is Massachusetts we're talking about.
posted by mr vino at 11:47 AM on March 31, 2012 [2 favorites]

I read an article yesterday (USA Today?) that looked at this. Two issues: First, it would take too long to do (you'd have to buy ~170m tickets). Secondly, when the jackpot was at \$540M, if someone else had a second winning ticket, each would have won ~\$140m, so you'd automatically lose \$30m trying.
posted by NotMyselfRightNow at 12:19 PM on March 31, 2012

See "Regression toward the mean". The more wagers you make, the closer your average take comes to the expected payoff for the game. And the lottery is a loser's game.

That's the reason casinos make money consistently. They're making a titanic number of wagers, with odds in their favor. Even in the week when someone wins a million dollars on a slot machine, the casino makes a profit.
posted by Chocolate Pickle at 12:20 PM on March 31, 2012

And the lottery is a loser's game.

Careful. The expected value of a ticket last night was \$2.85.

Of course, the probability that you've thrown your dollar away was 97.5%.
posted by King Bee at 1:22 PM on March 31, 2012 [1 favorite]

Two mathematicians answered your exact question and won an award for it. The article (free at that link) does get equation-heavy in spots, but their commentary throughout the article is stellar and is very readable for non-mathematicians.

They conclude that although sometimes lotteries will have an expected payout higher than the price of a single ticket, neither Powerball nor MegaMillions will ever reach that level. For other lotteries, getting involved in a lottery buyout syndicate could theoretically be profitable but that the absurdity of implementation would be problematic.

Their conclusion: "f you are seeking good investment opportunities, then our results in Section 11 suggest that this doesnâ€™t happen in the lottery, due to the astounding variances in rates of return on the tickets. What if a syndicate intends to buy out a lottery drawing, and there is a positive expected rate of return? Our mean-variance analysis suggests that you should invest a small amount of money in such a syndicate."

A. Abrams and S. Garibaldi. "Finding Good Bets in the Lottery, and Why You Shouldn't Take Them". The American Mathematical Monthly, vol. 117, no. 1, January 2010, pp. 3-26.
posted by wondercow at 1:36 PM on March 31, 2012 [6 favorites]

Regression to the mean has nothing to do with why this is a bad idea.
posted by Flunkie at 2:58 PM on March 31, 2012

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