Can You Guarantee a Powerball Win?

Irfan Kahn | Los Angeles Times | Getty Images

Mark Nelson, left, shows off $460 worth of Powerball lottery tickets he bought at Bluebird Liquor, a shop with a reputation for lottery luck, in Hawthorne. On right is owner of liquor store James Kim.

Now that the Powerball jackpot is worth over $500 million, it has become theoretically easy to guarantee a win. Picking the right numbers isn't the problem anymore—it's all a matter of logistics.

And the logistics are a nightmare.

Ordinarily, guaranteeing a win at Powerball is a money-losing proposition. In order to assure that you will win the jackpot, you have to buy up every single combination of numbers. That would cost you nearly $400 million. But when the jackpot gets very high, it begins to make sense to play for a guaranteed jackpot.

(Read more: Plan on Winning That Powerball Jackpot? A Little Advice)

Five numbers are drawn from a tumbler with 59 white balls and the final "powerball" is drawn from a different tumbler with 35 red balls. Because each of the six white-ball drawings removes a possible number from the pool and the order of the numbers doesn't matter, the odds aren't quite as bad as they might seem.

You need to buy just over 175,223,510 tickets to guarantee a win by buying every single combination.

Actually, if you buy all the numbers you'll wind up better than guaranteeing a win. You guarantee multiple wins, since a few of the tickets will have winning combinations of numbers short of the jackpot.

So why don't we have syndicates organized to buy up all the tickets?

Well, for one thing, multiple syndicates buying the tickets would become self-defeating. They would wind up splitting the jackpot, diminishing the returns from undertaking the project. (Although the syndicates would also increase the size of the jackpot, ameliorating some of the damage to the returns.)

(Read more: Mysterious Hedge Fund Gets Even More Mysterious)

This highlights one of the big risks in undertaking the guaranteed-win strategy: You might be forced to split the jackpot with one or more lucky players. Splitting jackpots can be deadly to the profitability of the guaranteed win. If just two other players also win, you wind up losing money.

Taxes are also a hindrance to profitability. They explain why you wouldn't want to undertake the guaranteed-win strategy for, say, just $200 million. You need a jackpot high enough to leave an after-tax profit. (Although, if you organized as a syndicate, it seems like you should be able to write off the cost of buying the tickets as an ordinary business expense, so that only your profits would be taxed. I don't know if the IRS would see it that way, however.)

(Read more: The Millionaires Who Pay the Highest Tax Rate)

The logistics of the operation are a bigger problem. Let's say it takes about one second to print each number combination. With 86,400 seconds in each day, it would take you five and one half years to print all the required combinations. But you only have four days between the Saturday and Wednesday drawings.

This time constraint means that you'd have to recruit other ticket purchasers into your syndicate. More specifically, you'd have to recruit 565 people, each of whom you'd supply with around $620,263 to play the $2 game. (Actually, they don't quite need that much but since you can't play fractional games, you wind up buying a few extra tickets.)

This creates a major problem: do you know 565 people you would entrust with $620,263 in cash? The incentive to take the money and run is pretty extreme. If your syndicate of 565 people divided a $425 million jackpot evenly, each one would get a bit more than $752,212 if you hit the jackpot. But each syndicate member would know that the defection of other syndicate members could put the jackpot at risk. Remember if even one of them absconds with the money, you lose your guaranteed win and must depend on luck. So a rational syndicate member would prefer to take the $620,263 in cash and not risk it buying tickets.

Actually, you probably need even people more than that. Lottery machines cannot really print tickets every second of every day for four days. They'd run out of ink and paper. The mechanics would break down. So you would likely need a few thousand people spread out at several locations to guarantee a win. This increases the odds of defection immensely.

It would be difficult to raise the capital to buy the tickets. Investors would demand a share of the returns, which would diminish the share of the jackpot spread to those who do the work of buying the tickets. Ideally, you'd want your labor and capital sources to be identical to resolve this problem.

The problem of monitoring to prevent defection and raising capital from your labor force indicates that ideally, you'd want to undertake the operation as part of a tight-knit community. A small village, for instance, in which people have bonds of loyalty that would help prevent defection, would be ideal.

Outside of a very tight-knit community, it is probably a practical impossibility to mobilize capital and labor to undertake the guaranteed win. So, if you play the lottery, you'll just have to take your chances like everyone else.

- by CNBC Senior Editor John Carney

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