As you've surmised, there’s plenty of talk among the pros about the merits, or lack thereof, of playing lotteries with various approaches in potential positive-return situations. Certainly it’s been done, and with success, but only in smaller lotteries, often held outside the U.S. Cornering a lottery the size of Powerball would be virtually impossible from both financial and logistical standpoints. That said, an edge is an edge, and an advantage player looks at anything with positive expectation as being worthy of investment.
There are several variables to consider besides the level of the jackpot when calculating the breakeven point of a lottery. They include the ticket price, the amounts of the lower payouts, whether you take a reduced lump-sum payment or an annuity, taxes, and the possibility that the jackpot will have to be split because another player (or players) had the same winning numbers. Tomorrow’s lottery drawing is currently projected to have a jackpot of $1.4 billion. While it’s generally understood that playing the lottery is a bad gamble, there’s never been a U.S. jackpot this high before, so it seems, intuitively, that it might be an overlay, meaning that a $2 ticket has an expected return of more than $2.
Making several assumptions that apply to the impending Powerball drawing, including opting for the one-time payment and counting the tax implications, Andy Kiersz, writing for Business Insider, says that "to even get close to a breakeven value, we would need the headline annuity prize to be a whopping $1,583,657,489.42"—more than the projected prize in tomorrow’s drawing. The analysis is a good one, but arguments can be made that different choices in the variables would produce a number well below the almost $1.6 billion breakeven point. And not even considered is the possibility of multiple winners having to split the prize. It’s this consideration that mucks things up when calculating a true breakeven, as the probability that a prize is split goes up as the number of players increases (in a non-linear fashion, no less), and many more tickets are sold as the jackpot rises.
This consideration leads to the only real lottery-playing strategy (besides playing high jackpots), which is to avoid choosing "popular numbers." Studies indicate that 1, 7, and 13 are considered popular, but the real demarcation point is 32, as picking numbers above 31 allows you to dodge birthdays. By avoiding popular numbers, you reduce the chances of splitting if you hit. Some purists argue that, because of the possibility of splitting, the lottery can never become a positive play. That may be, but it’s close enough and you won’t get many arguments for taking a shot when the jackpot is $1.4 billion, so don’t worry about being called a chump for playing. You’re not.
Much more important at this point is your utility in playing the game. That is, does participating give you enough pleasure compared to the cost and effort involved in doing so? For many, the answer is an unequivocal "yes." Holding a ticket or ten allows the opportunity to think (dream) about a life-changing event. It’s fun, and in an entertainment context, not much different from paying for a movie ticket or a round of golf, with the difference being that your breakeven expectation on the gamble means that you’re theoretically not paying anything for the experience.
It gets stickier when you factor in the costs. Are you a Nevadan driving to Primm to get your tickets? That’s $10 or so in gas (more if you count wear and tear on your car). Then there are the lines that form, especially at towns bordering non-lottery states. Are you waiting two hours? Four? Five? What’s your time worth? Tally up the costs and make your decision. But when you do, make sure you're considering the true expected value, which is the theoretical return for buying a ticket, as well as the extreme variance, or risk, involved in locking it in (this is the part of the question that refers to "potentially a single draw").
It's 1 in 292 million that you knock off the big jackpot, and although there are non-jackpot prizes, you'll get zero back on a single ticket about 96% of the time. From a bankroll-preserving standpoint, that absolutely has to be considered. Say you throw out the tax considerations and the EV of each $2 ticket is something like 175% (a $2 ticket is worth $3.50). That EV applies only to the total amount of your purchase. So if you buy a single ticket, your expected profit is $1.50, 10 tickets are worth $35, and 100 tickets are worth $350. Is it worth risking $200 for $350 in EV, considering the time, effort, and the likelihood that all or most of your investment will be lost? It’s a personal decision, but even the most aggressive advantage players understand that big edges in high-variance situations such as this have to be treated as special cases.
Even if you’re a purist, though, and don’t want to risk a dollar on something that doesn’t yield a clear edge with everything considered, the one thing you almost can’t do is decline to be part of a pool where someone else is doing all the work. Fading even the ultra-slim chance that lightning strikes and all of your friends move to their own private islands while you don’t is too much to risk. Go ahead and buy in, even if it’s a single ticket that gets you 2% of a $100 pool. Think of it as a really cheap life-insurance policy.
