As you have probably heard by now, the Powerball lottery jackpot is pretty big. Any time it gets this big, some people who don’t normally play the lottery start to wonder if buying a lottery ticket might be a good deal.

I’m one of those people. Normally I have no interest in lottery tickets because they’re such a horrible waste of money (unless you can figure out their system, like this guy did). But when the jackpot gets up to $550 million, it’s worth plugging a few numbers into a spreadsheet.

I like the approach taken in this BusinessInsider article, so I’m stealing it. I made a couple of changes.

First, rather than give the stated value of the lottery ($550 million), I’m giving the actual lump-sum payout ($350 million), which is what most people take. The higher number actually represents the total value of annuity payments over many years, and the lump sum is what those payments are worth right now.

Second, since you have to pay taxes on your winnings, I used the after-tax value in my calculations. I only did this for the three highest prizes, as most people won’t bother to pay income taxes on a $7 winning ticket.

Here’s how it looks:

So if these calculations are correct, you can expect to lose $.42 out of every $2 ticket. Except it’s worse than that in two ways.

First, the chart does not take into account the probability of sharing the jackpot, and with so many people buying tickets right now, that probability is higher than normal. In fact, lotteries like this actually see diminishing returns to a high jackpot because so many more people than normal are induced to buy tickets.

Second, most of the expected gains are concentrated into the grand prize outcome. The most likely outcome, by far, is to lose everything you spent on the ticket. If you spend $200 to buy 100 tickets, you would expect 97 of them to be losers, and you would expect a total of $12 from the other three, maybe a little more if you’re lucky.

But on the other hand, if you derive $0.42 or more of entertainment from purchasing a ticket, you’re at least breaking even. I would expect diminishing returns to purchases beyond the first ticket.

Therefore, the official Personal Finance Digest recommendation is: buy one ticket–exactly one, no more. Think about all the great things you’d do with a few hundred million, get your $0.42 worth of dreaming done, and then throw the ticket away on Sunday morning after you verify that you’re not the lucky jerk who won the lottery. At least you tried, right?

Okay, that headline is overpromising just a bit. We can’t tell you how to win your March Madness office pool, but we can tell you how to improve your odds a bit.

To start, you need a good way of ranking the teams. The NCAA tournament committee seeds the teams using RPI, but RPI doesn’t work as well as it should. The true test of how good your team rankings are lies in their predictive value, and on that measure Ken Pomeroy’s ratings are the best we’re aware of.

There’s a fascinating article at the Harvard College Sports Analysis Collective which delves deeper into the issue. The author of that article looked at how RPI has performed vs the Pomeroy ratings for the past six years, and then added in his own survival model which incorporate Pomeroy’s numbers and adds other factors. The results:

Here are last year’s Survival Model rankings. They were released the day before the tournament last year, so if you’re gung-ho about winning your pool, it might be worth checking the HCSAC blog the next few days.

Another principle to keep in mind: avoid bias. We tend to have higher opinions of things we’re familiar with, and NCAA pools are no exception. If the people in your pool live in, say, Indianapolis, more people will pick Indiana than would be justified by the team’s chances of winning. Even if you’re a one seed, you’ve got about a 50-50 chance of making the Final Four.

So if you’re a Hoosier, you can increase your odds by picking against the Hoosiers. You have little to gain by picking them, since everybody else will already be picking them, but if they lose before the Final Four–and remember, there’s a very good chance they (or any other team) will–you stand to gain significantly if you called it and nobody else did.

A related principle: people tend to pick 1-seeds more than they should. It’s the familiarity bias again, plus the fact that it’s just hard to pick against the 1-seeds. After all, they usually are the best teams in their region. Here’s an interesting table based on last year’s team which illustrates what we’re talking about:

You’re not trying to pick the best teams; you’re trying to pick teams where the actual probability of winning the tournament is greater than the perceived probability. The numbers above are from last year. Granted, Kentucky actually did win, but we’ll also point out that while 55% of the population expected UNC in the Final Four last year, the Tar Heels did not make it. If you didn’t feel comfortable picking against an overwhelming favorite like Kentucky was in 2012, you could have picked them to win but then picked UNC to get upset. 

To avoid bias with your own college, you may want to consider emotional hedging. This is the practice of picking your team to lose earlier than you think they will. It’s a win-win situation for you: either they advance past where you picked them, or else they lose early but their loss doesn’t screw up your pool.

Try to take advantage of any quirks of your pool’s rules. For example, suppose your pool offers double points if you correctly pick a lower-seeded team to defeat a higher-seeded team. The 8-9 game is usually a coin flip, so you’d probably want to pick the 9-seed in all 8-9 games.

Have fun, and good luck!

$425 MILLION! With no winner last night, the Powerball lottery went to $425 million. Since the goal of this blog is to get money for free (or at least at a discount), we’re naturally thinking about whether or not it’s worth it to buy a few tickets.

Obviously, lotteries and other games of chance are, generally speaking, for suckers. They’re a tax on the poor, the math-deficient, and those with a short time horizon. The most famous exception is card counting in blackjack, and of course it’s possible to do okay in poker if you know what you’re doing. But even lotteries are not immune to the skilled. Last year, for example, Wired magazine ran an article about a man in Ontario who cracked the code of a scratch lottery game. This year it was revealed that some bright folks at MIT have been gaming the Massachusetts state lottery for years. And long ago, an Australian syndicate saw an opportunity and pounced on the Virginia State lottery.

All of which is to say, lotteries are meant to separate people from their money, but they are not 100% successful in doing so, which is why math geeks are known to take an interest in them from time to time. The next Powerball lottery will supposedly be worth $425 million, and the cash payout on that would be maybe two-thirds of that, say $280 million. If you lose a third to taxes, that leaves you with around $185 million. Your odds of winning on a $2 ticket are 1 in 176 million. Worth it?

Well, we still have more to consider. There are other prizes besides the grand prize, and you have to take these into account in determining the payout ratio. If, as some contend, certain numbers are more likely to be drawn, that can increase your odds of picking the right number. On the other hand, if you do win, you may not be the only winner. Bigger jackpots are more likely to have multiple winners, so that will reduce the expected value of a ticket.

Of course, you also have to consider the entertainment value of the ticket, not to mention the fact that regardless of how poor the odds are, this is as close as most of us will ever get to being centimillionaires.

In conclusion: though lotteries are to be shunned in almost all cases, massive jackpots like this change the odds sufficiently that you can at least consider buying a ticket or two without feeling too bad about burning your cash. As with an other aspect of personal finance, your mileage may vary.