Playing the lottery? Do the math

If you think lotteries are harmless fun, read on.

Brigham Young University math professor Tyler Jarvis has pointed out: “The chances of winning the California Lotto Jackpot are approximately one in 18,000,000. If you have to drive 10 miles to buy this ticket, you are three times more likely to be killed in an automobile accident on the way than to win the jackpot.” He added that if you stood all the losers of this lottery in a line, it would be 6,800 miles long, more than the distance from Manhattan to Tokyo. Here’s another way to think about it: If you bought 50 tickets per week, you ought to win once every 6,923 years. So you’d be due to win today — if you’d started playing around 5000 B.C.

McMaster University mathematics and statistics professor Fred Hoppe asked this question: “Would you pay $1 to bet on 24 heads in a row? The chances of that happening, as anyone who flips coins knows, is virtually impossible.” Yet millions play lotteries, pinning hopes on similar odds. Hoppe has explained that if you spend $25 on lottery tickets each week for 20 years (total: $26,000), you can expect to lose $13,000. The Gambling Free Tennessee Alliance reported: “If a person bought 100 $1 lottery tickets every week for his entire adult life from age 18 to 75, that $296,400 investment would still only give him less than one chance in 100 of hitting the jackpot.”

Payout rates for lotteries stink. Lotteries often keep about 50 percent of gambled money, while slot machines keep 5 percent to 25 percent, roulette games keep 5 percent, and horse racing keeps 13 percent to 17 percent.

The biggest lottery losers are the poor. Those in the lowest income bracket are much more likely to play the lottery, heavily, than wealthier folks. As many have quipped, lotteries are “a tax on people who aren’t good at math.”

Don’t buy more than occasional tickets for fun. Humorist Fran Lebowitz is reputed to have observed, “I figure you have the same chance of winning the lottery whether you play or not.”

Ask the Fool

Q: What does rebalancing a portfolio mean? — O.M., Philadelphia

A: It refers to the practice of adjusting the percentage of your portfolio that various holdings make up by reallocating funds. Imagine that five years ago, you invested in 10 companies, putting about 10 percent of your portfolio’s value in each. If today one of the firms has grown to represent 40 percent of your portfolio, you might rebalance by selling off some of that, and reinvesting the money elsewhere.

Rebalancing isn’t always best. Sometimes it’s good to let your winners keep winning.

Q: What are “defined contribution” and “defined benefit” plans? — T.F., Rutland, Vt.

A: These are the two main kinds of retirement plans. Traditional pension plans, offered by many of our parents’ employers, are defined benefit plans. With them, employees know exactly what they’ll receive upon retirement. It’s the employer’s responsibility to make sure that the needed sums of money are available for retired employees.

Defined contribution plans, such as 401(k)s and 403(b)s, have now replaced many traditional pension plans. With them, the amount of money contributed into the plan is defined. As an employee, you know how much you and your company are depositing into the account. The amount available at retirement is uncertain and will depend on how you invested the contributions while you were working. You typically have more control over these kinds of accounts, as you’re usually able to specify what kinds of investment vehicles your dollars are plunked into (growth mutual funds, company stock, bonds, etc.).