The House's Edge In Lotto

(Excerpted from True Odds by James Walsh, Merritt Publishing, 1996, Santa Monica, CA. 1-800-638-7597.) Reprinted with permission of Merritt Publishing. All rights reserved.

If you want to win $1 million for $1, play a single number on a roulette wheel and win. Put all the winnings on another single number and win again. Do it again. And again. You'll have just over $1 million. The odds of doing this are often 1 in 2 million.

That's still sever time more likely to happen than winning a standard 6/49 Lotto game.

If $20 million is bet on a Lotto jackpot, the state will take between 40 and 50 percent out of that figure immediately. From the half left, smaller prizes are deducted. In most cases, you're left something like $5 to $8 million for winning a 14 million to 1 bet. And if 20 million people play, it's likely 2 people will win. So they'll have to split that pot.

Criticizing lotteries can sound like a humorless exercise in cultural snobbery. What's the harm in someone spending a few dollars a week on a long-shot rip-off?

The best defense that proponents of state lotteries make is that the cost of playing is small and you have to play to have a chance--no matter how slight--of winning. But a small rip-off is still a rip-off.

Many state lottery directors insist that the demographics on people who play lotteries contradict the common criticism that poor people spend their food money on lottery tickets. But, even if only 1 in 4 Lotto players makes less than $25,000 a year (as is the case in Illinois), that's still a lot of people playing who'd be better off saving.

Relative to other arguments, the demographics defense makes sense. The people who defend lotteries more actively often sound intolerably cynical.

Social critics and some politicians argue that the desire for legalized gambling is a sign of the fraying of a country's social fabric. These people say that, in healthy societies, people believe that hard work and perseverance will make their fortunes. In sick societies, people have to rely on luck. They conclude that lotteries--more than other forms of gambling--prey on the poor, selling a false hope of an easy life.

Other less moralizing critics look at lotteries as a tax on the stupid...because the odds of winning are so slight and the payoff, when someone does win, doesn't reflect the odds.

Social commentary aside, gambling is useful issue for risk analysis because it is the purest practical application available. Stripped of politics, special interests and other baggage, gambling is risk assessment at its core.

Economic studies have a hard time quantifying why and how people gamble. They come up with basic conclusions like: The bigger the jackpot, the more people play. "It appears that there is a perceived value equation that's going on," said one academic. "I don't think it's an intellectual process. I think it's very emotional. They think, well, for a million, it's not worth a dollar. But if it gets over $5 million, they'll spend a dollar this week on Lotto."

When people behave irrationally, opportunities exist for others to profit. That's why casino gambling became a Wall Street darling in the 1980s.

The three most common lottery products are instant (or scratch-off) games, numbers games, and Lotto. To win the grand prize in a typical Lotto game, a player buys a one-dollar ticket and must correctly match six numbers drawn randomly without replacement from, say, forty-four numbers. This is called a 6/44 game. The probability of any ticket winning the jackpot in 6/44 game is 1 out of 7,059,052.

Lesser prizes are often awarded for matching fewer than six of the numbers. Lottery agencies take out from 40 to 50 percent of each dollar bet, some of which covers operating costs and the rest of which is turned over to the state.

Individual rationality is put to the test in the gambling market. In order to win 6/49 Lotto-style game, you have to match 6 numbers picked at random out of a 49 number universe. The odds of doing this are nearly 1 in 14 million. The average jackpot in this kind of game in 1994--on a $1 bet--was less than $2 million. That's a risk-reward ratio of 7 to 1, in favor of the lottery agency.

There are lesser prizes than the jackpot in most of these games. But the risk-reward ratio for these prizes aren't much better...and can be worse. The odds of matching 5 numbers out of 49 is 1 in 2.3 million. For one Canadian Lotto game, the average award in 1994 for matching five numbers was $113,666. That's a risk-reward ratio of 20 to 1.

The way to make money in a lottery is to be the one running it.

In 1995, Great Britain started a national, state-run lottery to compete with the various privately-run games that exist in that country.

By July 1995, 30 million British people were betting 100 million pounds a week on the National Lottery.

As one Brit pundit said, "When tickets for the National Lottery go on sale, I'll bet you a pound to a penny you won't find many true gamblers in the queues."

The reason: True gamblers recognize a bad bet when they see one.

To give yourself an even-money chance of winning the British National Lottery, you'd have to spend five pounds a week on tickets for 28,000 years. And, when you finally won, you might have to share the prize money.

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