It's the latest American success story: Save your pennies, invest in an organization that donates a third of its income to good works and walk away with a big nest egg, say $161 million.

Maybe Powerball and the state lotteries with more modest seven-figure prizes aren't what Horatio Alger had in mind. But for the vast majority of people, lotteries are merely a harmless pastime that diverts funds from illegal gambling. "The original idea was to replace the numbers racket and raise some revenue painlessly," says Charles Clotfelter, an economist at Duke University.As the states work ever harder to persuade people to play, though, this reasoning is growing weaker. "Once you make it legal," argued Peter Reuter, an economist at the University of Maryland's School of Public Policy, "you inevitably lose control of the promotion."

For economists, locked in utilitarian reasoning, gambling is hard to explain among people who spend tens of billions of dollars to reduce personal risk. Why, for example, would someone shell out hundreds of dollars every month for medical insurance to eliminate the small risk of having to pay $20,000 in hospital bills - and then turn around and trade the sure thing of a dollar in hand for one chance in 50,000 of winning $20,000?

And why do lottery players seem to be attracted to the games with the highest payoffs? So-called progressive games, in which uncollected jackpots are carried forward, might explain this phenomenon: As the prize accumulates, the expected return to each dollar wagered does rise, in some cases actually exceeding the amount bet.

But psychological research suggests a simpler explanation. People, it seems, just aren't up to the challenge of comparing tiny probabilities of unlikely things happening. So they may assess the chances of winning a $100 million jackpot as roughly the same as winning a $10 million jackpot.

Besides, noted Robert Frank, an economist at Cornell University, there's a sense that a few million dollars no longer counts as much because it no longer symbolizes true, drop-dead wealth. "Great fortunes are far more visible today than a few decades ago," he said.

No matter how the frenzy is explained, there's no doubt that business is booming. Last year, according to La Fleur's World Lottery Almanac (www.lafleurs.com), Americans paid $34 billion for lottery tickets - up from $16 billion in 1988. Of the $34 billion, prizes absorbed 54.5 percent, and selling costs 5.8 percent. That left $11.5 billion for state-financed causes like education or aid to the elderly.

While states almost always earmark lottery proceeds for the needy at the outset, Reuter notes that the revenues do not seem to change government spending priorities in the long run: One way or another, an extra $100 million from the lottery for schools means roughly $100 million less for education from general revenues.

Lottery proceeds, like taxes on cigarettes, are widely perceived as "good" taxes because they are voluntary. No one, after all, is forced to buy lottery tickets. But while no one can deny the popularity of this back door to revenue, economists are generally appalled by the states' increasing dependence on lotteries. "This is a large, terribly regressive tax on a service sold by a state monopoly," Reuter argued.

What would he do about it? A modest step would be to eliminate advertising aimed at expanding the market. Massachusetts, where lottery spending (at 1.7 percent of personal income) is twice the national average, has been shamed into gestures in this direction.

A much bolder step would be to slash the effective tax rate by increasing the percentage paid in prizes. If one state did it, others might be forced to follow. On the other hand, why would a state kill the goose that is laying those billion-dollar eggs?

Robert Frank of Cornell argues that the state monopoly itself is a mistake because it links government to the socially destructive impulse to try to get rich quick. "I think states should be out of the business entirely," he said, perhaps by licensing and taxing private lotteries.

There is some hope that advertising for the lottery will subside, if only because the market is saturated. But even economists aren't naive enough to believe that the states will abandon a vastly profitable - and popular - monopoly in the name of civic virtue.

Besides, great things are sometimes done with lottery proceeds. "They built the Sydney opera house, perhaps the most interesting building in the country, with lottery money," recalled Reuter, who is Australian born. "Of course, it cost many times the amount originally budgeted," he said, "and that meant the hospitals did without lottery proceeds for a few extra years."