“Sure there was luck involved, but this wasn’t just a wild guess,” Gomes said. “Gray caught my eye in training camp, and the Colts were weak against the rush in 2014. So it was a calculated risk. With state lotteries, a machine issues a number — how do you know if other numbers really won? With online fantasy sports, yes it’s gambling, but you watch the games and know for sure whether your choices were good or not. This is more honest to the public than lotteries based on random numbers.”

Hanson lives in Pasadena, Calif., was an elementary schoolteacher for a while, worked as a sports analyst for the analytics website ProFootballFocus, and this year is playing daily fantasy sports full-time. Hanson’s insight late in the 2014 season was to select little-known Cincinnati tailback Jeremy Hill when the Bengals were facing the Browns and the erratic rookie quarterback Johnny Manziel.

Hanson said, “I figured Manziel would turn the ball over, giving Hill some carries in the Cleveland red zone, where he’d score.” Both things happened. Hanson also tabbed the Carolina backup quarterback Derek Anderson, whom few other players wanted. Anderson threw a touchdown pass but no interceptions, which was great value in fantasy-sports terms.

“FanDuel and DraftKings are more like stock investing than you’d probably expect, including the need to diversify,” Hanson said. “Don’t wager a lot unless you really know what you are doing. If you’re just in it for some fun, don’t spend more than $20.”

Gomes and Hanson converted their smarts into winnings — though both say they are down so far this season. FanDuel and DraftKings are run by plucky entrepreneurs, the type of people society rightly admires. On the flip side, both enterprises are using national television, and the imprimatur of the highly subsidized N.F.L., to make incredible promises while leaving the public no way of knowing whether the claims are true — and while tempting the unsophisticated to throw their money out the window.

In fiscal 2014, Americans’ largest gambling outflow was on state-sponsored lotteries: about $63 billion spent that year, about $255 per adult. If fantasy-based sport betting reaches even a fraction of that sum, it’s a substantial economic development.

David Brooks contends that most gambling targets those who can’t afford to lose. Neil Irwin of The Upshot, in contrast, thinks that legalizing wagering on point spreads would improve the situation for small-money players.