Las Vegas ? The NFL has always had a strained relationship with this gambling city, though the case could be made that if it weren’t for Vegas point spreads the league never would have become the giant it is today.

The league is so skittish about the city that a few years ago it refused to allow a television ad promoting Las Vegas to air during the Super Bowl. Not long after that, it threatened to sue the city’s casinos for hosting Super Bowl viewing parties on giant screen televisions.

And just last week a former NFL lobbyist who now works in the Bush administration was credited with helping create new rules to enforce the ban on Internet betting in the United States.

So it’s more than a little ironic that the league’s increasingly bumbling referees actually lent a helping hand to bookies by making a mess of the end of the game between the San Diego Chargers and the Pittsburgh Steelers.

It wasn’t intentional. The NFL would rather stop playing on Sundays than do anything that might benefit its sworn enemies.

But it was a gift of millions of dollars from a very unlikely source.

“For us it was going to be bad,” said John Avello, director of the race and sports book at the Wynn resort. “We were going to take a pretty big hit.”

The big hit turned to a big win when referees incorrectly waived off a touchdown scored by the Steelers’ Troy Polamalu as time ran out in an ugly game in Pittsburgh. If allowed, the final score would have been 17-10 and the Steelers would have covered the 4-point spread and made everyone who bet on them — about seven out of 10 bettors — a winner.

Instead, the final went down as a quirky 11-10, and the bookies — who needed the Chargers to cover to avoid a costly afternoon — caught a break. No one knows what the exact totals are, but Avello estimates $10 million was bet on the game in Nevada alone, and many more times that when online and illegal betting is added in.

The bettors will be back next week, of course, and could turn the tables. This season they’ve been doing better than normal at the city’s betting parlors, where NFL football reigns as supreme as it does on the nation’s television screens.

That doesn’t sit well with the NFL, which nearly a half century after being burned by the illegal betting of star players Paul Hornung and Alex Karras, continues to fear its games might somehow be compromised because of all the millions wagered on them.

It’s pretty much nonsense born of fears rooted in a time that no longer exists, but it’s nonnegotiable in a league that worries more about its players placing a bet than almost anything else. Pacman Jones can still bust up Strip clubs in Las Vegas without much fear of penalty, but place one bet in a sports book and he’s gone.

But try as it might — and it tries mightily — to separate itself from the betting industry, the NFL and gambling are still inextricably linked to each other. They have been since the early days of the league, when bookies discovered point spreads and fans discovered that it was fun to have a few bucks riding on the team of their choice.

The fear in the league always has been that players would fall into the grasp of bookies and begin throwing games. But players are so well paid today that there isn’t much incentive to risk their careers for a few more dollars, and games are watched so closely that anything suspicious would immediately draw attention.