They pulled a fast one on their coaches, who were out enjoying a round of golf when the vote went down that will make their jobs even harder. It’s one of the advantages of being a billionaire NFL owner.

In this case they wanted to change the rules of overtime, something Minnesota Vikings fans surely wish had happened a season earlier. Too many games being won by coin flips and 150-pound kickers, including one big game that put New Orleans into the Super Bowl.

The changes are simple, but brilliant. They take a weakness that fans have been complaining about and turn it into a strength.

The only problem is that they didn’t go far enough.

Hopefully, that will change in May when owners revisit their vote to implement the new rules just for playoff games. By then everyone will be adjusted to the new reality and it won’t be as difficult to expand it to cover regular-season games as well.

Meanwhile, coaches will have some studying to do. Because sudden death isn’t so sudden anymore.

“Fourth-and-2 at the (opponent’s) 22, what are you going to do?” Giants coach Tom Coughlin asked. “What you have to do now is looking at a situation where you better have thought out how you want to play it against who you’re playing against.”

Coughlin and his fellow coaches seemed to have been surprised by how quickly owners moved to implement the new rules, just two months after the Vikings lost a trip to the Super Bowl in an overtime where they never got to touch the ball on offense.

There was some grumbling going on among them Wednesday in Orlando, with Saints coach Sean Payton saying the change “kind of got slipped in the back door.”

Payton was outspoken in saying he dislikes the new rules, while coaches who didn’t win the Super Bowl were more circumspect. Clearly, though, the coaching fraternity wasn’t happy, and for good reason.

Because as good as the average NFL coach might be in scouting players and implementing intricate offenses, these are guys who need cheat sheets just to figure out when to go for 2-point conversions.

How do you expect them to decipher the far more complex calculations that come with deciding whether to kick a field goal on your first possession or gamble and go for a touchdown that would win the game?

Give commissioner Roger Goodell credit for quickly pushing the rule changes forward even while acknowledging they don’t solve everything. They never will as long as you rely on chance — in this case a coin flip — as a cornerstone of overtime.

As recently as the Super Bowl, Goodell said he liked overtime the way it was and that the league hadn’t been able to find a better way to run it. But, faced with statistics that showed the team winning the coin flip wins 60 percent of overtime games, the league did find a better way.

“There’s no perfect system,” Eagles owner Jeffrey Lurie said. “But we were running into a situation where there is a distinct advantage for the winner of the coin toss, and that’s unacceptable. To have all that preparation and what goes into a game, to have a coin flip help determine the odds, that’s not right.”

No it’s not. Not in the playoffs, certainly. And not in the regular season, either.