Imagine that the Washington Redskins and Dallas Cowboys were so vastly superior to every other team in the NFL that they had combined to win the past 19 Super Bowls, ultimately forcing the commissioner to change the rules to give other teams a chance. Imagine they played each other upwards of 10 times a year, allowing their disgust for each other to simmer and stew. Imagine that, on occasion, the animosity overwhelmed them and the respective players paired off in full-scale, 11-on-11 brawls.

Imagine all that, then picture them all on ice skates, with ponytails hanging out the backs of their helmets, and you have a pretty good idea of what it looks like when the U.S. and Canadian women’s hockey teams face off. And if the gloves stay on during the 2014 Sochi Olympics tournament, which begins Saturday, it will be because the stakes are too high to risk the penalty minutes or suspensions – not because everybody suddenly decided to get along.

“This rivalry,” said Team USA forward Meghan Duggan, “fuels our fire every day.”

This may be the best rivalry you’ve never heard about -- arguably the fiercest in all of international hockey and in all of women’s team sports. It was only six weeks ago that a five-on-five brawl broke out at the end of the Americans’ 4-1 victory in Grand Forks, N.D., in the fifth of a seven-game, pre-Sochi tune-up series. As the arena DJ quickly cued up the theme from “Rocky,” the players went at each other, some wrestling on the ice, some on their skates trading haymakers. When it was all sorted out, the referees had called 10 major penalties for fighting, as well as assorted minors.

“If [Canadian] players are going to take cheap shots at our players,” U.S. coach Katey Stone said at the time, “there’s going to be an answer for that. We will not get pushed around.”

It was the second time during the seven-game “friendly” series that the American and Canadian women staged an all-out brawl, the other one coming in October in Burlington, Vt., when the Canadians objected to a U.S. skater running into their goalie.

“It just got pretty intense,” Canadian veteran Meaghan Mikkelson said of the brawls. “We play each other a lot. They’re not going to let off the gas pedal and neither are we.”

But a good rivalry requires mutual relevance, in addition to mutual hatred, in order to take off – and the international dominance of the Americans and Canadians represents an instance of overkill. Since 1990, when the sport’s international governing body introduced the women’s version, the U.S. and Canada have won all 19 world championships – 13 by the Canadians, but four of the past six by the Americans -- including the four Olympic Games (the U.S. in 1998, Canada in 2002, 2006 and 2010).

It reached the point -- following the Vancouver Games, when the teams drubbed their preliminary-round opponents by an aggregate score of 72-3, before Canada beat the U.S., 2-0, in the gold-medal game – that Jacques Rogge, at the time the president of the International Olympic Committee, warned that the sport could lose its Olympic standing unless it became more competitive.

Partly as a result, the Sochi Games will feature a tweaked format, with the world’s four top-ranked teams – the U.S., Canada, Finland and Switzerland – grouped together in the same division. But to ensure they don’t all knock each other out of the tournament in the preliminary round, all four teams from Group A are already qualified for the medal round, with the prelims only mattering for seeding purposes.

The Post Sports Live crew debates whether hockey during the Winter Olympics or the NHL Playoffs are more exciting to watch. (Post Sports Live/The Washington Post)

In addition to preventing – at least theoretically -- a rash of 18-0 scores, the unique grouping ensures that the U.S. and Canada will face each other in the preliminary round, a matchup that comes on Feb. 12 at 4:30 p.m. Sochi time (7:30 a.m. in Washington) at the Shayba Arena. If the tournament plays out according to form, they would meet again in the gold medal game on Feb. 20 (9 p.m. in Sochi, noon in Washington) at the larger Bolshoy Ice Dome.

In the lead-up to Sochi, both the U.S. and Canadian teams have tried to lay claim to the underdog mantle, the Americans citing the Canadians’ historic dominance, the Canadians citing the Americans’ recent success – including four wins in the recent seven-game tune-up series. But when it comes to what matters most, the Olympic gold, it is the U.S. that has the added motivation, having lost three straight to the Canadians.

“Obviously it stinks,” Team USA’s Duggan said of the 2010 loss in Vancouver. “It’s devastating in that moment. When you step away from the moment and move forward, you use it as training fodder. You encourage your teammates [by reminding them] that you don’t ever want to feel that way again.”

They have traveled halfway around the world, the Americans and Canadians, to resume their bitter rivalry. They will face off at least once. Will they do so a second time, with the gold medal at stake, on Feb. 20? To suggest otherwise would be fighting words.