TORONTO — It wasn’t pretty the last time the United States played Canada. Ryan Kesler was ejected after boarding Shea Weber. T.J. Oshie briefly knocked Logan Couture out of the game. Joe Pavelski left a mark on Claude Giroux. Even Sidney Crosby got in on the act, cross-checking Kyle Palmeiri from behind and precipitating one of the night’s many skirmishes.

And that was just an exhibition, a week before the World Cup of Hockey even began.

When the arch-rivals meet again Tuesday night in Toronto, the United States will be playing for its life after an opening loss to Europe. If the U.S. loses, it can’t advance to the semifinals. It’s that simple. Even before Europe’s 3-2 overtime victory over the Czech Republic on Monday made it that simple, American coach John Tortorella — the primary force behind Team USA’s grit-over-skill style — called it their “championship game.” This team was built to beat Canada, and it worked in that 4-2 exhibition victory in Columbus (Canada returned the favor the next night in Ottawa).

So the stacked Canadians are braced for anything and everything.

“Oh, for sure,” Canada’s Jonathan Toews said. “There’s going to be some bad blood out there, for sure.”

This is the game the United States has had circled since the World Cup was first resurrected. Canada always has been the big brother — if not the neighborhood bully — in the relationship, but ever since the Americans beat Canada for the 1996 World Cup in Montreal, the rivalry has gotten more and more heated. Canada beat the United States for the gold medal in the Salt Lake City Olympics in 2002, and beat the Americans en route to Olympic gold in both Vancouver (2010) and Sochi (2014).

Throw in the must-win mentality for the Americans after they face-planted against Europe, and the intensity is sure to be as high as any game in the tournament.

Tortorella knows his team can’t be too aggressive against the Canadians, who will turn any mistake into an odd-man rush the other way, and any power play into a golden scoring opportunity. But this is still the coach who famously said, “safe is death” while coaching the Tampa Bay Lightning.

“We’re coming,” Tortorella said. “We’re going to come. That’s no secret. It’s the way we’ve been built. Bloodbath? I don’t want to call it that. We’re going to play the game the right way. It’s not about yapping after the whistle.”

Canada, which blitzed the Czechs 6-0 in its opener by sending line after line of superstars over the boards, is hoping to stay out of any extra-curricular activities.

“Our game plan is not to back down, but also to stay out of the stuff that we know is only going to hinder what we’re really focused on,” Toews said. “We’ll worry about ourselves. We know what they can do well, and what they try to do. … We knew those those two [exhibition] games would be a good preview, but not necessarily even close to what we expect in this tournament when we’re going to bump into them. Add to that fact that they’re probably unhappy about what happened [Saturday], and it’s going to be a tough game.”

Tortorella said that everybody in Toronto wants to see the United States knocked out of the tournament, and surely the crowd at Air Canada Centre will be raucous in favor of the home team. But the Americans think that could just fuel their aggression and the irritating style they want to play.

“There’s one sound better than your home crowd cheering loud after a goal, and that’s the silence of a road crowd,” said American forward David Backes, who is on the lineup bubble for the game. “When you can hear a pin drop and hear each other screaming when you score a goal. We’re looking to have a few of those tomorrow night.”

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