BEIJING — Andrea Braendli, a Swiss goaltender, had no delusions of an Olympic gold medal.

“If we play for a gold medal,” she said ahead of the Beijing Games, “it’s going to be a miracle on ice.”

Her assessment was as cleareyed as any about the women’s hockey tournament. For all of the talk about, and hope for, parity in women’s hockey, the tournament will conclude like all but one other at an Olympics: with Canada and the United States dueling for gold, and two others — this time, Finland and Switzerland — seeking bronze.

Measured by the average victory margins of the Americans and Canadians when they played any team besides one another, the tournament is the most lopsided at a Games since 2010, when there was open talk over whether to keep women’s hockey as an Olympic sport.

That discussion is now more confined to social media and newspaper columns, and the International Ice Hockey Federation is even talking about expanding the women’s tournament, which this year grew to include 10 teams, to match the 12-nation men’s competition.

It could ultimately prove something of a competitive cure, and give more countries new incentives to support women’s hockey programs. In the meantime, though, another Olympic cycle is yielding an outcome that can feel as preordained as any in international sports.

It is true that the Americans and Canadians did not win every game by double digits, and that a spirited squad from the Czech Republic, making its debut in the Olympic women’s tournament, had the United States veering toward a debacle last week. But Monday’s semifinal matchups pitted Canada and the United States against teams they had already handily thwarted.

Monday brought more of the same. Canada routed Switzerland, 10-3, while the United States topped Finland, 4-1.

Names to Watch

• Kamila Valieva: The doping case surrounding the Russian figure skater, who will be allowed to compete but won’t be able to receive medals, echoes another dark Olympic era.
• Kaillie Humphries: The bobsledder, who left Canada after accusing her coach of mental abuse, won gold for the U.S. in monobob.
• Erin Jackson: The speedskater’s gold ended a U.S. drought and made her the first African American to medal in the sport.
• Chris Corning: The American snowboarder, who is more calculating and quiet than his competitors, thinks his sport has an image problem. He wants to fix it.

The bronze medal will be settled on Wednesday in Beijing, while the perennial American-Canadian clash for gold will be played on Thursday (Wednesday night in Canada and the United States).

North American players insist that women’s hockey is rapidly nearing more consistently engrossing competition because of increased spending and interest around the world. Their game, like many other women’s sports, is in catch-up mode; men’s hockey made its Olympic debut 78 years before women’s hockey.

“The gap is definitely shrinking, which is awesome from a 30,000-foot viewpoint,” said Hilary Knight, an American in her fourth Olympics. “From a competitor standpoint, you always want to win, but it’s wonderful to see other countries investing more in women’s ice hockey and also allocating resources because that’s really what the different teams need to compete.”

As the American captain, Kendall Coyne Schofield, put it: “If they don’t have the tools to be successful, you’re handing them a sentence that doesn’t allow them to be successful. That’s so often the case in women’s sports: Go out and be out as good as the men with half of the resources.”

Both women have sought to improve pay and brighten the sport’s spotlight. The battle for public attention, though, is relentless, and there are still entrenched inequities in player development, even in a women’s hockey power like the United States. In a report last year, for instance, investigators said that the N.C.A.A. had spent more than $9,800 per student who participated in its national men’s hockey tournament in 2019 — and $3,421 per player in the women’s competition.

The headwinds notwithstanding, there have been signals of possible pitfalls ahead for the Americans and Canadians, evidence that North American teams have seized upon to energize the public — and themselves — that their opponents are drawing closer.

European expectations have stayed tempered anyway.

“It’s gotten a lot better where other countries are giving the U.S. and Canada a hard game, but I don't think we can say that they’re not the favorites,” said Zuzana Tomcikova, the Slovak goalie in 2010 game that the Canadians won, 18-0. “Europe is coming. It’s getting there, and, if you look at it one way, slowly because it’s going to take years until other countries are going to be able to compete with the U.S. and Canada.”

Tomcikova, who predicted the Czech team’s potential to induce some North American heartburn in Beijing, sees two developing, if far from quick, strategies to growing the game.

One is the simple fact that women’s hockey, populated with elite players who remember when they were the only girls at their hometown rinks, is more visible than ever before, with widening television exposure encouraging the next generations of players to start training sooner. Another is the kind of training available, with greater sophistication, more frequency and easier access to high-quality coaching and competition.

Monday, though, showed how far the game has to go. In just more than three minutes, Canada scored five goals. Switzerland had gotten off just two shots.

So Braendli and Switzerland will play for bronze.

“Playing for a medal, it doesn’t matter what kind of medal it is,” she said. “It’s a huge deal.”

It was also, just about everyone knew, the best anyone beyond North America could have aspired to this time.