As the Capitals likely head into the playoffs, the Post Sports Live crew debates whether the Capitals are one of the top three teams in the Eastern Conference. (Post Sports Live)

Tuesday night is Hockey Night in Washington. With a regulation or overtime win, the Capitals earn the Southeast Division title and an automatic playoff berth. With a loss, well, then Thursday becomes Hockey Night in Washington.

It’s not often a team so clearly holds its fate in its hands. No scoreboard watching. No hoping for help from a division or conference foe. Win and you’re in. The Caps (52 points) face Winnipeg (51 after Monday night’s win in Buffalo). After Tuesday, the Caps have two games remaining, both at home: Thursday against Ottawa and Saturday against Boston; the Jets have just one, Thursday at home against Montreal. That gives the Caps an advantage.

Another advantage is this: The Jets will be playing the second of back-to-back games, in which they are 3-4 this season. One of those four losses was to the Capitals, who defeated the Jets twice in two days in Winnipeg last month.

“To be honest, a lot of us weren’t too positive going into those two games,” goalie Braden Holtby said Monday. Those two victories put the Caps solidly in the division hunt and knocked the Jets off-balance a bit. They’ve bounced back: On Saturday they completed a six-game homestand in which they earned 11 of a possible 12 points.

But the Caps have been hot as well. They were unbeaten in April before last Thursday’s loss at Ottawa. That was just their third loss in their past 15 games, and they were riding an eight-game winning streak at the time. They’ve won nine of their past 10 entering the Jets game.

It’s hard to believe those Caps are the same ones who started the season 2-8-1, out of sync with each other under a new coach and in a new system.

“We started off as bad as a team can start,” Matt Hendricks said. “To be where we are now, it’s great. We have the team the organization thought we had.”

They also have the goalie the organization thought it had last spring, when Holtby became an overnight sensation in the seven-game series win over Boston and the seven-game loss to the Rangers. Holtby was 7-7 with a goals against average of 1.95 and a save percentage of .935 during the postseason.

Yet during the Caps’ 2-8-1 start, Holtby was a startling 1-4, with a 3.5 goals against average and a save percentage of .857. He has found his game as the shortened season progressed, although he says he feels pretty much the same now as he did at the beginning of the season. He is now 21-12-1 with a 2.59 GAA, a save percentage of .920 and four shutouts (only three goalies have five).

“Braden has gone through a lot,” Hendricks said. “It’s been a long season for him. He had the great playoff run, then the lockout came and he was back down in the American league, even though I’m sure he felt like he was an NHL goalie, then he came back here and the pace is different, the shots are fast, the shots are hard. And he was going through contract negotiations.

“Once that was all done you could see him start to get comfortable back there. He’s got that confident feel. If he makes a mistake, he brushes it off and waits for the next shot.”

He was brushing off a lot of shots Monday at practice. After a Sunday off, the players gathered Monday morning for a team photo and then a workout of about an hour in preparation for the big game against the Jets. Despite the importance of Tuesday’s game, there seemed to be more more milling than drilling at Kettler, and the mood was loose.

Sure, Alex Ovechkin lost his good humor momentarily during a scoring drill when he failed to execute a pass. “Bang!” went his stick against the glass. Troy Brouwer skated over and offered Ovi his in exchange, and No. 8 was all smiles again. And why shouldn’t he be? He’s leading the league in goals with 30.

During shooting drills, players await their turns along the boards, joshing with each other and their coaches. Then they go like the devil at the goalie. So Holtby and Michal Neuvirth weren’t enjoying a lot of light moments Monday.

Afterward, Holtby talked about the importance of those two wins in two days at Winnipeg — “Before we were chasing them, now the tide has turned” — but emphasized that the Caps are not trying merely to get into the playoffs, but to make a run if — or when — they get there.

“We’re playing our game in order to improve going into the postseason,” he said.

First, though, they’ll have to win Hockey Night in Washington — no matter what night that happens to be.