There is no telling which team will win Game 1 of the Rangers-Senators Eastern Conference semifinal. But there is one safe bet about Thursday’s contest in Ottawa: Expect overtime.

Such is the price – or benefit, depending on how you look at it – of having Brian Boucher serve as the “inside-the-glass” analyst on CNBC. (He also will work Game 2 on NBC on Saturday.)

The guy, quite simply, is an overtime magnet. He worked seven games across five series in the first round, and six went to overtime – a total of 108 minutes and 21 seconds of extra action.

The only exception was a 1-0 game – the Senators’ victory over the Bruins in Game 4. So he’s 7-for-7 on one-goal games.

“I know, it’s crazy,” said Boucher, who joked he gets paid time-and-half for his overtime work. “It was a crazy first round, that’s for sure. I don’t know if it’s me. I just think it’s that the parity in the league is incredible. The games are so tight, it’s crazy. But fun to be a part of, that’s for sure.”

There were a record 18 overtime games in the opening round, even with none of the eight series going to a Game 7, part of yet another spring of volatile unpredictability in the Stanley Cup playoffs.

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“I think that’s what’s great about the game, for sure,” Boucher said. “There may have been people who picked Nashville to beat Chicago, but I can tell you that nobody picked them to sweep them. So that was a shocker.

“This year the proof is there that anything can happen. The games are so tight. The coaching is so advanced now, the pre-scouting is so advanced, there are really no surprises heading into a series . . . It’s a matter of execution. It’s a matter of discipline. And sometimes it’s a matter of puck luck.”

Boucher is not new to overtime drama. As a Flyer in 2000, he was the winning goaltender in a 2-1 victory over the Penguins that went five overtimes – the longest NHL game of the post-World War II era.

“I look back at it and yeah, I’m proud to have played in that game; it’s pretty cool to say you played in that game,” he said. “You never prepare for something like that. You never know it’s going to happen when you walk into the rink that day. It was a real neat experience.

“When you play in games like that it just shows how much you can dig inside yourself. You don’t realize you have that type of fight inside of you, just to hang in there like that. We did it in 2000, but you see year after year guys that are able to come up with performances you can’t believe can happen and you wouldn’t be able to picture it happening.

“That’s the greatest thing about the Stanley Cup playoffs. You see a different hero or guys just perform extraordinarily when you didn’t think they had it in them. That’s probably the biggest thing I take away from having an experience like that, but also seeing it year after year in the playoffs.”

Boucher said he recently watched a replay of that 2000 game with his 14-year-old son, Tyler. “He said to me, ‘Dad, this hockey is awful. Look at these guys, they can’t even skate.’ I said, ‘Well, listen, we’re talking eight periods of hockey here!’

“He’s like, ‘I don’t care how many periods; these guys are awful.’ It’s funny when you look back at it, it probably was pretty boring for him to watch when he knows the result. But at the time, when it was live and you have no idea the way it was going to shake out, it’s drama in the highest form.”

Boucher said the key for the Rangers will be dealing with the Senators’ disciplined commitment to their system, which many fans have deemed less than exciting.

“Ottawa’s structure is what stands out the most to me,” he said. “With their club they have a tremendous team structure. They’re well-coached in that regard. Their players have bought into their structure.

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“They play a 1-3-1 in the neutral zone, which means if they can’t get pressure in on the forecheck they’ll just kind of sit back and set up in the neutral zone. They’ll have one forward forechecking and then they’ll have two forwards in the neutral zone with their left defenseman jumping up in the neutral zone, so they’ll have three guys across.

“Then they’ll have their right defenseman sitting back, waiting for a dumped puck, and it’s usually Erik Karlsson, who’s a really good skater and he’s able to get to those pucks with ease and then able to break them out with ease. That’s the way they play.

The Rangers will have to find a way to get through the neutral in a timely fashion and still execute their offense, Boucher said.

“Not passes to the feet, not passes behind guys, maybe getting pucks to the red line and getting it in deep so they can get in on the forecheck and make it difficult for guys like Karlsson to find that puck,” Boucher said. “That’s going to be the key.

“If the Rangers do that, I think they should have some success in that series. If they can’t do that, then it’s going to be a matter of whether or not they can have the patience to play a 60-minute game and wait for their opportunities. Because I think what oftentimes happens is teams get impatient. They try and force things a bit much, and Ottawa makes you pay. They’ve got a couple of guys who can make you pay. That’s probably the biggest challenge.

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“With all of that, if it ends up being a five-on-five stalemate, it’s going to come down to special teams, and the Rangers in that first round their power play was not very good. It’s going to have to get better in the second round if they want to advance here.”

Boucher, 40, who played 13 NHL seasons for seven teams, said he is “not surprised at all” by what the Rangers’ Henrik Lundqvist did in the first round at age 35 after an uneven regular season.

“When you get to the postseason, you get a rejuvenation of sorts,” he said. “You realize, OK, we’ve been running this marathon a long way here and we’re starting to get to the end of the tunnel. The first round is still a long way to go; don’t get me wrong. But it becomes a singular focus now. The noise kind of settles down a little bit. You know you don’t have to talk about the whole league now, it’s talk of just select, certain teams.

“For players, I think it really rejuvenates guys. For a guy like Lundqvist, who is a big-game performer, he really enjoys that. I think that first-round matchup against Carey Price [of the Canadiens] was just what the doctor ordered for a guy like Lundqvist. You’re talking about a head-to-head matchup of two of the best goalies in the National Hockey League. He looked down at that other end of the ice and didn’t blink an eye.

“So for Lundqvist, I’m not surprised at all. I think that even at 35, he has the ability to steal games and steal series. As long as he plays the way did in round one, I wouldn’t count the Rangers out at all.”