TAMPA -- Winning the Stanley Cup is a dream for millions of youth hockey players, and ends up remaining a fantasy for most.

Winning it twice is an incredible achievement. Moving beyond twice is when the really exclusive clubs start to come into play, and that is the opportunity at hand for many of the core members of the Chicago Blackhawks.

Seven Blackhawks (Jonathan Toews, Patrick Kane, Patrick Sharp, Marian Hossa, Duncan Keith, Brent Seabrook and Niklas Hjalmarsson) are four wins from having their names engraved on the Cup for a third time.

Their quest begins Wednesday with Game 1 of the 2015 Stanley Cup Final against the Tampa Bay Lightning at Amalie Arena (8 p.m. ET; NBC, CBC, TVA Sports).

"I definitely feel lucky to be with this great group of guys and again on the dance floor competing for the Stanley Cup," Hossa said. "It's a special moment, even if this is my fifth time in the Finals. I've won two Cups, but every time you get here it is exciting. It is something new with new teammates and it is amazing to be here again."

In the 121 years since the Stanley Cup was first awarded, 238 players have had their names engraved on the silver trophy three or more times. Most of those players came before the 1990s, before an age of parity that does not allow for the dynasties that used to rule the NHL.

Since the Edmonton Oilers last won the Cup, in 1990, ending a run of five titles in seven seasons, 24 players have had their name engraved on it three or more times. That means about 10 percent of the players with three or more titles have done so in a time span that is about 20 percent of the life of the Cup.

There is one active NHL player with his name on the Cup three times, and that is Justin Williams, who won it in 2006 with the Carolina Hurricanes and in 2012 and 2014 with the Los Angeles Kings.

That group of 24 would grow by 29 percent if Chicago can defeat Tampa Bay and secure a third championship in six seasons.

"It would be special," Kane said. "You have that opportunity in front of you, right, and you want to take advantage of it. These are moments you don't want to let slip away and look back on and say you wish you'd done this or that. It is a great opportunity.

"The thing that I like about our team is we've learned from our mistakes in the past. We were in this situation last year in Game 7 of the Western Conference Final, and you come back a year later and take advantage of that opportunity. We realize the magnitude here. We realize you don't get this opportunity every year or every couple years even. We need to take advantage of it."

The 24 players who have won the Cup three or more times in the past 24 seasons is dominated by the Detroit Red Wings and New Jersey Devils. Those are the only two teams with three championships (Detroit has four) since the start of the 1990-91 season.

Four players won three times with the Devils, and nine won three or four times with the Red Wings. Parity has ruled in the NHL since the end of the Oilers dynasty. No team has won the Cup three times in a row in either of the past two decades, and none has repeated as champion since the Red Wings did in 1997 and 1998.

The Blackhawks do not want to talk about the idea of a dynasty on the eve of the Stanley Cup Final. Calling this group one is debatable and needs the "modern" tag in front of the word anyway.

Still, what the Blackhawks have accomplished -- five appearances in the Western Conference Final and three trips to the Cup Final in seven seasons -- while keeping so many pivotal players together is incredible.

"It's not easy to do that. When we set out years ago, we wanted to be a team that continually had a chance to win the Cup," Chicago general manager Stan Bowman said. "So every year that's our goal. There's a lot of factors that go into it. Ultimately it's the players. They're the ones that get on the ice.

"The job our coaching staff has done has been outstanding to prepare these guys and to make the adjustments. We've had a lot of continuity in our organization, which I think helps. If you look back at the organizations that have been able to sustain success, they have stability from the top, with [owner] Rocky [Wirtz] and [president] John McDonough, all our staff, our scouting staff, the development group we have -- they all play a part in this."

While the Blackhawks stand four victories from the precipice of more history, the future is less clear than usual. There are potential salary-cap constraints, and this core group of seven may end up being six, or even five, by next season.

It could also be seven, depending on how creative Bowman can get. There are others, particularly Brandon Saad and Teuvo Teravainen, who are squeezing their way into the long-term plans in Chicago.

The future might be fuzzy, but the present is quite clear: These Blackhawks have a chance to do something rare and remarkable in the next couple of weeks.

"There's a lot of talk about [changes coming] all the time, but we've been through this before," Bowman said. "It's a challenge. The salary cap, it's a system we all play under. We've been through it before. There's changes to be made to every team, and we're no different. We certainly have expectations that we want to keep this going. The main players are going to be back. You have to rely on some young guys to step into bigger roles. We're seeing that play itself out here over the season, players like Saad and Teravainen, young guys that are going to play bigger roles going forward. We have some other young players that are going to get opportunities next year as well.

"I think that's not so much the focus for this right now. We do get a lot of questions on that, but I think we're pretty excited for the game tomorrow night, and we're focused on that. We'll take care of the other stuff over the summer."