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There are no ties in the NHL. At least not since 2005 when the league instituted a rule that calls for a "shootout" during which the opposing teams alternate taking a "penalty shot" to break a tie after the designated "overtime" period. Some definitions to explain all of the quote marks in this opening paragraph:

OVERTIME

Every NHL game goes into overtime when the score is tied after three 20-minute periods. Overtime during the regular season is five minutes and involves just three skaters (a combination of forwards and/or defensemen) plus a goalie on each side. The first team to score gets two points for the win and losing team gets one point in the standings. It makes for lots of offense and some quick endings to games because superior playmakers thrive with more open space on the ice. In fact, some coaches don't even ice a defenseman in their OT lineups because they are banking on their own playmakers to control the puck in a wizardry flow.
Before explaining the shootout rules, one important distinction about NHL overtime: The five-minute overtime and shootout are only deployed during the regular season. There are no shootouts during the Stanley Cup Playoffs. If teams are tied, they get a normal between-periods rest time, then head back to the ice for a 20-minute fourth period. The first team to score is the game winner and the defeated team lose ground in the best-of-seven series (first team to four victories wins the series).
Playoff overtimes are legendary and, all due respect to playoff beards, make hockey so especially fun to watch in April, May and June. Some overtimes are famed for length--second overtimes (a fifth 20-minute period) are not uncommon, players hydrating and eating for energy between periods. Other memories stem from unlikely heroes scoring the goal because he had "fresh" legs from not playing much during regulation. Some overtimes decide a series and, arguably, can propel a team to a decade of Cup contention.
NHL overtimes bear their own set of statistics. Two-thirds of regular-season overtimes end with a winning goal. That goal is typically scored two-plus minutes into the overtime period.

SHOOTOUTS

If a regular-season game is tied at the end of the five-minute overtime, the game goes to a shootout, with each team given three "penalty shots" (will explain). It is possible that only two penalty shots are completed by each team-one team would have to score twice while the other misses twice.
If the score remains tied after three attempts each in the best-of-three scenario, the shootout will go to format in which each team sends out a different play to attempt to score. If one player scores, the other must score to continue to the next round of the shootout or else the scoring player's team wins. If both players miss, the shootout goes to the next round.

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The "penalty shot" is used during games when an offensive player is clearly on a breakaway toward the defending goalie when a defending player hooks, trips otherwise impedes the offensive player's path. There's a bit more to it, but awarding penalty shot is a judgment call for referees and they tend to be rare (though there was one just this week during an overtime period).
Before a penalty shot commences, players from both teams move to the ice in front of their respective benches to clear the way. The referee places the puck in the face-off spot at the center circle and signals the penalty can begin. Once the player touches the puck, he must keep it moving toward the goal line at all times until he takes the shot. The puck cannot stop during the shot attempt or it is disqualified. The play is considered complete once a shot is taken or the puck crosses the goal line. There are no rebounds.
The goalie for each team defends the same goal where he played the third period. The goalie must remain on the goal line until the offensive player touches the puck. From that point, the goalie may do anything to stop the puck, except throw his stick or any other equipment.
The NHL rulebook is lengthy and not exactly light reading. But here is an excerpt to explain other nuances of the shootout:
Rule 84.4-Shootout: …No player may shoot twice until everyone who is eligible has shot. … Regardless of the number of goals scored during the shootout portion of overtime, the final score recorded for the game will give the winning team one more goal than its opponent, based on the score at the end of overtime.
There are other shootout guidelines that vary from interesting to weird:

REGULATION & OVERTIME WINS (ROW)

The five-minute, three-on-three overtime encourages scoring, which decides games. The shootout absolutely is designed to decide winners and losers in a timely fashion for both teams and fans.
What NHL general managers determined a few seasons ago is that regulation and overtime wins should count more in the standings than shootout wins. That's why there is ROW column in the NHL standings. At the end of the season, the first tiebreaker for teams with the same number of points is the number of regulation and overtime wins or ROW.
Shootout wins do not count in the tiebreaker formula. The thinking is coaches and players will be motivated to win in overtime. It has been the difference between making the playoffs and missing. In the 2015-16 season, the Boston Bruins and Detroit Red Wings in the 2015-16 each finished with 93 points. The Red Wings qualified for the postseason over Boston because they had 39 ROW to the Bruins' 38.