This is a 2017 stat for regular season OT. Guessing playoffs are even greater:
According to STATS, 23.6 percent of games since the 2005-06 season have gone to overtime, but in the last few seasons games are going beyond regulation at an even higher rate. The seasons with the most overtime games are 2013-14 (25 percent), 2014-15 (24.9) and this season (24.8 through Feb. 10).
OK - found 3 year old data for playoff games:
Rate of NHL playoffs going to the overtime
In the past 20 years, from the 1996-1997 NHL season to the 2015-2016 NHL season, there have been 1646 playoff games played(2). Thus, the 20-year average (376/1646) is around 22.8%.
Montreal won 10 OT games in the 93 playoffs.