Given the Dallas Stars' OT marathon to take their series over the San Jose Sharks, you might want to place a wager on the Detroit Red Wings to take Game 1 and, possibly, the series.
Since the 67/8 Expansion, only five series have ended with a triple (or better) OT game. With a short turnaround to the next series, that dog-tired hockey team was dragging and quite naturally lost Game 1 of the next series.
The NY Islanders beat the Caps in the memorable 4-OT Easter Sunday marathon Game 7. Two days later they lost to the Flyers and fell behind 3-1 in the series before getting their legs and pushing that series to seven before losing.
The Lightning beat the (snakebit again!) Caps in the 3rd OT. That left the 'Ning with little left in the tank after a four-day break and the Devils shut them down and out 4-0 in Game 1 of their Eastern Conference Semi-Final. Worse was to come as the 'Ning would have the tables turned on them as NJ beat TB in Game 5 in triple OT.
Of course, NJ after a triple OT win would lose Game 1 to their next opponent, the back then underachieving Sens. This happened despite an eight-day layoff so rest did them no good other than the fact the Devils did win end up beating Ottawa in seven before going on to take the Cup.
The only two success stories as far as these series ending post-OT marathons have been the '96 Blackhawks and the '99 Stars. Both had a full nine days off between series as their triple-OT series clinchers were in Game 4s vs. the Flames and the Oilers respectively.
Overall, in games following marathon OT (3 OTs or more) wins since the '67/68 playoffs, the winning teams are 11-10. In the actual series results, there is a clearer winner by 15 series taken to 6 lost to the marathon OT game winning team.
Draw your own conclusions, but if there's an early marathon OT game in any series, you're odds on (at a nice 2 1/2 to 1) that that team will take the series in question.