2018 - Le Golf National
After the thumping 17-11 victory at Hazeltine two years earlier, there's a feeling that this American team could be about to embark on a new spell of dominance. They boast plenty of fresh, hungry players and Tiger Woods and Phil Mickelson are drafted in as wildcards to add experience.
They go into the match at Le Golf National in Paris as odds-on favourites and there are mutterings that Thomas Bjorn has played it too safe by opting for four experienced wildcards rather than exciting talents such as Matt Wallace.
The USA win the morning fourballs 3-1 but Europe sweep the afternoon foursomes to lead 5-3 overnight.
With the course set up to negate the Americans' big hitting, Europe extend their lead to 10-6 after day two with Francesco Molinari and Tommy Fleetwood - dubbed 'Moliwood' - the stars of the show as they win all four matches.
Europe, the 13/10 underdogs before a ball was hit on Friday, win the Sunday singles 7.5-4.5 to close out a dominant 17.5-10.5 victory.
2016 - Hazeltine
As usual, the Americans look far stronger on paper, as Europe field six rookies.
Davis Love, the beaten skipper in 2012, captains again and is 4/7 to guide his team to victory and gain revenge for the stunning loss at Medinah four years earlier. Europe are 2/1.
The tone is set on day one as the hosts sweep the opening foursomes 4-0 although Europe rally with a 3-1 win in the fourballs to reduce the overnight deficit to 5-3.
With all the Americans contributing, they pull away to lead 9.5-6.5 after day two and there is to be no miracle comeback for Darren Clarke's men on Sunday.
The USA win the singles 7.5-4.5 to score a convincing 17-11 victory and win the Ryder Cup for the first time since 2008.
2014 - Gleneagles
Despite a feeling that Gleneagles could suit a US side desperate for revenge, Europe justify their status as 4/6 favourites by making it six wins out of seven in the Ryder Cup.
That leaves the Americans winless on European soil since their 1993 triumph at The Belfry.
Trading at just under 2/1 before the off, Tom Watson's men win the morning fourballs 2.5-1.5 but end the day 5-3 behind after taking just half a point from the afternoon foursomes.
Scorelines from those two sessions are repeated on Friday to put Europe 10-6 up ahead of the singles and Paul McGinley's meticulous planning is further rewarded on Sunday as his team run out convincing 16.5-11.5 winners.
2012 - Medinah
Later termed 'The Miracle at Medinah' after Europe's seemingly impossible come-from-behind victory, Jose Maria Olazabal's men start the event as 6/4 underdogs.
Their odds get bigger and bigger as the Americans (4/5 at the off) dominate the opening two days.
Trailing 5-3 after day one, Europe go 10-4 down on Saturday before an inspired Ian Poulter birdies the final five holes of his four-ball to reduce the gap to 10-6 overnight and give the visitors fresh hope.
A potential European fightback looks to have been snubbed out on a never-to-be-forgotten Sunday though as the hosts hit 1/33 with not enough blue on the board.
But Justin Rose holes a monster putt across the 17th green and a 12 footer on the last to somehow win his match against Phil Mickelson, Rory McIlroy beats Keegan Bradley despite nearly missing his tee-time and Martin Kaymer nails a nerveless five-foot putt to secure the 14pts that keep the trophy in European hands.
Tie backers at huge prices are rubbing their hands with glee when, in a match now dead, Tiger Woods looks set to beat Francesco Molinari.
But Woods takes three to get down from the side of the green at 18 and concedes the Italian his putt.
That act of generosity turns the 14-14 tie into an incredible 14.5-13.5 victory for Europe.
2010 - Celtic Manor
Much has changed two years on from defeat at Valhalla and Europe, with Colin Montgomerie now skipper, are clear 4/7 favourites to win back the trophy at Celtic Manor.
As a regular European Tour stop, it's a course they know well and Corey Pavin's unfancied visitors drift to 2/1 at the off as their waterproof suits start falling apart in the bad weather.
It's an awkward betting heat as the foul weather and lengthy delays mean the format is changed to two sessions of six matches each on Saturday and Sunday, with the singles carried over to Monday.
The USA trade at odds-on after opening up a 6-4 lead but Monty's men fight back to lead 9.5-6.5 going into the singles and they just have enough to get over the line.
Graeme McDowell is the hero, defeating Hunter Mahan in the final match to secure victory by the minimum margin.
Tiger, despite being rusty after his break from the game due to a sex scandal and further injury, is joint top US scorer with playing partner Steve Stricker.
2008 - Valhalla
After being on the end of two absolute demolitions in 2004 and 2006, the Americans need fresh thinking and they find the perfect candidate in feisty Paul Azinger.
Azinger divides his team into carefully selected 'pods' and turns the tables on Nick Faldo's men by using the old Euro trick of declaring his side the clear underdogs.
It's a statement helped by the fact that World No.1 Tiger Woods is out injured.
The odds say Azinger is right. Europe are put in as 8/11 favourites, with the Americans 6/4 outsiders.
Day one is a disaster for Faldo's men as they fail to win a single match and trail 5.5-2.5 but they're cut back into 12/5 after having the better of day two and reducing the US lead to 9-7.
The canny Azinger outwits Faldo again in Sunday's singles and the Samuel Ryder trophy returns Stateside for the first time since 1999.
Fate of the favourites
2018 - LOST
2016 - WON
2014 - WON
2012 - LOST
2010 - WON
2008 - LOST
The favourite has only prevailed in three of the last six Ryder Cups so that 50% strike-rate should make punters wary of backing Steve Stricker's side this time.
Two of the three defeats were suffered when the favourites were the away team - Europe failing in 2008 and USA not able to justify their status in 2018.
An odds-on favourite away from home is the danger recipe for punters so bettors were correct to oppose the Americans on French soil last time.
However, given their home advantage this year, the USA look a more robust betting proposition.
In short, Padraig Harrington's men have a huge task on their hands.