The mask rarely slips, but when it does it is all- revealing. At the conclusion of The Open Championship at Hoylake, the face of Tiger Woods, which had been carved in stone, dissolved in tears as relief, the joy of winning and the still-raw grieving for his father, his guiding influence, came in a flood.

On another occasion, at the 2004 Ryder Cup, on day one at Oakland Hills, we saw another slip. On the 18th tee, Woods waited for his foursomes partner, Phil Mickelson, to drive. It was a critical moment for a host of reasons: Woods and Mickelson needed to win the hole to beat Darren Clarke and Lee Westwood; they needed to redeem themselves after losing their morning fourball match against Colin Montgomerie and Padraig Harrington; they needed to halt Europe’s runaway momentum; and they needed to spare the blushes of their captain, Hal Sutton. Sutton’s match strategy was simple: use Woods and Mickelson, the two best players in the world, as a double- barrelled blunderbuss.

Mickelson’s drive was grotesque, a carving slice that sent the ball away from the fairway, even away from the golf course, for it came to rest beside the fence marking out of bounds. Woods’s face betrayed disgust, followed by fury. When he arrived at the crime scene, he took a penalty drop and hacked out the ball. The hole and the match were lost; Europe finished the day ahead by 6Å points to 1Å and went on to a crushing victory.

Those two snapshots expose the strange duality of the greatest golfer of the age, and represent the conundrum of the Ryder Cup at the K Club. As an individual, Woods is peerless and in the prime of his maturity and accomplishments. But as a team man, and as a Ryder Cup player, he has been fallible, ordinary and selfish. And on this occasion the problem of Woods, as we might term it, is more relevant to the outcome than ever. In every Ryder Cup match before this one, the United States were favourites and had the greater strength in depth, while Europe (and Great Britain and Ireland before 1979) had to rely on great deeds from a few notables while hiding as best as possible the shortcomings of others. Now it is the other way around. Europe are favourites and have the stronger 12; the US will rely on their shining stars: Mickelson, Chris DiMarco, Jim Furyk and, above all, Woods. If those four, who will probably play in two dynamic duos, reap a bountiful harvest of points, the US will be on their way to victory; if not, they will be scuppered.

Woods has played in four Ryder Cup matches, starting at Valderrama in 1997. He has played in every round, 20 individual matches. Of those, he has won seven, halved two and lost 11. In fourball and foursomes matches, Woods has had nine different partners in 16 matches. He has combined with degrees of empathy varying from warm to frosty, but any partner, it seemed, diluted his power.

Meanwhile, from his Ryder Cup debut to the present day, he has won 11 major championships, far more than the combined total for all the other Ryder Cup players during that period.

The roots of such individual success and comparative failure in combination lie deep. Almost from the cradle, Woods was taught by his father that he would be special, a champion in an exclusive sport. Only one partnership was envisaged, that between father and son.

In the Ryder Cup Woods has appeared disconnected from the team. At Valderrama his captain, Tom Kite, expected far more than his two points from five. At Brookline the only match he has played in which the US won, he was the only member of the team reluctant to celebrate a remarkable comeback from a four-point deficit with the singles to play. Woods was roused from his sleep to join the party, but soon returned to bed. Further evidence the Ryder Cup ranked low in his priorities came the week before the 2002 match at The Belfry. While playing the American Express championship at Mount Juliet, he was asked which event he would rather win. “This one,” he said. When asked why, he said: “One million reasons.” The first prize at that event was $1m. Woods, one recalls, was among the militants in the American team campaign for payment for Ryder Cup duty.

With the sorry catalogue concluding with two points from five during the rout of Oakland Hills, it would seem likely that the pattern will continue, that Tiger cannot change his spots.

But there are two counter- arguments. The first takes us back to Hoylake and that mixture of achievement and emotion. “It just came pouring out,” he said when he recovered his composure. “And of all the things that my father has meant to me and the game of golf, I just wish he could have seen it one more time.” What his father would have seen and appreciated was the completion of Woods as a championship golfer. At Hoylake we saw maturity and a calm, commanding brain. In the absence of a credible challenger, Woods has been left with one primary objective: beating Jack Nicklaus’s record of 18 majors. At Hoylake he proved that he has learnt to be Nicklaus’s equal in the brain department, in the assessment of risk and reward on every shot, in making good decisions and executing them with detachment in the most vital circumstances. When he won his 12th major, the US PGA championship in August, he underlined the likelihood that eclipsing that record is just a matter of time. That leaves the Ryder Cup, the irritating blot on his record that Woods will badly want to eradicate.

Further, he has at last found a partner in whom he has full confidence. The revelation occurred at the President’s Cup, the biennial match between the US and the Rest of the World, excluding Europe. On the first day Woods was partnered with Fred Couples and lost. Thereafter, he was paired with Jim Furyk. They were unbeaten in three matches, winning two. They even helped each other in the reading of putts, an unthinkable collaboration between Woods and most of his previous partners.

In the greater scheme, the first-round losses suffered by Furyk and Woods in the World Matchplay on Thursday were insignificant. What matters is whether they can forge a winning Ryder Cup partnership, and whether Woods can deliver for his team and country.