The cheer started on the 10th, when thousands of people broke out in one long, spontaneous shout of excitement as the ball landed hard by the pin. It’s been a long time since they have heard anything like it in Carnoustie, or anywhere else they play majors. It was unfamiliar, but unmistakable. The Tiger roar. It echoed around the links, and the rush of excitement spread wherever people were watching, or listening, to the golf. Tiger Woods was back, at last, and on the charge. By the time he had made it to the green, they had started chanting his name, beating out the syllables, “Tiger! Tiger! Tiger!”

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Even Woods was not sure he had this in him. Just this week he admitted “there were definitely points in time that I certainly thought I’d never play in this championship again”. And now here he was, at 4:15 on Saturday afternoon, top of the board, tied for the lead at six under par. It didn’t last. He dropped a shot, the only one he lost all day, when he made two bad putts at the par-three 16th. And then Jordan Spieth and the other late starters swept by him. But still, he finished in 66, five under, and come Sunday he will be in the hunt. Like he said: “It’s going to be fun.”

It was Woods’s best round at the Open since he shot 65 on the second day at Hoylake in 2006, and his best at any major since his 66 at the Masters in 2011. He could not even remember the last time he played like this in a major. “That was good, that was good, I played well today. I really did,” he said afterwards. “It’s been a few years since I’ve felt like this, not like this in one of these big four events. Given what happened [in the] last few years, I didn’t know if that would ever happen again. But here I am with a chance coming Sunday in a major championship.”

Woods had been smouldering all week. He shot even par in both the first two rounds, when he played steady, shrewd, golf. He wanted to avoid unnecessary risks, but the upshot was he was not winning too many rewards either. He hardly trusted himself to use his driver all week, but has been playing irons off the tee, which is one reason why he is leading the field in driving accuracy this week, when he is ranked 154th over the rest of the season. It was all ever-so-sensible and safety-conscious, as if he would not play his hand until he had the perfect cards.

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The crowd have been pulling for him anyway, because at his age, after everything he has been through, there’s something of the underdog about him. And as he came down the first fairway there was a loud and affectionate shout of “Ga’wn Tiger! We got ya’ back in Glasgae”, which must be what passes for a compliment in some parts. But truth is Woods had not given them all that much to shout about on the first two days. And he played it pretty steady through the first few holes here, too, the two birdies he picked up at the 4th and 6th offset by one he missed from close range at the 2nd.

Then Woods finally decided it was time to start gambling. At the 9th, he pulled out his driver. He had already used it at the 2nd and 6th, but this was the first time here. “We just thought that, with some of the pin locations, that if we missed on the correct side, that we could still have easy shots into the greens today,” he explained. Here he got lucky, the ball hopped over the bunker and fetched up in the rough. Then he raked in a long putt from 35ft, and rode the wave of good feeling right through the next two holes.

At the 10th, Woods hit a nine iron to a foot from 140 yards or so. And on the 11th he drove the green, and took two putts for this third birdie in three holes. Woods burned up the turn, so hot that he sucked up the oxygen of everyone’s attention. His partner, poor old Shaun Norris, had never experienced anything like it. “It’s crazy,” Norris said, “Absolutely crazy to think so many people can follow a person. There’s a couple of holes that people may be standing 15, 20 deep on each side. I think best word to describe it all is the way Russell Knox put it, it’s like playing with a mythical creature. It doesn’t feel real.”

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Norris smoked through a couple of packets of fags just trying to keep his head in the game. He did well to shoot 69 in the circumstances. Woods made one more birdie at the par-five 14th, and then his run dried up. He had an outrageous piece of luck at the 18th, where his tee shot was one bad bounce away from the burn. It stopped right on the bank in thick seagrass rough. Then he made an 80-yard pitch, which he said he’d “practised in the backyard” and a clutch putt from five feet. “That was big for me,” he said, “just to not finish with two bogeys on the last three holes, playing as well as I did.”

The par save meant Woods was in touch overnight. “At least I know that I will be there with a chance. They won’t be too far out of reach. If they get to double digits, I’m still only five back,” Woods said, “That’s certainly doable.” There’s a generation of golfers here at Carnoustie who have no idea what it’s like to tangle with Woods on the Sunday of a major. They are about to find out.