Tiger Woods told a story Tuesday, and it is worth noting, because Woods is not exactly half of golf’s Brothers Grimm. Gather round, then, and pull up a chair.

“I played with Jack and Arnold on Wednesday in ’95,” Woods said at Augusta National. A practice round in his first Masters, when he was still a teenager, half a lifetime ago. This was before the Jack in question (Nicklaus) said that Woods would win more green jackets than he and the Arnold in question (Palmer) combined (10). This was before Woods won the first of his 14 major championships. This was when potential hardly seemed a burden, when it only brought possibilities.

That day, Palmer asked if the young Woods would like to put some stakes on the game.

“Well, I don’t have any cash,” said Woods, still an amateur.

“Don’t worry about it,” Palmer said. “Just play hard.”

That day, Woods yapped away on every hole. “What do you do here? What do you do here?”

“I’m sure they got sick and tired of me,” he said.

As a storyline, the evidence — television ratings, attendance, Q-rating — suggests the golf-watching public simply doesn’t tire of Woods, love him or loathe him. They didn’t when he wore a Stanford cap and stayed in the Crow’s Nest, the room atop the clubhouse that serves as home to any amateur entrants. And they don’t now that he’s 36, now that he will open his 18th Masters on Thursday. The circumstances have changed, because he is now the one dispensing tips, the legend to be tagged along with. His intentions, clearly, have not.

“I’m here for the green jacket,” he said Tuesday.

That seems a reasonable assessment. More so than in 2009, when he played here in his first major championship since missing more than half a year after reconstructive surgery on his left knee and leg.

More so than in 2010, when this served as his first tournament following a self-imposed layoff following a sex scandal. More so even than last year, when Phil Mickelson was the defending champion, and Woods lagged behind, still in the midst of rebuilding his swing, winless since November 2009.

But on the first weekend of March, Woods shot the best final-round score he’s ever had, a 62 that put pressure on leader Rory McIlroy to close the Honda Classic.

He was, there, “starting to hit shots where he would hold it against the wind or drive it with a little bit more shape on it,” said Lee Westwood, a playing partner that weekend, “where you need to have total control.”

Woods then answered any further questions — about his health, the state of his game, his mental fitness — by crushing the field at the Arnold Palmer Invitational in his most recent appearance. That win, his 72nd on the PGA Tour, resonates here.

“I think it’s a huge win for him to be successful this week,” Mickelson said. “I think it really increases the opportunity, because it gives him a lot of confidence and it makes being in that situation after having already closed the deal a lot easier to do.”

And then, Mickelson offered the remark that shows Woods might really be back. “Sucks for us,” he said, chuckling.

This Masters could be the tournament when golf returns to its previous reality, one in which Woods contended in nearly every major, when his pursuit of Nicklaus’s record 18 major titles was a weekly discussion. Tuesday, as he hit shots on the range here, his work with Sean Foley — the previously obscure coach with whom he began working in late 2010 — seemed complete.

Woods has repeatedly described his swing overhaul as a “process”; he did so again Tuesday. Still, it’s clear he believes his game is, in some ways, better than when he was at the height of his powers.

“Consistently, with this kind of control, it’s been a few years,” he said. “But as far as having the speed and the pop in my game” — essentially, the length and power — “it’s been a very long time. I think I have more shots than I did in 2000.”

In 2000, Woods won three majors. Yet from the outside, that doesn’t seem an absurd notion. He is, certainly, longer. He can shape the ball more consistently.

“We could all look at Tiger’s swing [two years ago] and see five or six or seven things that we didn’t like, and so would the great instructors,” said former Ryder Cup captain Paul Azinger. “But if you look at Tiger’s swing now, if you were picky, you might find one or two. . . . He is more fundamentally sound now than he was before he had the accident.”

If that’s true, then his status as the favorite seems appropriate. Since his last Masters title, even with his physical and personal problems, he has finished no worse than tied for sixth. That includes ties for fourth each of the past two years.

From the 2002 U.S. Open through the 2004 PGA Championship, Woods played in 10 majors without winning one — previously the longest drought of his career.

This is the 11th major Woods has played since his most recent victory, the 2008 U.S. Open. The spell seems likely to break at some point.

“One thing is for sure about people that are winners,” Westwood said. “When they get back into the situation of trying to win a tournament, they know how to generally finish it off.”

That day back in 1995, Woods hadn’t yet finished anything off. His practice-round playing partners had combined for 25 major titles.

Woods was two years from taking his first. The story that day ended with Nicklaus, Palmer and Woods on Augusta’s par-3 course, messing around for nine more holes. He listened to Nicklaus.

“I thought, ‘You know, I never looked at it that way,’ on some of the holes,” Woods said.

Some day, that may be Woods, hanging on to memories rather than creating them. But he is here this week feeling as if he has much more of a story still to tell, and many more years to tell it.