'I realized that it matched the number on the entry form of the British Open,' he said.
That was Monday morning in Austin, Texas.
Twenty-four hours later, Estes was dressed in blue jeans and a shirt as he stood outside the Royal & Ancient Golf Club, soaking up a sun-splashed view of St. Andrews Bay and anticipating a chance to play the Old Course.
He might have to settle for only a practice round.
What makes this appearance so compelling is that Estes wasn't even guaranteed a spot in the field when he decided to fly through the night across the Atlantic Ocean.
He was the second alternate when he left Texas. By the time he arrived in Scotland, Padraig Harrington had withdrawn following the death of his father, and Estes was next in line.
The 39-year-old Texan still might not being teeing it up Thursday, but so what?
'I wasn't worried that I might not get in. I would be more concerned if my number was called and I wasn't there,' Estes said. 'This is the most prestigious championship in the world, played on the most famous course in the world. And it was killing me that I wasn't here.'
Estes played his first major in 1990 at the British Open, when he qualified at nearby Ladybank, then missed the cut at St. Andrews. He returned in 1995 and finished three shots out of a playoff, done in by a three-putt late in the final round. Five years ago, he played four consistent rounds and tied for 20th.
He loves St. Andrews.
More than that, Estes has deep respect for golf's oldest championship. He would have risked flying 5,000 miles as an alternate even if this Open were held at Royal Birkdale or Carnoustie.
The same can't be said for some other Americans.
Some of them didn't even bother trying to qualify, even though the R&A has made it easy by staging final rounds of qualifying in the United States. A year ago, 52 tour players didn't show up for the 36-hole qualifier at Congressional, and six players snubbed the R&A further by not calling to say they weren't coming.
The R&A even offered a spot for the highest finisher in two straight PGA Tour events, the Western Open and the John Deere Classic, and two spots for PGA Tour players atop a special money list. Billy Mayfair captured one of those spots, then decided not to go to St. Andrews because he had 'personal and professional' commitments to honor.
'I love Billy,' Estes said. 'But he just doesn't get it. And it's a shame. I feel sorry he's not here.'
Arnold Palmer must feel the same way.
The King restored the Open to its glory when he came over to St. Andrews in 1960, leading a resurgence of American interest. Jack Nicklaus never thought twice about coming, recalling how Bobby Jones once told him that a great champion's career is not complete until he wins a British Open at St. Andrews.
Estes wants that chance, and a transoceanic flight with no guarantee he would play sure wasn't going to stop him.
Ditto for Brad Faxon.
Faxon couldn't play in the U.S. qualifier this year because it was opposite his CVS Charity Classic, a two-day event that has raised some $3 million.
Instead, he flew to St. Andrews with the odds against him. Faxon had to play 36 holes on the links of Lundin, where only three spots were available for 96 players. He made it by one shot.
'If you win a tournament like this, it changes your whole life,' Faxon said. 'And I'm not going to win it staying at home. There is a special feeling playing these links courses and competing in the oldest major in the world.'
Turns out Faxon did not have to qualify. Because five players have withdrawn through injury or a death in the family, he would have made it on his world ranking, which was above Estes.
Estes was in search of something to eat and then on his way to the practice range when Faxon, of all people, walked out of the clubhouse with his bag over his shoulder.
He looked at Estes and smiled, two Americans with a common love for the British Open.
'It's awesome that he came over,' Estes said.
Even more impressive was Estes' willingness to play, even realizing that his 17-hour trip to St. Andrews might turn into a waste of time.
Of course, Estes doesn't see it that way.
'I imagine there are some players who look back on their career and are kicking themselves that they didn't come over here more often,' he said. 'This is like the world championship of golf. In my opinion, this is the most important championship you can win.'
And what if he doesn't get into the tournament? How will he feel flying home?
Estes turned toward the Old Course and gazed out at the rolling links where golf has been played for 500 years.
'At least I get to play St. Andrews,' he said. 'And you never know when you're going to get that chance again.'