For all Duke’s success/splendor/snootiness, the great school with the great coach conducts its daily business in the shadow of its greatest rival. A Duke fan cannot turn around in North Carolina’s Triangle without seeing two or three or 10 Tar Heel backers. Duke has produced one U.S. president – Richard Nixon – but only two North Carolina governors. UNC Chapel Hill, as it’s sometimes known, has seen 32 of its attendees become head of the Tar Heel State.

In 1986, Duke reached its first Final Four under Mike Krzyzewski. The moderator for NCAA press conferences was the arch UNC publicist Rick Brewer. A questioner mentioned that Duke’s lovely campus sits 8 miles from Chapel Hill. Brewer, to whom the question was not directed, nodded to the Duke contingent and said, “Imagine how much nicer it would be if you were only 7 miles from Chapel Hill.”

Under Krzyzewski, Duke became the nation’s biggest program – bigger than Kentucky and Kansas, bigger even than Carolina. In the Triangle, though, the Heels are forever the people’s choice. (A much larger school generates many more alums.) As grand as Coach K has been, even he hasn’t made Carolina disappear.

Krzyzewski has won five national titles. Carolina has won five since he arrived in Durham. Krzyzewski’s record against the Heels is 50-47. On Saturday night in New Orleans, he will face the ancient enemy for the 98th time.

As improbable as their meeting in the Final Four is – North Carolina is a middling No. 8 seed; Duke was the lowest-ranked of the No. 2 seeds – it’s also inevitable. There could be no Krzyzewski Farewell Tour without the participation of Krzyzewski’s nemesis. We neutrals can revel in the spectacle: Coach K’s last bow features the first NCAA Tournament meeting of Duke and Carolina. But here’s what the two sides are thinking:

Duke fans: “We have to play THEM?”

Carolina fans: “We have to play HIM?”

John Wooden took 10 national titles at UCLA. Those came over a span of 12 seasons. Had freshmen (mostly meaning Kareem Abdul-Jabbar) been eligible in 1966 and had the Bruins not faced N.C. State in Greensboro in the 1974 semis, the Wizard might have taken 12 in a row. Wooden’s 12 Final Fours came over 14 seasons. Only in 1975 was UCLA required to win more than four NCAA Tournament games.

In Krzyzewski’s 13 Final Four runs, it took four wins to reach the national semis. Those 13 Final Fours have come over 36 years. The Big Dance got bigger in 1975, offering admission to conference non-champs and dumping regional guidelines. That was also Wooden’s final season.

Krzyzewski and Duke have dealt with whispers – OK, screams – that they got the benefit of every officiating doubt. (Once upon a time, Coach K accused the ACC of hewing to a double standard, ref-wise: Then it was Dean Smith getting the calls.) Nobody has done these Blue Devils any favors. They were placed in a regional with Gonzaga, the No. 1 overall seed. They faced arduous opposition in Round 2 against Michigan State and in the Sweet 16 versus Texas Tech. They won both, barely.

Duke entered the NCAA coming off a double-figure loss to Carolina at Cameron Indoor Stadium in what ESPN presented as Coach K’s valedictory. It lost to a so-so Virginia Tech team by 15 in the ACC final. For one of the times over the past 35 years, the Devils weren’t seen as a chic Final Four choice. But when they overrode a five-point deficit to beat the Spartans, Krzyzewski reacted in a way he hadn’t over any previous Round 2 win. He was giddy. He’d begun to believe again.

Against Texas Tech, he did a little thing that became a huge thing. He switched to a zone, which Duke scarcely even practices, because his men couldn’t halt the Red Raiders’ drives. (Krzyzewski apprenticed under Bob Knight, to whom zone was his least-favored four-letter word.) That changed the game just enough for Duke to nose ahead and hang on. Even at 75, the greatest coach ever – yeah, I said it – is the greatest coach ever.

In a 1975 Final Four semifinal, Wooden’s UCLA outlasted Louisville in overtime. Wooden then announced the final against Kentucky would be his last game. Coach Joe B. Hall – who died in January at 93 – heard the news and knew his Wildcats, who’d already toppled an unbeaten Indiana, had no chance. Sure enough, UCLA prevailed 92-85.

This is a bluebloods-only Final Four, and not just in color scheme. These schools have 17 national titles among them. Any of them could win. The one coached by the GOAT will win. Not much in life is scripted. This ending seems written on the wind.