The Post Sports Live crew offers bold predictions for which teams will advance to the NCAA Tournament championship game, and which team will win it all. (Post Sports Live/The Washington Post)

Larry Shyatt, the basketball coach at Wyoming, has been to the Final Four more times than he cares to count. Twice, he enjoyed the experience — in 2006 and 2007, when he was Billy Donovan’s top assistant at Florida and the Gators won back-to-back national championships.

Other years weren’t quite as much fun. So this year, he decided to skip the trip here and take his wife on vacation.

“Enough is enough,” he said. “You go to the Final Four, you spend hours and hours in that lobby hugging people you can’t stand. I can miss that scene for a year.”

Unless Florida makes it to Monday’s final. Then he’ll make it here to watch his old boss and old school play for a championship. “But I won’t go near the lobby,” he said. “Just the game.”

“The lobby” is basketball’s answer to Nathan Detroit’s famous “permanent, floating crap game” in the musical “Guys and Dolls.”

On Thursday, the lobby was awash with coaches checking in to the hotel, checking in for the coaches’ convention and looking for old friends. Or old non-friends. There were very few handshakes. Almost everyone hugged.

Not far from the front desk, UCLA Coach Steve Alford was talking to Craig Neal, his former assistant who succeeded him this season at New Mexico. As Neal and Alford talked, Southern Cal Coach Andy Enfield walked past.

Alford and Enfield took some not-so-subtle shots at each other this past season. Enfield was quoted as saying, “If you want to play slow, go to UCLA.” Without ever mentioning Enfield or USC, Alford responded by saying he was pleased with where his team was and noted that the Bruins were ranked in the top 10 nationally in most offensive categories. “They can say whatever they want,” Alford said without ever identifying who “they” was.

Now, as Enfield approached, everyone was all smiles.

“How are you guys?” Enfield said in a friendly tone, though not slowing down as he spoke.

“Good, Andy,” Alford said. “Good to see you.”

There were no hugs. UCLA beat USC by 34 at Pauley Pavilion and by 10 at Galen Center this past season. There probably won’t be any hugs next year either.

The lobby floats, but it always looks the same: It’s a sea of sweatsuits and logos, coaches everywhere, ranging from a kid in a “Maret Basketball” outfit to Hall of Famers. Former Georgetown coach John Thompson Jr. is the king of the all-lobby team, a presence every year.

On Thursday afternoon, Thompson camped out in the hotel’s coffee shop with old friend Dave “Smokey” Gaines, the former coach at Detroit Mercy and San Diego State. Thompson and Gaines were never alone — people stopped by the table almost nonstop to (metaphorically) kiss Thompson’s ring.

Thompson and Gaines are both 72 with long basketball memories. As they watched the parade of young coaches move past the table, they talked about Wil Jones, the former University of the District of Columbia coach who died last month at age 75.

“Willie was the second-best player to ever come out of D.C.,” Thompson said. “Rabbit [Elgin Baylor] was the best. Willie was next. He could play and he could talk and he backed it up.”

Jones was 5 feet 9, 13 inches shorter and probably about 150 pounds lighter than Thompson. Jones won a Division II national championship at UDC in 1982. Two years later, when Thompson won a national championship at Georgetown, Jones was asked about what it had been like playing against Thompson in the D.C. schoolyards in the late 1950s.

“He was nothing but a . . . jump shooter,” Jones said. “That’s why he coaches his players to be so mean and tough — because he wasn’t.”

Thompson laughed when that line was repeated to him Thursday. “He always told me I was the first European-style player,” he said. “I played European-style before there was a European style.”

Jones was a Division II all-American at American but never played in the NBA. “If he was so good, why didn’t he ever play in the NBA?” Gaines asked.

“Because he was 5-9 and he was black,” Thompson said. “Back then there were only eight teams and there were quotas.”

The Hall of Fame was on the minds of many in the lobby. The announcement on who will be inducted this September won’t be formally made until Monday, but already word had leaked out that both Spencer Haywood and Alonzo Mourning, one of Thompson’s former stars, had made it.

Thompson, who was elected to the Hall of Fame in 1999, was talking about how frustrated he was the first two years he was nominated but didn’t get in.

“I remember when I didn’t get in the second time, one of the first calls I got was from Mike Krzyzewski,” he said. “He was really angry. He said, ‘John, this is wrong. There’s no way you shouldn’t be in there.’ I never forgot that.

“All I knew was there were a lot of guys in there whose butts I’d been kicking. Made me mad. But then I got in and all was forgiven.”

He laughed and turned to Gaines. “Time to get going,” he said. “I got work to do.”

Thompson is here doing the three games on radio as an analyst. That makes him unusual for a retired coach in that he has more to do than just work the lobby.

Perhaps the most frazzled person in the lobby Thursday afternoon was George Washington Coach Mike Lonergan. You would think Lonergan would be relaxed. His team won 24 games this season, and he recently signed a new contract that will keep him at GW through 2021. He was on the short list for the Boston College job but told the school he had no interest in leaving GW.

“I like where I am,” the Bowie native said. “I’ve got a good job. My family’s happy. I get to see my dad all the time.”

So why then did Lonergan look so frazzled? Perhaps because had brought his wife, Maggie, and all five of their children on the trip.

“I could miss this and be fine,” he said. “But Maggie’s an ex-coach, so she wanted to come, and we brought all the kids.”

Sadly, the two men involved in the most famous lobby hug were nowhere to be found Thursday. Twenty years ago, then-Temple coach John Chaney burst into then-Massachusetts coach John Calipari’s postgame news conference after a taut game because he was angry Calipari had screamed at the officials, even though the Minutemen had won the game. The two men had to be kept apart, with Chaney ending the exchange by yelling, “I’ll kill you.”

Seven weeks later in Charlotte, Chaney walked up to Calipari with a big grin on his face. Calipari put his arms out. Chaney did the same. The two men hugged.

Naturally. They were in the Final Four lobby.

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