The visit, an exercise in what some have optimistically termed "basketball diplomacy", has been marked by Rodman's ill-tempered, incoherent response to accusations that his presence lends legitimacy to a singularly brutal regime.

One wonders what his host - reportedly a basketball fan since his days being expensively educated in Switzerland - made of the spectacle.

In a strange echo of Marilyn Monroe's birthday tribute to JFK, Rodman serenaded Kim with a rendition of , to wild applause from the capacity crowd of 14,000, while the "dear young general", his wife, Ri Sol-ju, and other senior figures in the regime watched from a special seating area.

"It started out as surreal, then people joined in and it sort of faded a bit, but it seemed pretty heartfelt from Rodman's side," Simon Cockerell, a tour guide who attended the game, said. "It was unexpected, and probably unplanned. Kim Jong-un appeared to smile, but he didn't appear to expect it."

Rodman, who described Kim as his "best friend", went on to deliver "a charmingly shambolic speech where he thanked Kim Jong-un and his wife for showing up, along with the other players for being brave enough to come with him and join in his engagement effort", Cockerell added.

North Korean state media said the song was "reflecting (Rodman's) reverence" for Kim Jong-un, and that he had organised the game as a gift for his birthday.

The , the official newspaper of North Korea's ruling Workers' Party, dedicated its front page to coverage of the basketball game and published photos of Kim sitting and laughing with Rodman.

"Dennis Rodman said he was overjoyed and teared up when he met the Dear Respected Marshal again," the newspaper said.

But how many candles were on Kim's cake? It says much about the world's curious relationship with the secretive North that for insights into its leader we must rely on Rodman, and for a detail as innocuous as his date of birth we must rely on his father's former sushi chef Kenji Fujimoto, who revealed in Tokyo last year that Kim was born on January 8, 1983 - making him 31.

On Thursday, Rodman accompanied Kim on a trip to the Masik Ski Resort.

A source with direct knowledge of Rodman's itinerary said the 52-year-old took a helicopter to a multibillion-dollar, luxury ski resort that is seen as one of Kim's showcase projects, but which has been condemned by some observers as a waste of money in a country where most of the population is malnourished.

What is quickly turning into a public relations nightmare for the irascible Rodman - whose fellow players looked like they would rather be anywhere but Pyongyang during his tetchy pre-game interview with CNN on Tuesday - can only have helped burnish Kim's reputation, at least at home.

Now he can add being feted by household names in a sport beloved of his country's nemesis to a list of achievements over the past year that have horrified observers but also induced grudging admiration.

In late 2012 Kim reportedly became a father, possibly for a second time. There was no official word on the happy event, only speculation sparked by the sudden absence of his wife's swollen tummy at a public appearance on New Year's Day. In February Kim oversaw North Korea's third nuclear test, and then made threats to launch nuclear strikes against the US, South Korea and Japan. It was an orgy of calculated aggression intended to enhance his domestic standing and put pressure on a rattled Washington.

Last year ended with the disturbing news that Kim, possibly under pressure from other members of the North Korean elite, had had his uncle, Jang Song-thaek, arrested and executed for a long list of alleged crimes, including treason.

Jang, whose fate was quickly confirmed in excruciating detail by the official news agency, KCNA, was commonly believed to be the regime's No 2, guiding Kim through his first two years in power.

Kim's longevity as leader will surprise North Korea watchers who predicted a quick end to the third incarnation of the communist dynasty as he stood sobbing beside the corpse of his recently deceased father, Kim Jong-il, in December 2011. Two years on, Kim has assembled a seemingly impregnable coterie around him.

As for Rodman, he is likely - as he predicted - to receive a cool welcome on his return to the US. He may yet achieve swift redemption in the eyes of the administration in Washington if his powerful friend reciprocates his show of goodwill by releasing Kenneth Bae, an American who has been detained in North Korea for 14 months.

That gesture looks a near impossibility, though, after Rodman, despite his insistence that this was a strictly apolitical event, appeared to suggest that the missionary - sentenced to 15 years' hard labour for "crimes against the state" - was to blame for his captivity.

Asked in the CNN interview if he would use his influence with Kim to make the case for Bae's release, Rodman had said: "I don't give a rat's ass what the hell you think."

The following day, he issued an apology, saying that he was upset at the time and had been drinking.

"Our family accepts Dennis Rodman's apology for his outrageous outburst," Bae's sister, Terri Chung, said. "As Rodman has stated, being drunk and stressed is not an excuse for what he said, but we acknowledge he is human and we all do make mistakes," it said.

"The fact is Kenneth's life is on the line. Though we understand Rodman enjoyed some laughs and smokes during a couple of basketball games in North Korea, to our family, this situation is no joke."

In Rodman's great cultural adventure in North Korea, the diplomatic gains, it seems, are all Kim's.