The tribute show is a peculiar beast. Unlike even the laziest jukebox musical, there is no invented backstage conflict, no dramatic narrative. Much of it relies on the pretend excitement of punters co-operatively whooping at being told they are in the presence of a megastar – even though they know perfectly well they aren’t.

The Rat Pack - Live From Las Vegas is a facsimile recreation of one of the famously chaotic song-and-horseplay evenings which Frank Sinatra, Dean Martin and Sammy Davis Jr used to put on at the Sands Hotel in the early Sixties.

A concert of classic numbers like “The Lady Is a Tramp”, “Mr Bojangles”, “I’ve Got You Under My Skin”, “That’s Amore” and “Fly Me to the Moon”, with added goofing around and joshing ad-libs, it has already played over 1,000 shows in London, and is now back in the West End once more.

No writer is credited for the script, so we can assume that all the banter – “I’ve had a very special request, but I’m going to sing anyway!” – is authentic. Some of it may be too authentic for its own good: much of the first-night audience cackled happily at the racist jibes directed at Davis and the plentiful ‘fruit’ gags.

Because of the limitations of the form, the evening’s effectiveness depends entirely on the quality of the impersonations. All three performers in this revival are old hands at the show, but the undoubted star is Giles Terera as Davis. A showman to the core, with a soaring voice and a brilliant vaudeville physicality, he is worth some genuine whooping, not just the pretend kind.

As Martin, Mark Adams has an infectious smile and a sultry vocal trill, lumbering amiably around the stage with his subject’s famous pretend-drunk shtick. You can see why audiences must have loved the real Dino.

With none of the other pair’s clowning to fall back on, Louis Hoover has the tallest order as Sinatra – and, sadly, anyone unfamiliar with the real Ol’ Blue Eyes might wonder what the fuss is about. The elusive magic of Sinatra’s voice is notoriously hard to carry off, but this evening is meant to be about recreating that magic. It’s not Hoover’s fault that he looks more like Ricky Gervais than Frank; but rendering the wonderful “Chicago” as “Chicargo” is unforgiveable.

All three performers warm to their task as the business grows ever more madcap, and an exuberant series of encores – supported by a first-rate band – create enough atmosphere that for a while you really might be watching the real thing. But Hoover’s solo “My Way” finale merely reminds us that we are not in the presence of greatness, and ultimately you wonder what the point of it all is.

Martin’s cheekily updated line during the penultimate number – “We’re making our producers very wealthy/ now that the Pack is back at the Adelphi” – may provide an answer.