While initially they did not look like the real thing, they had the movements, the style and above all the voices to make you believe.
The idea of the show is that they were filming Ocean's Eleven by day and appearing at The Sands Hotel by night where they had a drink-fuelled ball on stage.
There is a script based on a film of the event which includes Martin, drink in hand, changing the lyrics of When You're Smiling to When You're Drinking and falling down the stairs while both he and Sinatra poke racist "fun" at Davis, referring to him as Smokey.
The result is a little awkward at times but relieved by the great songs and performances.
Mann is a fairly tall Sinatra but has all the mannerisms, the look (dressed in a tuxedo) and especially the voice. His version of I've Got You Under My Skin complete with Sinatra's well-known introduction ("Cole Porter's finest hour") and his swinging The Lady is a Tramp with his additional words, were both classics.
But it was the maudlin My Way which really stole the evening in Mann's Sinatra-styled version. There were some damp eyes.
Neilson had a great time as Dean Martin and Campbell was a pocket dynamo playing Davis, his best moment the Anthony Newley ballad What Kind of Fool Am I?
Danielle Calvert, Lucie Florentine and Clare Maurer were tremendous as a vocal trio and sexy dancers in 1950s slinky outfits while the band led by Mitch Sebastian on piano wailed in grand fashion.