For proof that life’s unfair, consider the case of Hugh Jackman. The guy’s in the 99th percentile of, like, everything. He’s dashing, rugged, rich, well-mannered, famous, at ease with himself, brimming with positive Aussie energy. He’s a devoted family man, can belt out a show tune, glide through a tap number, embody an action hero, look good in gold lamé.

Your swooning mother doesn’t have to say it, but you know she’s secretly wondering why you couldn’t have been more like him.

And here’s the worst of it, as is eminently evident in his vivacious new revue, “Hugh Jackman, Back on Broadway”: He’s just so confoundingly likable. A suave star who sends out the vibe that he feels lucky to be in your presence: What sort of monster would you have to be to provoke a quarrel with so much effortless talent and magnetism?

That the material he has selected with director-choreographer Warren Carlyle is a tad presumptuous is beside the point. His songbook includes “Luck Be a lady,” “Singin’ in the Rain,” “I Got Rhythm,” “Mack the Knife,” “Oh, What a Beautiful Mornin’ ” and even, gulp, “Somewhere Over the Rainbow”: not exactly envelope-pushing. And the sentimental patter — about his love of the Outback and his father and aboriginal culture and his wife and his kids and film-making and Manhattan — waltzes right up to the edge of eye-rolling cheese.

But hold on! The testimonials, after all, come from the lips of Hugh “Wolverine” Jackman, who for all we really know landed among us from a distant planet of super-personable, super-fit song-and-dance people. Yes, he’s just that pleasant to be with, hip-swiveling alongside his six-girl chorus line.

And so, you forgive the cliches that are sprinkled over the stage of the Broadhurst Theatre, where the limited-engagement show officially opened Thursday night. “Hugh Jackman, Back on Broadway” is just a plain old good time. In that Down Under accent that extends a natural bridge of camaraderie, Jackman presides over the fast-moving evening as if he were the star of an old-fashioned TV variety show, the sort in which the host smiles rakishly through some lame skits and inevitably is tossed a top hat and cane for a bit of applause-wrangling soft shoe.

He pays tribute to his homeland and shows clips from his movies, which taken as an artistic résumé (The “X-Men” series, “Australia,” “Kate and Leopold”) is decidedly second-rate: Although he makes a crack about the widely panned “Van Helsing,” one would like him to cop more fully to this disappointing reality.

His theatrical bona fides were confirmed when he played Curly in Trevor Nunn’s revival of “Oklahoma!” and even more emphatically, in his captivating impersonation on Broadway of the late songwriter Peter Allen, in the 2003 musical “The Boy From Oz.”

He reprises that performance in the second half of “Hugh Jackman, Back on Broadway,” and it is by far the production’s most satisfying sequence. He has a powerful if not memorable voice, so the renditions of the towering standards he tries to scale only remind you of the far more supple versions by the likes of Frank Sinatra or Judy Garland.

Yet he’s the best Peter Allen you’re likely to come across, and, as a result, you feel his authentic affection for his subject when he slips on the gold slacks, effects some fey mannerisms and launches into signature Allen tunes such as “Best That You Can Do” and “Don’t Cry Out Loud” and an apparent favorite among Australians, “Tenterfield Saddler.” (So that you don’t get the wrong idea, apparently, Jackman also reminds the audience at other points how much he loved real-man things such as getting bloody on rugby pitches and trying out for school plays because it provided chances to meet girls.)

Whatever else he does, Jackman brings joy to the stage. Comparisons are being offered to the deep impression made by a solo artist such as Garland. But the rapturous emotional intensity that lingers is not what this performer provides. Garland left blood on the stage. Jackman leaves sweat, and a smile.

Hugh Jackman,
Back on Broadway

Directed and choreographed by Warren Carlyle. Costumes, William Ivey Long; music direction, Patrick Vaccariello; lighting, Ken Billington; sound, John Shivers; set, John Lee Beatty; videos, Alexander V. Nichols. About two hours. Through Jan. 1 at Broadhurst Theatre, 235 W. 44th St., New York.

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