The war raging around young lovers Troilus and Cressida is pointless. But that’s precisely the point of Shakespeare’s tragedy with a wickedly comic undertow now playing — for just five more performances — in Central Park.

If the Grecian-Trojan war that pervades “Troilus and Cressida” brings to mind current conflicts, that’s no accident. Director Daniel Sullivan brings Shakespeare’s seldom-produced anti-war, anti-hero, anti-romance farce into sharp 21st century focus, complete with selfies, social media and assault rifles — all framed by David Zinn’s industrial set accessorized with his modern-dress costumes.

Troilus of Troy, played with earnest naivete by Andrew Burnap, swoons over Cressida, daughter of a Trojan priest. Played by Ismenia Mendes with a flirtatious transparency too innocent to be coquettish, Cressida rivals the desirability of Helen (Tala Ashe), the cause and prize of the war and, in Greek mythology, Zeus’ daughter.

John Glover as Pandarus, Cressida’s uncle/matchmaker, panders with delightful debauchery manifested by his syphilitic deformity. Maurice Jones as Paris, Helen’s partner in adultery, frowns mightily on both military and romantic fronts.

But (spoiler alert!) lovers are no match for warriors, led on the Greek side by a dignified-when-sober Agamemnon (John Douglas Thompson). Among his cohorts are aged Nestor (Edward James Hyland) and wily Ulysses, played by Corey Stoll with conniving duplicity.

Lust and violence collide in the trade of human war booty engineered by Cressida’s father, who sends her to the Greeks in exchange for a Trojan POW. Though they profess undying love, Troilus doubts Cressida’s fidelity, spying on her encounter with Diomedes (Zach Appelman), her Greek protector.

The balance of power hangs on the Greek challenge to Hector, Troy’s war hero. Brawny but brainless Ajax (Alex Breaux) is recruited as a foil whose defeat will draw Achilles into the fray. While Louis Cancelmi, who replaced injured David Harbour, cuts a hunky figure as gay Achilles, he appears to be no match for Bill Heck’s smolderingly imposing Hector. (The late cast change delayed the official opening a week.)

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A furious firepower battle, choreographed by fight directors Michael Rossmy and Rick Sordelet, will jolt you awake if the preceding 2 1⁄2 hours somehow fail to engage you.

Ironically, the only one to make sense of it all is the fool, Thersites, impudently played by Max Casella. “War and lechery confound all,” he declares. In this tale of love and war, everyone’s a loser.