Sochi 2014 is the least wintry Winter Olympics ever. Yes, there’s a bit of downhill shimmying going on in the slalom. And a few figure skaters are pirouetting around the rink. Midair daredevils, with their feet lashed to planks of bendy plastic, are performing spectacular twirls and somersaults and crashes. And there are speed freaks on tea trays racing down ice-packed gulleys in tribute to the Hadron Collider. But the real action is off-piste and off-chute. It’s a political grudge match. Two implacable foes are angrily denouncing each other as shameful and perverted barbarians.

The Hope Theatre’s verbatim drama, Sochi 2014, taps into this febrile mood with a documentary history of gay Russia since the collapse of the Soviet empire. At first all was rosy. When the Russians finally emerged from beneath the commie jackboot, they welcomed homosexuality as an emblem of freedom and openness. Gay people could stroll around Moscow hand-in-hand, unmolested, in the early 1990s. But with the rise of Putin, the clouds darkened. Homosexuals were identified as an internal enemy and used to divert attention from Russia’s economic woes.

In this brief and gripping drama there are accounts of gay-bashing and gay murder that harrow the senses more horribly than anything I can recall hearing. The script also has astute political antennae and reveals Putin as a master of public rhetoric. He exploits anti-gay sentiment by eliding it with Russia’s traditional mistrust and envy of Europe. Everyone in the European Union, claims Putin, is gay. Our continent is riddled with infertile and unChristian pederasts who have no interest in children except as sex toys. Incapable of procreating, we rely on an army of migrants to keep our economy on the boil but their presence now threatens our bloodline. This conflation of half-truth and wishful thinking delivers huge political benefits. By defining himself against an all-gay EU, Putin can pose as the champion of Russian nationalism, of Christian virtue, of family values, of racial purity, of Darwinian manliness, of economic dynamism and of child protection. That’s a potent list of hot-button issues and he sustains it very cheaply with one brutal insult: ‘Oi, Europe, you’re a bunch of poofs, right?’ To detach Russia from this popular and politically lucrative falsehood won’t be easy. Sochi is a start.

Stroke of Luck, at Park, is the world première of a strange chameleon play that keeps changing its colours. It opens as a formulaic comedy. Lester Riley, a crippled widower, announces his plan to marry his sexy young nurse. This threatens to deprive his grown-up children of their inheritance. The characters are crudely drawn. Lester is a charming dimwit, his three kids are hard-nosed graspers. Not the sort you’d invite round to dinner. The eldest son is a mean-eyed Gekko-ish lawyer. His younger brother is a paranoid jailbird. And their woe-stricken sister is a widow whose husband bought it in a ski-ing disaster. His Alpine crumple-up has left her with enough phobias to fill a medical encyclopaedia. Battle commences as the greedy nippers face up to their besotted dad and his beautiful bride, who is Japanese and claims to be a Catholic. (This bit of whimsy is characteristic of the play’s rather forced quirkiness.)

The script then takes a scenic diversion. We explore the Riley family past. Lester, it turns out, is sitting on a fortune. He worked as a TV technician for a family of gangsters who rewarded his services with so much loot that he opened a private investment fund and multiplied his income many times over. He’s a multimillionaire TV repairman. Not very likely but at least it intensifies the dramatic tussle for his legacy. The play is fun (kind of) and moving (sort of), but I wasn’t sure if I was enjoying it until the final revelation. This felt like a complete swizz, which erased all the foregoing action at a stroke.

The cast struggles bravely with a cumbersome set that features five hinged flats, 20ft-high, arranged adjacently. That’s right: 20ft-high. Doesn’t sound too tricky? Imagine entering your bathroom by opening a door as tall as a double-decker bus. The star, Tim Piggott-Smith, plays Lester with a winning blend of guile and dippiness but an actor of his powers is misspent on this frothy and uncertain play. Age has amplified the depth and interest of his face. He has a long and ruminative skull with inscrutable little eyes, ruddy jowls, and a woolly mane of receding white hair. He looks, all in all, like a scholarly and slightly quizzical sheep. He also bears an uncanny resemblance to Brian Sewell, whose autobiography is ripe for dramatisation. The day cannot be far off when Piggott-Smith will impersonate the great art historian. I can’t wait to hear the voice.