It is a coup de grâce of American filmmaking that in “The Putin Interviews,” Oliver Stone first strongly recommends and then sits down to watch “Dr. Strangelove,” Stanley Kubrick’s 1964 comedic masterpiece about nuclear apocalypse, with Russian President Vladimir Putin. It’s a combination of proper nouns that sounds like the setup to a one-liner. Putin shifts uneasily in his chair, apparently unused to even the simulated experience of leisure time, as onscreen President Merkin Muffley calls the Russian premier, Dmitri, to inform him that America is about to accidentally nuke the U.S.S.R. Stone then gifts the dinky DVD to Putin, as a kind of good-faith gesture between the director/documentarian/journalist and a strongman leader famously suspicious of anyone who questions his motives. Putin takes it into his office, but just before the door closes, he pushes it back open, confronting Stone and the cameras with his gift. The DVD case is empty; the producers left it in the DVD player. Through his translator, Putin jibes: “Typical American gift.”

The setup has a punch line after all.

Showtime’s “The Putin Interviews,” which might be the most high-stakes documentary the network has ever aired, occasionally carries the lighthearted tone of farce. Love them or hate them, both Stone and Putin — men whose ideologies and reputations precede them — are so idiosyncratic and arresting that their dynamic has a hint of slapstick comedy. “The Putin Interviews” makes use of seemingly dozens of camera angles in every sit-down interview, building a portrait of Putin that is both comprehensive and dizzying — as if no matter how we approach the subject, we cannot slide under his defenses. Stone approaches the material with a slight buffoonery that may be just for show; he has just enough entitlement to blunder past Putin’s politesse, which reveals the Russian leader’s steely reserve underneath. Putin, on his part, is an adept self-spinning machine, with much more deadly charm than comes across in his state appearances. While discussing the Reagan presidency, Stone observes that the former president would have said he faced many of the same obstacles that Putin did. The Russian president retorts, with a sliver of a smile on his face: “Almost being broke and actually being broke are two entirely different things.”

Stone, a leftist firebrand who has advanced both well-regarded critiques and fringe conspiracy theories in his body of fiction and nonfiction work, put together “The Putin Interviews” from more than 30 hours of footage spanning 12 different conversations with the controversial Russian leader. Stone is less invested in investigating Putin than he is in re-narrativizing the history of American dominance in the post-Vietnam era; Putin is eager to assist him on this journey. The two go deep on America’s long game with NATO and its Middle East strategy that threw arms and money, catastrophically, at fundamentalist Muslims in unstable states. More often than not, Stone and Putin agree — on Edward Snowden, on American overreach, on Hillary Clinton. At times, Stone is skeptical of Putin, but for a leader strongly criticized for his civil rights abuses, it hardly seems that Stone is skeptical enough. On the other hand, there is some value in a profile that the subject finds flattering—it reveals who he wants to be. And Putin is revealed to be a terrifyingly competent leader, with a wide-ranging skill set that has spun circles around American presidents since the Clinton era. Putin gets many opportunities to brag about himself, in a disarming, down-to-earth way. It makes his baldfaced lies and bigotry all the more shocking. But it does not make him seem less dangerous. While enumerating what he sees as American betrayals of Russian trust during the Chechen War, he flicks a speck of dust off of his trousers with controlled, focused intensity. He gives the impression of carefully stoked simmering rage, hovering just at the edge of boiling over. To complete the image of sprawling feudal dominance, in one scene on Putin’s private jet, his administration’s press secretary Dmitry Peskov holds the boom mic as if he’s a lackey waving a palm frond. “The Putin Interviews” identifies him with cheeky specificity, delighting in his embarrassed look to the wide-shot camera.

In the two installments released to critics, Putin and Stone have not yet broached much on the topic of President Trump’s ties to Russia or the widely acknowledged Russian involvement in influencing the American 2016 election. But in the interviews that precede the election, Putin repeatedly points out that America meddles in Russia’s internal affairs, and the internal affairs of other countries, with impunity. He is, as far as we know, entirely right about that. So now what?

“The Putin Interviews” is a destabilizing documentary that challenges Americans’ narratives about ourselves and asks the viewer to engage in a conversation with a slippery subject. It’s riveting in how dangerous and intimate it feels, leveraging its multiple camera-angles and hand-held shots to make the viewer feel as if they, too, are in the room with Vladimir Putin. Foreign Affairs will likely have much to dissect in the dialogue, which often sounds like Stone and Putin are playing an invisible game of chess. It’s sobering to realize that if Putin is playing invisible chess with Stone, he is playing garishly lit 3-D chess with America — playing, and winning.