Last week, in advance of the third season of “House of Cards,” “Sesame Street” aired a parody of the series, in which a purple puppet in a power suit named Frank Underwolf terrorizes three little pigs along the way to his desired destination, the White Brick House. The bit is a funny send-up of the Netflix show’s distinctive attributes, from its theme music and opening-credits sequence to its frequent dramatization of texting and the gold ring that the main character bangs on tabletops. The wolf sounds like a slightly batty Southern soliloquist in a damp Tennessee Williams production—which is to say, he sounds like Kevin Spacey as Frank Underwood—and he drawls out Frank-inspired aphorisms like “As we used to say back home, sometimes to get what you want, you’ve got to be a bit of a blowhard.” The spoof is supposed to teach kids subtraction and to give their parents a laugh, but watching the new “House of Cards” episodes this past weekend, I realized that it also illustrates the central problem with the show’s third season.

Underwolf and Underwood covet similar things for similar reasons: each wants to live in a big house, well, just because, basically. “House of Cards,” at its best, is a simple show: Underwood wants power, and he looks at the camera and tells us that this is what he wants. When we left him at the end of Season 2, he was standing behind the desk in the Oval Office, staring back at us, having ascended to the Presidency by means of manipulation and outright murder. It was a season finale that could have been a series finale: the highest office in the land was the culmination of Underwood’s scheming, and, short of declaring himself king, he could rise no further. “There is but one rule: hunt or be hunted,” he once said. By continuing, the show would have to become something different.

It turns out that the imagined implications of an Underwood Presidency were more menacing than any dramatic manifestation of them could possibly be. “House of Cards” struggles to maintain its devilish momentum when it asks us to believe that Underwood cares a lick for real governance—or when it asks us to care whether Frank passes an education bill, say, as he attempted in Season 1, or a radical new jobs program, as he attempts in Season 3. The show is about the will to power, not the wielding of it: public policy seems at once above Frank’s ethics and beneath his talents. The same is true of his wife, Claire (Robin Wright). In the new season, her efforts as Ambassador to the United Nations to install a peacekeeping force in the Jordan Valley have less to do with geopolitics than with her own future ambitions. And if neither believes in what they’re doing, why should we?

The journey toward power for its own sake is a story that, like a children’s bedtime story or a ghastly Grimm fairy tale, begins at A and should end, naturally, and after a few twists, at B. Last season, “House of Cards” arrived there, but, like the British series on which it is based, it has continued, shifting its focus from the acquisition of power to the protection of it, and to thoughts of legacy. Unlike the British version, which ended after three parts, the American “House of Cards” isn’t ready to let go; this year’s finale sets the stage for more. Successful American TV shows typically expand and, in so doing, drift. It’s hard to end a popular show in this country, especially if it’s merely in the name of narrative tidiness.

This latest season is not without its gifts, and some may feel that there is plenty of entertainment to be had in watching Frank and Claire play out the string on more scenes of treachery—still borrowing from and remixing the ghastliest bits of “Richard III” and “Macbeth.” (If there are multiple seasons to come, perhaps they’ll eventually get to “King Lear.”) This season’s story line involving the Russian President, Victor Petrov—a taller, better-looking Putin—is mostly a delight. (It helps that Petrov is one of the few “House of Cards” characters who is genuinely funny; in a knowing wink at knocks on the show’s constant doom and gloom, Petrov tells Underwood that people need to see that their President “doesn’t take himself too seriously.”) At one particularly enjoyable moment, it seems almost possible that Underwood may personally attempt to assassinate his fellow head of state. The show continues to up the ante in its attempts to shock, with behavior that ranges from the improper (the First Lady playing beer pong with the Secretary of State in the White House residence) to the sacrilegious (Underwood pissing on his father’s grave and later spitting on a statue of Jesus Christ). But, for all of this, the season, interrupted as it is by long scenes of brooding and political maneuvers that signify nothing, feels like an extended epilogue.

In the “Sesame Street” parody, once Underwolf thinks he has outsmarted the pigs, he proclaims, “Now the White Brick House is mine. Finally, I get what I deserve.” And then the whole thing comes crashing down around him: it wasn’t a house of bricks, after all, but a house of cards. Viewers of the British series may expect that punishment of some kind awaits our American antihero, but perhaps more seasons like this new one are justice enough for Underwood. The excitement of backstabbing his way to the highest office in the land has been replaced by the tedium of domestic governance and the impossibility of peacekeeping in the Middle East. Running for election in an honest-to-goodness campaign is less fun than rigging the game by moving pieces on both sides of the board. And the trappings of the position are clearly beginning to grate: it is harder to sneak a cigarette; it takes a full security detail to get out for a midnight jog; there’s no good place in the White House residence to put his old rowing machine. It’s lonely at the top, and grim, and, to be honest, a bit dull for us to be there with him. But, after all his fun, and ours, perhaps we’ve gotten what we deserve.