With his sons disappointing him left and right — and with his wife Marcia sniping at him over how much he is letting Rhea guide his decision-making — Logan turns to one of his most trusty confidants. He calls a truce with Siobhan, mainly so he can commiserate with her about his Rhea problems, and laugh about his dopey sons. What he doesn’t realize is that Shiv, stung by the series of betrayals in London last episode, is already working stealthily to weaponize whatever sentimentality remains in her father.

The cat-and-mouse game between Shiv and Rhea energizes what is, overall, a very entertaining “Succession.” When the men in Shiv’s life ask whether Logan’s affair with Rhea is their business, she is righteously incredulous. (“The business with our name on it? Is it our business?”) She harangues her husband into using his middling powers of seduction on Ms. Jarrell, telling him to be “not dirty flirty, but hurty flirty” — which Tom, predictably and hilariously, does poorly. Siobhan also convinces Kendall to get Rhea to offer a toast to Logan’s dead sister, Rose, which they know will annoy him.

Rhea counters by cozying up to Ken, hinting that if she’s put in charge, he’ll remain in the mix to take over someday. She also tells Roman he has “the best instincts,” which inspires an all-time great eruption of poetic Roman nonsense: “I see your thing. It’s good. It works. It’s like a peppy fun-gun, set to MILF, with like a lean-in woman-y branding that works with the Fitbit moron whatever people.”

Rhea, though, can’y see that Marcia has set her up to fail by letting her plan a surprise party Logan will loathe. At the same time, Shiv is using her insider info to assure that Rhea will be in the line of fire when the latest development in the Waystar cruise scandal breaks. When Logan uses his big speech at the party to announce Rhea as his successor, it’s in no way a win for Rhea. She just doesn’t know it yet.

For all of its cringe-comedy and corporate intrigue, what’s most surprising about “Dundee” is the melancholy tone, cued by Logan’s mood. He livens up only while sparring with his brother Ewan, who comes to the various celebrations to remind Logan he’s “a nothing man” and to tell Cousin Greg to stop working for Waystar or risk his quarter-billion dollar inheritance. (Ewan cites Tacitus to his grandson, who replies, “Classic Tacitus … All killer, no filler with him.”) Logan tells Greg he would be better off sticking with “Uncle Fun” than with “Grandma Grumps,” and he bristles at his brother’s suggestion that their mother — who they last saw when there were preschool-aged — would have disapproved of his journalism.