Sherlock and Arkady playing chess
I would love to put the two of them in a room together and watch the fireworks. I don’t think the above scene would happen (though I do think Arkady would beat Sherlock at chess) because they are both incredibly prickly people. More likely scenarios: Sherlock deduces that Arkady is agoraphobic; they get into a roaring argument; Arkady eventually punches Sherlock. Arkady offers Sherlock some vodka; they get drunk; Pippa shows up and Sherlock deduces something about her; Arkady finds it hilarious; Pippa doesn’t. Sherlock talks to Arkady about Rosemary; Arkady runs away. On a case, Sherlock is more interested in finding facts to deduce motive, and Arkady is more interested in finding motive to postulate fact.
Basically these guys are both awesome.