Ah, she understands this challenge. She simply has to work around the fact her hands aren't responding to her will properly.

She is definitely not smiling. She is SERIOUS. Ignore what her lips are doing.

"Shadowheart, you want a turn?"

She stands up. "I can't promise I'd be any good."

"I can wear a blindfold if you want."

"I still feel like you would win. As long as you aren't against missing out on your own liquor--"

"Not at all! Liquor is for sharing. --You could spin me around three times first."

"I think a blindfold will do. Don't want you falling on anyone."

The conversation has moved on to an intercity rivalry between Baldur's Gate and Waterdeep.

Cayden blindfolds himself and also throws the darts backwards.

...Now he gets to drink his own liquor.

That's one way to do it. 

It becomes clear over the course of the game that Shadowheart could not hit the broad side of a barn, let alone a dart board. She's not putting it on, she's legitimately not good at aiming.

She may be a little drunk. That's fine. She gets to be undercover as a sober person. As a sober cleric of a god people don't worry about (Wyll legitimately doesn't even know.)

She likes being undercover.

Eventually Cayden says, "we should stop playing or Lae'zel will stop being the fun kind of drunk."

"I'm fine." How heavily Lae'zel sits down afterwards is evidence against that claim.

"Oh my."

"Did you ever expect to see a githyanki shit faced?"

He smiles. "I have seen a lot of things I didn't expect in the past two days."

Hey, kiddo. Pay attention to this, okay? If you have any questions let me know. 

"The cool thing about being drunk," Cayden says to Lae'zel, "is that if you're drunk, and there's something you want to do, you can just... do it? If you want to sing or dance or play a game or kiss someone or talk to a stranger or tell someone you love them or for that matter tell someone you hate them, you just can. No one can hold it against you, because you're drunk, and drunk people do stupid shit all the time. And everyone else here is drunk and doing stupid shit." 

Well, okay, Gale and Wyll probably had a shot each, but that's not the point.

"For example--" he says, and swings into Astarion's lap and kisses him very thoroughly.

Judge THAT, Mr. Paladin Man. 

He has nothing against being drunk, and also this is importantly not a murder. 

... he may have just met the first group of people who being drunk improves their decision making?

Oh, is he getting used as a demonstration?

He'll show everyone here how it's done. 

As tempting as Astarion is, there is serious important party business happening here. 

He stops kissing Astarion and says, "I'd teach you some of my extensive repertoire of bawdy drinking songs but unfortunately songs work poorly with a Ring of Tongues."

He has a ring of Tongues? "I'd imagine our songs wouldn't translate well either."

"There's something to be said for the experience of hearing words that are absolutely not the ones being sung. A bit like eating a weird mushroom."

"I wonder if you could get the same affect with illusion magic, without needing Tongues..."

"Nerd."