Keep them. You can use them in the Nadir on the ~10% Persuasive challenge on the Rosers card, which gives you a Searing Enigma on success.
You may also want to use them on the “one’s public” card, which is another high level persuasive challenge that is, I think, at best ~60% even when you’re maxed on Persuasive. That one gives 2 confident smiles on success, as well as lots of other stuff, so it’s worth using one.
Not contributing to your question but just making a related remark.
I’m a relatively low-level player but Confident Smiles seem to be dropped a whole lot more than their Shadowy or Watchful counterparts. As I remember also card of romances past used to drop them but that seems to have changed. Nonetheless they pile up fast.
Fallen London seems very biased towards Persuasive and Watchful activities (both second chances and number of extremely difficult skill checks). Is it because statistics show that most players focus on those two areas, whereas players who want to do Shadowy and Dangerous stuff might choose to do so in various 3D games instead?
I think the bias might actually be lore-based. Think about it; what benefits the Bazaar most? The production of love stories and closer enmeshment of people in the Fifth city. Persuasive and Watchful, therefore, are encouraged. I think that’s also why Author is the only 2nd-tier profession that doesn’t require notability.
If you haven’t noticed, when you use a second chance if you fail you can hit “perhaps not”, which costs an action and the confident smile and raises your stat but doesn’t trigger the consequences of the storylet, such as discarding the card, which is how you can burn tons of confident smiles on “Where Did the Rosers Go?”
Not quite “tons of confident smiles” though. More like ten per week, on average. That’s only a lot if every source was restricted to the limits put on the social actions.
Huh, that hasn’t matched my experience. I’m almost always running low on Watchful second chances… but that may be because you gotta burn those to get rid of nightmares via the social action.
I’ve always had more Confident Smiles than anything else, though.
Still a lot more then you’ll use anywhere else if your persuasive is maxed, though.