I’ve been referring to the the original post every single Fallen London Christmas so far and as it’s still correct, I’m reposting it here:
Part I:
Increasing Putting the Pieces Together: The Taste of Lacre (ToL)
Day 2: The day with the most options: for ToL +1 you can give him Greyfields First Sporing, or play on your Violin (the latter needs Connected: The Masters 2). If you have neither, “Take my good name” is another option (requires Renown: Bohemians, Society & Great Game 10, Connected: Masters 1, Notability 1). Or you can give him a Touching Love Story (caps at ToL 5)
Day 4: Today you “only” have to decide whether you’ll want to spend Fate. If you did not finish a Fate-locked investigation last year, choose to continue it now!
Day 5: Align yourself with the Celestial school of poetry at the Singing Mandrake and “Give Him Your Dream of Skies Untainted” for ToL +1.
Day 8: Invite the man in, whether you know him already or not, and receive ToL +1.
Day 9: “Accept his Heart and Lights” will get you a Pail of Lacre!
Day 11: Now’s the time to be a Doctor or Notary as only they will receive a further ToL +1.
Day 12: “Take Advantage of the Situation” will get you ToL +1 and a Pail of Lacre! You’ll lose 1 CP of Connected: Masters though. Note that this is a rather heartless choice that some role-playing characters might feel uncomfortable with - the Rubbery and Devils Fate-locked options grant the same rewards without Connected: Masters loss.
Part II:
Here are the options that increase Connected: The Masters! (it’s usually just 1CP)
Day 1: Would you care for a little of the '68? or Would you care for something… spicier than wine?
Day 2: Would you care for a little of the '68? or Take this eery air! (both give ToL as well)
Day 3: Take this rather larger diamond!
Day 5: Take this dream of mirrors! (requires Recurring Dreams: Is Someone There? 5, and then docks 10 CP off it!)
Day 6: Take this exalted hymn to patriotism! (requires you to have written A Patriotic Adventure) or Take these tales of joy and woe! (requires 10 Touching Love Stories)
Day 7: London is the crucible of desires (GAIN 1 CP Masters, 1x FiHP + 3 CP Hedonist (up to 10!), LOSE 1x Docks & Revs Favour) or Take this work of mine… (only for Bazaarines; GAIN 1-2 CP Masters, 1x FiHP + 10 Echoes cash, LOSE 1x Docks Fav. & 3 Revs Favours!) or It is peaceful here (just 1CP Masters)
Day 11: Accept the invitation (not available for the top-tier Professions)
Day 12: Assist the wreck of Sacks (3CP Masters, 1x FiHP)
Last but not least:
Day 10 isn’t useless either: while there’s no ToL or Connected: The Masters on offer, you can get a rare Scrap of Parabola-Linen in exchange for a Storm-Threnody.