A mildly helpful guide to solving the Face Card Puzzles. Disclaimer: All the info here is ‘as far as I know’. If I missed an interaction, it won’t be here.
What are the Face Card Puzzles?
At the start of any run, you will select a set of Face Cards to add to your deck. “The Royals” are the only ones initially available, but you can unlock more of them by beating each of the bosses a certain number of times. The sets corresponding to the bosses are; Morgan | The Vice, Ivel | The Shame, and Better | The Family.
Each set of three Face Cards has a Puzzle that you play out over your run by playing the Face Cards together in a certain order. They’re somewhat intuitive, but I’m writing this to save you some trial-and-error.
Why do the puzzles? Well, the cards interacting with eachother tends to lend them permanent improvements. Why do them “correctly?” Well, aside from tending to give the ‘best’ improvements, completing each puzzle “correctly” will unlock an artifact named after the set of Face Cards that you can buy on future runs to add them to your deck. One purchase that adds three self-improving 10s to your deck? Pretty snazzy.
If you want to figure out the puzzles yourself:
Cards that will act on eachother will typically exhibit a small change in their art when you go to place them next to eachother (IE: Differing expression or interacting with something they’re holding)
It also doesn’t matter which order you play the cards when having them act on eachother. Playing the King next to the Queen will always have the same result as playing the Queen next to the King.
The Royals
The Face Cards in The Royals are: Queen, King, and Jack.
The “Correct Path”
Playing Jack together with either of the other two will cause him to cut them in half, killing that monarch (making them hollow, granting them a second score of 0, and looking visibly distinct). The Jack will become “The Murderer” (causing it to become blood-soaked and visibly distinct).
After this, playing the remaining living monarch next to The Murderer will cause them to execute him and transform him into the “Hanged Jack” (Making him Hollow and granting him a second and third score of 5 and 0 respectively) .
Executing The Murderer unlocks the achievement and artifact named “The Royals.”

Other interactions: Playing both living monarchs together will cause the queen to grant the king 1 more score and turn him golden.
Also I think it’s fun that the effects on The Royals are less flashy but their distinct visual changes make them easy to tell apart from other diamond cards.
The Vice
The Face Cards in The Vice are: Morgan, Virtue, and Vice.
The “Correct Path”
Playing Morgan and Vice together will make them toast and give Morgan “demand a card valued 8 or higher.” Playing Virtue and Morgan together after this will have Morgan kill Virtue (10/0, Hollow, “fill your other slots with -1 of hearts”) and transform her into Mania (11/0, “Raise 1. Fill your slots with 1/0 of Diamonds.” also visually distinct via blood).
Killing Virtue unlocks the achievement and artifact named “The Vice.”

Other interactions: Playing initial-Morgan and Virtue together will cause Morgan to lose a point of score and gain an Insight 2 effect. It also makes her sad. This doesn’t prevent Morgan from becoming Mania later, so a valid strat for achieving the “Correct Path” is to just play all three face cards on the same turn if you can swing it.
Playing Virtue and Vice together will cause Vice to kill Virtue. Vice doesn’t change, apart from becoming bloody, so really this is just a shortcut to dead Virtue that doesn’t get you Mania.
The Shame
The Face Cards in The Shame are: Ivel, Ward, and Crowd.
The “Correct Path”
Playing Ward and Crowd together will transform Ward into Outcast (10/0, “Shuffle 1 (permanent) Shame card into your deck”) and Crowd into… Crowd (10/0 “Purge: Shame. Claim 2 per card purged.”) Then, playing Ivel with Crowd will fill him with regret and transform him (10/0, “Decrease each broken card by 2.”) Then, playing Ivel with Outcast will cause Outcast to run away, replacing him with Gone (-8 “Swap with the opposing slot”) Permanently. Swapping Gone with an opposing slot transforms it into Vagabond (-8. That’s it) temporarily.
Finding The Vagabond unlocks the achievement and artifact named “The Shame.”

Other interactions: Playing Ivel and Ward together without following the correct path will cause him to shame Ward (results the same as if the crowd did it). If both Ivel and Crowd shame Ward he’ll become EvenMoreDepressed™ and generate two shame instead of one.
The Family
The Face Cards in The Family are: Elisabeth, Niv, and The Black Jacket.
The “Correct Path”
Playing The Black Jacket together with Elisabeth or Niv will break and transform them into Broken (-10, “Break the opposing and its adjacent cards”) and Abandoned (-10, “Shuffle two Languish cards into their deck”) respectively. Playing Broken and Abandoned together will transform them into Intervention (10/0, “decrease the opposing and its adjacent cards by 2”) and… Intervention (10/1, “Put a Languish card on top of their deck”) respectively. Playing both interventions around The Black Jacket at the same time will cause all three to combine into The Family (21/10/1.)
Reuniting The Family unlocks the achievement and artifact named “The Family.”

Other interactions: Playing Elisabeth and Niv together will transform Niv into Playtime! (10, “Rotate all cards clockwise 2 spaces”). This doesn’t prevent following the “Correct Path” since Playtime! can still be broken by The Black Jacket in the same way as Niv.