Two principles for building a Puca's Mischief deck:
1. Do not turn it into a Donate. If you want to use Donate, do, but this card is more expensive, slower, AND more conditional. The reason to use Puca's Mischief is because it's repeatable—not because it can win the game in one swoop. (You will notice a lack of Illusions of Grandeur and Lich in my below decks.)
2. Be able to win without it. Any combo revolving around this card is bound to be fragile. Or you might not even draw the Mischief. Have a backup plan!
So,
What permanents should we swap?
Cards with drawbacks
I'm not paying those drawbacks. You're paying those drawbacks.
Symmetrical cards
I can have them, you can have them; they work just the same.
Most Auras
Changes in control don't affect what these do. (Of course, with some auras it does: don't trade your Detainment Spell or Freed from the Real!)
Do-nothings
These cards' utility is in the casting, not in the having.
Moribund cards
"You can have it—you just can't keep it."
Self-swappers
Trade the same thing over and over. (It's like tying a string to your quarter.)
Swapping bonuses
It's perhaps gimmicky, but when else would you use them?
And of course there are far more cards in each category than are listed above (especially for the symmetrical and aura categories), so we have plenty of directions we can take a deck in.
Speaking of which,
Deck 1 BWU Enchantments
This deck started by just making piles of the most powerful cards to swap, then picking ones that went together thematically. I ended up with a defensive enchantment-based deck, using Sigil of the Empty Throne and Caustic Tar
What enchantments have we? There are many of white's targeted ones, like Oblivion Ring, Faith's Fetters, and (my favorite in here) Hobble. Why not the stronger Journey to Nowhere? Hobble draws a card—and we don't care if it prevents the creature from blocking. Not in this deck we don't. (In this deck, the higher cmc can even help, as it increases what we can steal with Puca's Mischief!)
Then there are the global black ones, like Engineered Plague, Night of Souls' Betrayal, and Curse of Death's Hold.
An interesting pattern was emerging—my deck was mostly full of permanents! Initially this was just for the sake of Puca's Mischief, but it ended up leading to the deck's most important innovation: Gate to the Aether.
Aside from being another swappable card, and helping us to steal those high-mana cards, it's hitting something every single turn. Our deck is 60 permanents. Our opponent's deck is usually 2/3 permanents. We have the upper hand. And if they do get something good? ...It'll be a permanent. We can just steal it.
The deck used to have 2x Idyllic Tutor, but I swapped them for Crystal Balls. 58 permanents isn't enough. And what's more... Crystal Ball is quite good after Gate to the Aether is out.
Adding in some defense, sifting, and acceleration, we have our deck. As an added visual, I've put all of the swap-friendly cards in bold. (There are a lot!)
Deck 2 Storm Cauldron
Storm Cauldron is swappable... and when I started pondering what cards paired well with it, I noticed that most of them were swappable too! This gives us our premise.
Ankh of Mishra is the first one that comes to mind. Then Ghostly Prison and Howling Mine. Phyrexian Tyranny was looking good but got cut for color reasons.
Another way to rack up the damage is Jinxed Choker. Have you ever seen this in action? It is unbelievable how quickly it racks up damage. It makes Sulfuric Vortex look silly!
Of course our opponent isn't the only one getting damaged here. I toyed with the idea of something like Palisade Giant, and I'm still not convinced it wouldn't work, but I ended up going with some lower-mana solutions: life gain. And what are the two most cost-efficient life gain spells out there?
(Arguably) they're Sunspring Expedition and Rest for the Weary, gaining 8 life each for only 1 or 2 mana. And it's a coincidence, but their landfall pairs quite well with the Storm Cauldron!
The last lifegain I'll include is Kabira Crossroads—not exactly a powerhouse, but it is fun to play it repeatedly after bouncing it with the Storm Cauldron. It's either boosting our life if there's no Ankh of Mishra out or at least keeping us even if there is.
This deck is pretty exciting because its game plan isn't just to damage the opponent a bunch, it's to damage everybody a bunch and just try to stay afloat. Makes for some zany, swingy games!
Deck 3 Missiles
Is there an existing slang word for cards that deal 7–10 damage in one shot? I'm pretending it's missiles. This deck lives the Timmy dream with a full eight of them:
It used to also have 4x Measure of Wickedness, but enabling these three non-overlapping strategies in one deck caused things to get spread a little thin. Each of them synergized with Puca's Mischief, but that was it.
How do we enable Bronze Bombshell? Donate effects are really the only way (assume we can't rely on an opponent casting Twist Allegiance). One playset of Puca's Mischief may not be enough, so for redundancy's sake, I'm adding 2x Juxtapose. Unlike actual Donate, this card is also useful when we don't have a Bombshell out, as we can steal useful things with it.
Enabling Booby Trap requires some different cards. Wizened Snitches are an underpowered but adequate solution. Moonring Island is too. The problem is... there aren't a lot of better options! Lantern of Insight is cost-efficient, but does even less! Well, we can't have every card be an all-star in a deck like this. At least we can deal 10 damage in one shot.
We'll sometimes want to recycle our missiles, so we can enlist cards like Academy Ruins, (Buried Ruins), and Argivian Restoration (shaves 1 to 5 mana off Reconstruction!).
The rest of the deck is defense and more enabling. Silent Arbiter slows our opponent down. Meekstone gets the big guys and Psychic Membrane gets the small ones.
Treasure Mage fetches the Booby Traps, a Duplicant, or a Spine of Ish Sah. And with a whopping 15 4-drops, we'll need some acceleration. Why did I choose Sea Scryer over Sky Diamond?
For the Moonring Island, of course!
Cotton out.