Paradoxical Outcome Combo has been a deck for a while but has never broken through the barrier and become an established archetype. With the printing of Sai, Master Thopterist, this seems to have changed.
This is a 5-0 list from Magic Online player Z00T:
This deck is now very real and can definitely take down a tournament. If you haven't seen it in practice, here is how it works.
The early stages of the game will be centered around setting up. You'll be playing some cantrips (Prophetic Prism, Glint-Nest Crane) and getting a few artifacts in play. At this point, you mostly want to deploy the board and, if possible, dig for Inspiring Statuary and Paradoxical Outcome. You don't need Statuary to win, but it makes things easier.
Once you have Outcome and a decent board presence, you're ready for your big turn. Start by playing some cheap artifacts if you haven't already, and then cast Paradoxical Outcome, returning all of them to your hand and drawing a lot of cards. If you have Statuary, then Paradoxical Outcome effectively costs one mana—zero if you have an active Mox Amber. At this point, if you have mana left and if it's not yet in play, you can play Aetherflux Reservoir (sometimes via the help of Baral's Expertise). You can then replay all your cheap artifacts, drawing new cards off Prophetic Prism and Glint-Nest Crane. Often, this is already enough to get the opponent dead.
If it isn't, then you can play another Paradoxical Outcome or a Baral's Expertise. Baral's Expertise can return your own cards back to your hand, which means each Baral's Expertise can count as five spells (the Expertise itself, three that you're returning, and another one that you cast for free). If you have Statuary in play, then it costs only two mana and can be used to play Aetherflux Reservoir.
This is an example of how a turn like this can go:
Cast Mox Amber.
Cast Ornithopter #2.
Play a land for the turn.
Recast Ornithopter #2.
Recast Mox Amber.
Tap your remaining two mana, Ornithopter, Ornithopter #2, and Mox Amber to cast Baral's Expertise. Return Ornithopter, Ornithopter #2, and Mox Amber back to your hand. Cast Aetherflux Reservoir for free.
Of course, turns aren't exactly the same—sometimes you have fewer artifacts and more mana, sometimes you find something off your Paradoxical Outcome, and so on—but this is the general idea.
The big addition from Core Set 2019 for this deck is Sai, Master Thopterist. It might not seem very important, given that it didn't even factor in in the example turn, and in fact is not needed at all to combo off, but it does a series of things for the archetype:
- It provides early defense. A 1/4 is hard to attack through, survives most removal spells, and the 1/1s that you will get naturally just by playing your artifacts do a good job of blocking.
- It provides a way to pressure your control opponents. If you get Sai, Master Thopterist in play, you can start attacking for 3 or 4 damage a turn, and even if they do remove Sai (which isn't easy, since it doesn't die to Fatal Push, Magma Spray, Abrade, or Cast Down), you get to keep attacking with the Thopters. This ensures they have to act first, and then you can combo them out.
- It turns on Mox Amber, which is a big boost to your combo turns, particularly once you replay it with Paradoxical Outcome.
The first 50 or so cards in any list are pretty standard, but after that there's room for some customization. Personally, I like Metallic Rebuke a lot in a deck like this, and I would move some to the main deck alongside Glint-Nest Crane. In turn, I'd move The Antiquities War to the sideboard (I don't think you need a plan B in Game 1), and trim some of the other cards. I'm also a fan of Karn, Scion of Urza in the sideboard, as it's an excellent card to pressure your opponent while also digging for more artifacts, and, very importantly, it can be played completely off Inspiring Statuary. It's weird to me that this deck is playing zero Karns. I would play a list like this: