So far, I've heard some buzz around Paradoxical Outcome in two contexts: One is in an Aetherflux Reservoir combo deck, and the other is with Moxen in Vintage. Today, I'd like to take a look behind door number three:
The deck is cheap, both in that it's inexpensive and in that the average converted mana cost of cards in the deck is a lowly 1.1 despite having only 19 lands. The main concept is to use Reckless Fireweaver for some face damage, as well as pushing through more from fliers, all while using Jori En and Paradoxical Outcome to keep the cards flowing, with many many free or cheap creatures. Paradoxical Outcome also has some extra synergy with Enter the Battlefield abilities, like those on Glint-Nest Crane, Prophetic Prism, and Oath of Chandra (this is why we're playing Oath rather than Incendiary Flow, even with 0 Planeswalkers). Speaking of Planeswalkers, this deck might be a reasonable home for Saheeli Rai (though I'm not really convinced she has a home anywhere in the format).
The sideboard is more about different ways the deck could go than it is actual sideboard cards. Specifically, Salivating Gremlins can be a lot of burst damage (though it's quite bad against removal), and Crush of Tentacles can cost 5 and be surged pretty consistently here, AND it also re-triggers all the ETB stuff we wanted to Paradoxical Outcome anyway. A 'real' sideboard plan might have us board into an Aetherflux Reservoir combo deck, but it would almost certainly have more counterspells - particularly Dispels, but also Negates.
The deck could be made even more budget-friendly by taking out a number of Wandering Fumaroles (there's diminishing returns, and activating them is not part of the gameplan very often). Spirebluff Canal is likely the most expensive card in the deck, but it's going to be hard to get around having it - with so few lands, we have to make sure we have enough sources for everything, and with the low curve, we want our lands untapped. (Indeed, 4 taplands may be too many as is, but 14/13 sources is kind of light). If you have to cut sources, you might want to up the number of Prophetic Prisms.
I've also taken a look at adding white to the deck, because we are running so many equipment, and that color has cards that do well in that regard:
Stone Haven Outfitter is obviously incredible here, and is the real pull to this version. Toolcraft Examplar is good, but it's hard to fit many in.
The mana is the biggest drawback to this version, and to get everything to fit, while still having enough artifacts, etc. is a challenge. Probably you need to be pushing harder in some direction or another than what I'm doing here, but this is merely a Rough Draft.