UB Combo
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The main plan with this deck is to assemble an infinite mana combo (with at least 4 colored mana) and win instantly with Oona. Infinite mana is usually obtained through Grim Monolith/Basalt Monolith + Power Artifact or through Basalt Monolith + Rings of Brighthearth. Rings of Brighthearth + Tolarian Academy (with at least 4 artifacts) + Minamo, School at Water's Edge also works occasionally, though this one is significantly harder to assemble.
When additional colored mana is needed to play Oona and win immediately (which is often), Gemstone Array can generate as much as you need, and is easily tutored for. Dark Ritual and Cabal Ritual can also help provide the necessary colored mana. Also, keep in mind that Beseech the Queen (getting Gemstone Array) can be cast without colored mana once you've gone infinite. Stroke of Genius provides a backup win condition if Oona is somehow disabled.
There's also the backup combo of Leyline of the Void + Helm of Obedience, which has ended games for me as soon as turn 2. Oona is usually not played until she can be used for the kill, but it's worth noting that she's very impressive as a control card too--if creatures are giving you trouble, she's great at stabilizing the battlefield for you. In those occasional awkward games where no one can seem to draw what they need, she's quite capable of putting the game away by herself.
It's also worth noting that this deck contains a slightly absurd amount of graveyard hate, between Leyline of the Void, Relic of Progenitus, Bojuka Bog, Shred Memory and all the specialized tutors that can find these cards (also Timetwister and Time Spiral, to some extent). This wasn't exactly the intention, but they're all very strong cards in this deck anyways, so the extremely strong matchup against graveyard-dependent decks is just gravy.
On top of the combos, we simply play the best cards available in this deck, from the two strongest colors in EDH. Without getting too focused in any one area (except perhaps tutors), we have the best tutors, the best card draw, the best counterspells, the best acceleration, and the best removal. What's not to like? All of the control cards chosen are among the best ever printed, so this deck plays control very well, even though the control cards are somewhat diluted by combo elements.
This deck is particularly powerful because, as a control deck, it tends to get more and more powerful as the game goes long...but it also has a very good chance of just comboing off and winning around turn 2 to turn 5. You don't get a god hand every game, of course, but just having the potential of winning extremely quickly if you draw well is one of the hallmarks of a great competitive deck. This deck has the best chance of getting god hands of any deck I know. I would play it again, card for card.
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