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(It's also an exchange that leaves the control player ahead on card advantage)
Because the last ability of each Opposition Agent is trying to exile the card and give permission to play it, the owner of the exiled card chooses which effect wins
Before I start, some caveats: I will not go through the whole deck list of each deck (so, please find them here) and I will be proposing cards that are US$10 or less
With Krark's Thumb in play, you have a 42.19% chance of drawing 9 cards and untapping all your lands
Since it's so low, you can copy multiple artifact abilities in one turn without investing a ton of mana, so you can hold it for other spells and interactions