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mill
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Mill without Jace's Phantasm and Thought Scour? Unheard of. Search the City is a terrible card no matter how you look at it. Costs 5, Lose 5 cards, Need to match 5 cards, and THEN take a turn? Might as well say "Take a physical beating for 5 minutes then cast Time Warp".
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Not bad, I would agree with cng and drop the search the city, it's too expensive, in general your running mana expensive especially for 20 lands. Thought scour is necessary for mill, one of the best, also Jace's phantasm is pretty damn good for a different win condition (however you have an interesting set up in place so maybe you don't need them but consider making them in sideboard and some dissipate or something). Also for defense fog bank (though I'm not 100% sure where to make room). I would also use 2x Jace versus Tamiyo. She is good control but doesn't fit the deck, it's a different kind of defense. Also I would use Cyclonic Rift and Unsummon versus vanishment and devastation tide. In general Remove: -1 Tamiyo -3 Search the City -4 Devastation Tide -3 Vanishment -1 Inaction Injunction Add: +3 Cyclonic Rift +3 Unsummon +3 Thought Scour +2 Island +1 Jace, Memory Adept (You could drop trepanation blade and invisible stalker for jace's phantasm and fog bank if you want to try it that way)