Nearly half your deck is removal. You're clearly optimized for fighting opponents that put their trust in playing minions which you then efficiently remove, before finishing them off with your fat legendaries.
Your deck is not well suited to beating a priest - who is probably quite stacked with removal himself, and as you say, has those card steals and mind controls to turn your fatties against you.
imho that sort of priest finds it hardest to deal with aggressive decks that don't rely on anything too huge. Obviously exploiting the 4-attack blind spot between Shadow Word: Pain and Shadow Word: Death is a big deal. His only AoE is gonna be Holy Nova and that won't sweep a table full of 4/4's and 4/5's.
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I pulled him in my second pack ever when first starting Hearthstone, and ever since he's been in my druid control deck. Thanks for all the wins buddy. :')
Bloody OP bastard. x3
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Ironically, priests have the lowest win rate in constructed I believe, something like 46%, haha. They're far from overpowered.
You have so much removal with all your spells that you can afford them taking minions from you. It's really kinda based on how lucky they are on what the those pesky cards that copy from your hand/deck end up netting them. Mind Control is a 10 mana card, so maybe you can beat them before then. You gotta remember two things: Control decks play for late game, and every deck has a weak match up. You can't expect to beat every deck easily, maybe priests are your weak points. Bad match ups happen. Personally Hunters get me a lot. x3
I would like to make a deck suggestion though, if you have Thalnos, replace Nat for it. Thalnos still offers a card draw on deathrattle and an early spell damage bonus early game if he lives. It might give you that tiny extra early game edge. After Nat Pagle got nerfed, he's not nearly as effective as he used to be. You pretty much have to have him down with a taunt to get any value from him I find.
Hopefully someone more knowledgeable helps you, as I don't run into many priests I'm afraid.
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I actually didn't know that creatures would come back with their divine shield! I should give that a try.