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If you've ever heard of Slay the Spire, this is the same style of mode. You'll start each run with a deck full of basic cards. After each battle, you'll be offered a choice of card to add to your deck. Also similar to dungeon run, but there should be random events and other such things mixed in with the battles.
Edit: disregard this!
We'll share more details later, but it really won't be similar to this at all. Mercenaries is different from constructed Hearthstone similar or even more than Battlegrounds is different than constructed Hearthstone.