Palace

Palace has a staircase for an endgame. Your cards sit in three layers: a hand you play first and refill from the stock, three face-up cards waiting on the table, and three face-down cards under those, played blind one at a time when everything else is gone. Each turn you play a card at least as high as the top of the pile, or pick the whole pile up.

The magic cards keep it moving: a two resets the pile so anything can follow, a ten burns the pile out of the game entirely, and four of a kind on top burns it too. Before play begins you may swap cards between your hand and your face-up row, and what you leave showing is what your opponent studies all game. First player to shed every card, blind ones included, wins.

The last three cards are played blind, one at a time, and you see what you played at the same moment your opponent does. A hand that looks lost can still turn, because a single card can send the whole pile to somebody else. Three computer strengths sit behind the same table. The weakest plays at random; the strongest matches the rank already showing so that it can build towards a burn. Palace has no draws, so its record is two numbers.