Mirrored Depths is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Whenever a player casts a spell, that player flips a coin. If the player loses the flip, counter that spell. Whenever chaos ensues, target player reveals the top card of their library. If it's a nonland card, you may cast it without paying its mana cost.