If both players pass priority with an empty stack during the main phase, does the turn automatically advance?

When the stack is empty during a main phase, the active player receives priority first (CR 117.3a). If the active player passes priority, the non-active player receives it. Only when both players pass priority in succession with an empty stack does the current step or phase end (CR 117.4).

It is not enough for just one player to pass. The game requires back-to-back passes with nothing on the stack. As soon as any player puts something on the stack (plays a land, casts a spell, activates an ability), the 'pass chain' resets — both players must pass again after that new object resolves before the phase can advance.

When both players do pass in succession on an empty stack during a main phase, the game moves to the next phase in turn order. For a first main phase, that means moving to the beginning of combat (CR 505.1, 505.4). No separate 'advance' action is needed — it happens automatically once the mutual-pass condition is met.

Example: It's your first main phase. You cast Llanowar Elves; your opponent responds with Shock targeting it. After Shock resolves and Elves dies, the stack is empty. You pass priority, then your opponent also passes priority — the game now automatically advances to the beginning-of-combat step.

Note that during the cleanup step, players do not normally receive priority at all (CR 514.3), so that step is a special case. But in any normal main phase, the rule is clear: both players must pass in succession on an empty stack (CR 117.4).