Does dredge work during your opponent's draw step if they have a dredge card in their graveyard?

Dredge is a replacement effect that modifies a draw event. According to CR 702.52a, dredge states: 'If you would draw a card, you may instead mill [N] cards and return this card from your graveyard to your hand.' The word 'you' is critical — it refers to the controller/owner of the card with dredge, not any player who happens to be drawing.

Replacement effects are applied by the player whose game event is being replaced (CR 614.1a). Since your opponent is the one drawing during their draw step, only replacement effects that say 'if you would draw' and belong to them can replace their draw. A dredge card sitting in your graveyard cannot replace a draw your opponent makes.

So dredge is only usable by the player who owns the dredge card, and only when that player would draw a card — whether on their own draw step, from a spell effect, or any other draw event that applies to them.

Example: You have Golgari Grave-Troll in your graveyard. It is your opponent's draw step. Your opponent draws their card normally. You cannot use Golgari Grave-Troll's dredge ability during their draw step because the draw event belongs to your opponent, not you.

The same logic applies in reverse: if you are drawing a card and your opponent has a dredge card in their graveyard, you still cannot use their dredge — it simply does not interact with your draw events at all.