If Ophidian Eye is enchanting Niv-Mizzet, Parun, the following loop of triggered abilities can occur: when any player casts an instant or sorcery, Niv’s trigger to draw a card is put onto the stack as the spell is cast ; when that trigger resolves you draw a card, which causes Niv’s "Whenever you draw a card, Niv-Mizzet deals 1 damage to any target" trigger to be put on the stack . If that damage is dealt to a player who is an opponent of the Ophidian Eye’s controller, Ophidian Eye’s triggered ability may trigger to let its controller draw a card [Ruling 2006-09-25]; that draw can in turn cause Niv’s draw-trigger (if the draw was by Niv’s controller) and continue the chain. The initial spell that caused the first draw is still on the stack while these triggers are happening, and per the official ruling you can act after Niv’s “draw on cast” trigger resolves but before that original spell resolves (so the drawn card could be used in response to the original spell) [Ruling 2018-10-05] and .
Step 1
An instant or sorcery spell is cast; during the casting it is put onto the stack (the spell is "cast" as described in ).
Step 2
As soon as the spell is cast, Niv-Mizzet’s ability "Whenever a player casts an instant or sorcery spell, you draw a card" triggers and that triggered ability is put on the stack (this is what happens to abilities that trigger when a spell is cast per ).
Step 3
Players receive priority and the stack resolves top-down. When Niv’s "draw a card" trigger resolves you draw a card (the draw happens while Niv-Mizzet is on the battlefield, so its other triggered ability will function normally per ).
Step 4
Drawing that card causes Niv-Mizzet’s "Whenever you draw a card, Niv-Mizzet deals 1 damage to any target" triggered ability to be put on the stack (this is a battlefield object’s triggered ability functioning as described in ).
Step 5
When the Niv damage trigger resolves, Niv deals 1 damage to the chosen target. If the chosen target is a player who is an opponent of Ophidian Eye’s controller, Ophidian Eye’s ability "Whenever enchanted creature deals damage to an opponent, you may draw a card" triggers (see Ruling [2006-09-25]).
Step 6
When Ophidian Eye’s trigger resolves its controller may draw a card. If Ophidian Eye’s controller is also Niv’s controller, that draw will cause Niv’s "Whenever you draw a card" trigger again and the chain repeats. If Ophidian Eye’s controller is a different player, that draw will only trigger that player’s draw-based effects, not Niv’s, because Niv’s draw trigger cares about draws by Niv’s controller.
Step 7
All these triggered abilities go on the stack and resolve in last-in, first-out order; the original instant or sorcery that began this sequence is still on the stack until it resolves or is countered, and you can take actions in between because triggers resolving doesn’t cause the original spell to resolve immediately (see Ruling [2018-10-05] and ).
Resolution
With Ophidian Eye attached to Niv-Mizzet, Parun (and assuming you control Niv): when an instant or sorcery is cast, Niv’s draw trigger goes on the stack as the spell is cast . When that trigger resolves you draw a card and that draw causes Niv’s damage trigger to go on the stack . If Niv deals damage to a player who is an opponent of the Ophidian Eye’s controller, Ophidian Eye’s trigger may trigger to let its controller draw a card (it is optional) [Ruling 2006-09-25]. If that draw is performed by Niv’s controller it will in turn trigger Niv again, and the pattern can repeat as long as the Ophidian Eye’s controller chooses to draw and legal targets exist for Niv’s damage. Also note that the original instant/sorcery that caused the first trigger is still on the stack while these triggers and draws are happening, and you can take actions in between because the draw-trigger resolves while the spell that caused it is still on the stack [Ruling 2018-10-05] and .
