Riku's first ability triggers, causing you to pay ({U} magic symbol) ({R} magic symbol) to copy Narset's Reversal, with the copy targeting the original Narset's Reversal.
Resolve the copy of Narset's Reversal, copying the original Narset's Reversal targeting Alchemist's Gambit, and returning the original Narset's Reversal to your hand.
Resolve the copy of Narset's Reversal created in step 5, copying Alchemist's Gambit and returning the original Alchemist's Gambit to your hand.
Resolve Alchemist's Gambit, causing you to take an extra turn after this one.
Repeat each turn.
Notes
You may pay an additional ({U} magic symbol) ({R} magic symbol) to copy the extra turn spell, and only need to do this loop during your second extra turn.