Cast Lava Spike by paying {R} and choosing to pay {1}{R} and reveal Desperate Ritual from your hand, adding Desperate Ritual's effects onto Lava Spike, with Lava Spike targeting an opponent.
Cast Desperate Ritual by paying {1}{R}, adding {R}{R}{R}.
Activate Izzet Guildmage's second ability by paying {2}{R}, copying Lava Spike, targeting an opponent.
Resolve the copy of Lava Spike, adding {R}{R}{R} and dealing three damage to an opponent.
Repeat from step 4.

Infinite damage

Infinite magecraft triggers

Izzet Guildmage

Lava Spike

Desperate Ritual

Cast Lava Spike, targeting yourself.
Splice Desperate Ritual onto Lava Spike.
Hold priority and activate Mirror Sheen, targeting Lava Spike.
Have the copy of Lava Spike target another player.
Resolve the copy of Lava Spike.
Using the RRR from the copy of Lava Spike's text from Desperate Ritual, activate Mirror Sheen, targeting Lava Spike.
Repeat.

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