Cast Aura Finesse by paying {U}, attaching the Aura to Codie and drawing a card (this is necessary because Codie's ability forces you to cast the Aura before Codie is on the battlefield).
Activate Codie by paying {4} and tapping it, adding {W}{U}{B}{R}{G}.
Activate the Aura by paying {U}, untapping Codie.
Repeat from step 2 any number of times, skipping step 3 on the final iteration.
Once you have an arbitrarily large number of Codie triggers, cast any spell by paying its mana cost, reduced by the {W}{U}{B}{R}{G} added in step 2.
Codie triggers for each time you activated its ability.
Resolve the first trigger, causing you to exile cards from the top of your library until you exile an instant or sorcery spell with lesser mana value, and allowing you to cast that spell without paying its mana cost.
Repeat step 7 for each remaining trigger.
You may also repeat this combo for each instant and/or sorcery card in your hand as mana permits, and on subsequent turns.

Cast a subset of spells in your library

Codie, Vociferous Codex

Aura Finesse

Freed from the Real

Cast Aura Finesse by paying {U}, attaching Power Artifact to Codie and drawing a card.
Cast Chain Stasis by paying {U}, targeting Codie.
Holding priority, activate Codie by paying {2} and tapping it, adding {W}{U}{B}{R}{G}.
Resolve Chain Stasis, untapping Codie and causing you to pay {2}{U} to copy Chain Stasis, with the copy targeting Codie.
Repeat from step 2.
Once you have an arbitrarily large number of Codie triggers, you may choose not to copy Chain Stasis and cast any instant or sorcery by paying its mana cost, reduced by the {W}{U}{B}{R}{G} added in step 1.
Codie triggers for each time you activated its ability.
Resolve the first trigger, causing you to exile cards from the top of your library until you exile an instant or sorcery spell with lesser mana value, and allowing you to cast that spell without paying its mana cost.
Repeat step 8 for each remaining trigger.

Infinite magecraft triggers

Chain Stasis

Power Artifact

Cast Aura Finesse by paying {U}, attaching Power Artifact to Codie and drawing a card.
Activate Codie by paying {2} and tapping it, adding {W}{U}{B}{R}{G}.
Activate Codie using the ability from Galvanic Alchemist by paying {U}, untapping it.
Repeat.
Once you have an arbitrarily large number of Codie triggers, you may cast any instant or sorcery spell by paying its mana cost.
Codie triggers for each time you activated its ability.
Resolve the first trigger, causing you to exile cards from the top of your library until you exile an instant or sorcery spell with lesser mana value, and allowing you to cast that spell without paying its mana cost.
Repeat step 7 for each remaining trigger.

Infinite red mana

Infinite green mana

Infinite black mana

Infinite white mana

Galvanic Alchemist

Cast Aura Finesse by paying {U}, attaching Power Artifact to Codie and drawing a card.
Activate Codie by paying {2} and tapping it, adding {W}{U}{B}{R}{G}.
Activate Vigean Graftmage by paying {1}{U}, untapping Codie.
Repeat.
Once you have an arbitrarily large number of Codie triggers, you may cast any instant or sorcery spell by paying its mana cost.
Codie triggers for each time you activated its ability.
Resolve the first trigger, causing you to exile cards from the top of your library until you exile an instant or sorcery spell with lesser mana value, and allowing you to cast that spell without paying its mana cost.
Repeat step 7 for each remaining trigger.

Vigean Graftmage

Cast Aura Finesse by paying {U}, attaching Power Artifact to Codie and drawing a card.
Activate Codie by paying {4} and tapping it, adding {W}{U}{B}{R}{G}.
Activate Codie using the ability from Umbral Mantle by paying {1} and untapping it, giving it +2/+2 until end of turn.
Repeat.
Once you have an arbitrarily large number of Codie triggers, you may cast any instant or sorcery spell by paying its mana cost.
Codie triggers for each time you activated its ability.
Resolve the first trigger, causing you to exile cards from the top of your library until you exile an instant or sorcery spell with lesser mana value, and allowing you to cast that spell without paying its mana cost.
Repeat step 7 for each remaining trigger.

Search Results