Cast Time Stretch by paying {8}{U}{U}, causing you to take two extra turns after this one.
At the beginning of your combat phase, Helm of the Host triggers, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Time Stretch from your graveyard.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take two extra turns after this one.
Repeat from step 2 (note that you may divide these steps among your multiple extra turns to reduce the mana requirements down to the amount shown in the prerequisites).

Infinite turns

Izzet Chemister

Helm of the Host

Time Stretch

Cast Temporal Manipulation by paying {3}{U}{U}, causing you to take an extra turn after this one.
At the beginning of your combat phase, Helm of the Host triggers, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Temporal Manipulation from your graveyard.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

Temporal Manipulation

Cast Walk the Aeons by paying {3}{U}{U}, causing you to take an extra turn after this one.
At the beginning of your combat phase, Helm of the Host triggers, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Walk the Aeons from your graveyard.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

Walk the Aeons

Cast Time Warp by paying {3}{U}{U}, causing you to take an extra turn after this one.
At the beginning of your combat phase, Helm of the Host triggers, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Time Warp from your graveyard.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

Time Warp

Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Late to Dinner from your graveyard.
Declare Initiate's Companion as an attacker.
Finest Hour's exalted and second ability triggers.
Resolve the first Finest Hour trigger, giving Initiate's Companion +1/+1 until end of turn.
Resolve the second Finest Hour trigger, untapping Initiate's Companion and causing you to get an additional combat phase after this one.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Capture of Jingzhou from your graveyard.
Move to your second combat phase, and declare Initiate's Companion as an attacker.
Finest Hour's exalted ability triggers, giving Initiate's Companion +1/+1 until end of turn.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's second ability by paying {1}{R}, tapping and sacrificing it, casting Late to Dinner and Capture of Jingzhou from exile without paying their mana costs.
Resolve Capture of Jingzhou, causing you to take an extra turn after this one.
Resolve Late to Dinner, returning Izzet Chemister from your graveyard to the battlefield and creating a Food token.
Repeat each turn.

Finest Hour

Initiate's Companion

Late to Dinner

Capture of Jingzhou

Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Late to Dinner from your graveyard.
Declare Initiate's Companion as an attacker.
Finest Hour's exalted and second ability triggers.
Resolve the first Finest Hour trigger, giving Initiate's Companion +1/+1 until end of turn.
Resolve the second Finest Hour trigger, untapping Initiate's Companion and causing you to get an additional combat phase after this one.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Temporal Manipulation from your graveyard.
Move to your second combat phase, and declare Initiate's Companion as an attacker.
Finest Hour's exalted ability triggers, giving Initiate's Companion +1/+1 until end of turn.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's second ability by paying {1}{R}, tapping and sacrificing it, casting Late to Dinner and Temporal Manipulation from exile without paying their mana costs.
Resolve Temporal Manipulation, causing you to take an extra turn after this one.
Resolve Late to Dinner, returning Izzet Chemister from your graveyard to the battlefield and creating a Food token.
Repeat each turn.

Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Late to Dinner from your graveyard.
Declare Initiate's Companion as an attacker.
Finest Hour's exalted and second ability triggers.
Resolve the first Finest Hour trigger, giving Initiate's Companion +1/+1 until end of turn.
Resolve the second Finest Hour trigger, untapping Initiate's Companion and causing you to get an additional combat phase after this one.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Walk the Aeons from your graveyard.
Move to your second combat phase, and declare Initiate's Companion as an attacker.
Finest Hour's exalted ability triggers, giving Initiate's Companion +1/+1 until end of turn.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's second ability by paying {1}{R}, tapping and sacrificing it, casting Late to Dinner and Walk the Aeons from exile without paying their mana costs.
Resolve Walk the Aeons, causing you to take an extra turn after this one.
Resolve Late to Dinner, returning Izzet Chemister from your graveyard to the battlefield and creating a Food token.
Repeat each turn.

Cast Capture of Jingzhou by paying {3}{U}{U}, causing you to take an extra turn after this one.
At the beginning of your combat phase, Helm of the Host triggers, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Capture of Jingzhou from your graveyard.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

Cast Capture of Jingzhou by paying {3}{U}{U}, causing you to take an extra turn after this one.
Activate Kiki-Jiki by tapping it, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Capture of Jingzhou from your graveyard.
At the beginning of your end step, Kiki-Jiki triggers, but you cannot sacrifice the Izzet Chemister token due to The Master.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

The Master, Multiplied

Kiki-Jiki, Mirror Breaker

Cast Temporal Manipulation by paying {3}{U}{U}, causing you to take an extra turn after this one.
Activate Kiki-Jiki by tapping it, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Temporal Manipulation from your graveyard.
At the beginning of your end step, Kiki-Jiki triggers, but you cannot sacrifice the Izzet Chemister token due to The Master.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

Cast Walk the Aeons by paying {4}{U}{U}, causing you to take an extra turn after this one.
Activate Kiki-Jiki by tapping it, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Walk the Aeons from your graveyard.
At the beginning of your end step, Kiki-Jiki triggers, but you cannot sacrifice the Izzet Chemister token due to The Master.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

Cast Time Warp by paying {3}{U}{U}, causing you to take an extra turn after this one.
Activate Kiki-Jiki by tapping it, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Time Warp from your graveyard.
At the beginning of your end step, Kiki-Jiki triggers, but you cannot sacrifice the Izzet Chemister token due to The Master.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take an extra turn after this one.
Repeat from step 2.

Cast Time Stretch by paying {8}{U}{U}, causing you to take two extra turns after this one.
Activate Kiki-Jiki by tapping it, creating a token copy of Izzet Chemister.
Activate the Izzet Chemister token's first ability by paying {R} and tapping it, exiling Time Stretch from your graveyard.
At the beginning of your end step, Kiki-Jiki triggers, but you cannot sacrifice the Izzet Chemister token due to The Master.
On your next turn, activate the Izzet Chemister token's last ability by paying {1}{R}, tapping it, and sacrificing it, casting the exiled spell without paying its mana cost.
Resolve that spell, causing you to take two extra turns after this one.
Repeat from step 2 (note that you can divide these steps among your multiple extra turns to reduce the minimum mana required to the amount shown in the prerequisites).

Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Late to Dinner from your graveyard.
Declare Initiate's Companion as an attacker.
Finest Hour's exalted and second ability triggers.
Resolve the first Finest Hour trigger, giving Initiate's Companion +1/+1 until end of turn.
Resolve the second Finest Hour trigger, untapping Initiate's Companion and causing you to get an additional combat phase after this one.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's first ability by paying {R} and tapping it, exiling Time Warp from your graveyard.
Move to your second combat phase, and declare Initiate's Companion as an attacker.
Finest Hour's exalted ability triggers, giving Initiate's Companion +1/+1 until end of turn.
Deal combat damage to an opponent using Initiate's Companion.
Initiate's Companion triggers, untapping Izzet Chemister.
Activate Izzet Chemister's second ability by paying {1}{R}, tapping and sacrificing it, casting Late to Dinner and Time Warp from exile without paying their mana costs.
Resolve Time Warp, causing you to take an extra turn after this one.
Resolve Late to Dinner, returning Izzet Chemister from your graveyard to the battlefield and creating a Food token.
Repeat each turn.

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