Attack with Preeminent Captain, putting Medomai onto the battlefield tapped and attacking.
Medomai triggers on combat damage, granting you an extra turn.
Tap Crystal Shard, returning Medomai to your hand.
Repeat.

Infinite turns

Lock

Medomai the Ageless

Preeminent Captain

Maskwood Nexus

Crystal Shard

Declare Preeminent Captain as an attacker.
Preeminent Captain triggers, putting Medomai from your hand onto the battlefield tapped and attacking.
Deal combat damage with Medomai, causing you to take an extra turn after this one.
Activate Crystal Shard by paying {U} and tapping it, returning Medomai to your hand.
Pass the turn.
Repeat.

Arcane Adaptation

Cast Artificial Evolution by paying {U}, changing all instances of "Soldier" on Preeminent Captain to "Sphinx".
Declare Preeminent Captain as an attacker.
Preeminent Captain triggers, putting Medomai from your hand onto the battlefield tapped and attacking.
Deal combat damage with Medomai, causing you to take an extra turn after this one.
Activate Crystal Shard by paying {U} and tapping it, returning Medomai to your hand.
Pass the turn.
Repeat from step 2.

Artificial Evolution

Cast Artificial Evolution by paying {U}, changing all instances of "Soldier" on Preeminent Captain to "Sphinx".
Declare Preeminent Captain as an attacker.
Preeminent Captain triggers, putting Medomai from your hand onto the battlefield tapped and attacking.
Deal combat damage with Medomai, causing you to take an extra turn after this one.
Activate Erratic Portal by paying {1} and tapping it, returning Medomai to your hand.
Pass the turn.
Repeat from step 2.

Erratic Portal

Attack with Preeminent Captain, putting Medomai onto the battlefield tapped and attacking.
Medomai triggers on combat damage, granting you an extra turn.
Tap Erratic Portal, returning Medomai to your hand.
Repeat.

Declare Preeminent Captain as an attacker.
Preeminent Captain triggers, putting Medomai from your hand onto the battlefield tapped and attacking.
Deal combat damage with Medomai, causing you to take an extra turn after this one.
Activate Erratic Portal by paying {1} and tapping it, returning Medomai to your hand.
Pass the turn.
Repeat.

Combos with "Preeminent Captain"