Activate Altar of Dementia by sacrificing Cavalier of Gales.
Cavalier of Gales and Verdant Succession trigger.
Resolve the Cavalier of Gales trigger, shuffling it into your library.
Resolve the Verdant Succession trigger, searching your library for Cavalier of Gales, putting it onto the battlefield and shuffling your library.
Cavalier of Gales enters the battlefield, causing you to draw three cards and put two cards from your hand on top of your library.
Resolve the Altar of Dementia ability from step 1, causing target player to mill cards equal to Cavalier of Gales's power.
Repeat.
This loop turns your library into a self-sustaining engine by manipulating colors and trigger stacking. With Painter's Servant painting every card the chosen color, Verdant Succession recognizes Cavalier of Gales as a green creature whenever it hits the graveyard. When you sacrifice the Cavalier to Altar of Dementia, its own death trigger tries to shuffle it into your library first, but because Verdant Succession lets you search for a card with the same name and put it directly onto the battlefield, you bypass the shuffle and immediately redeploy the Cavalier. This fresh entry triggers the Cavalier of Gales to draw you three cards and restock your hand, while the Altar simultaneously mills your opponent down to nothing.