how does obsidian destroyer counter anti-mage
Arcane Orb deals pure
damage (it is not reduced by spell resistance or armor or anything ever).
Essence Aura makes sure that OD will never
run out of mana by himself so Anti-Mage will not have an opportunity to cast mana void on OD unless he is allowed to hit OD multiple times.
There are really only two items that OD needs to defeat Anti-Mage in a fight: Scythe of Vyse and Ghost Scepter. Meanwhile, Anti-Mage will probably purchase a BKB in order to become spell immune for a duration. The following scenarios could then happen:
1. Obsidian starts the fight by turning Anti-Mage into a chicken, and then wails on him with Arcane Orb. If Obsidian is farmed enough, he can probably kill Anti-Mage with just his Arcane Orb alone before Anti-Mage is able to recover from hex.
2. Anti-Mage activates BKB so he can't be hexed and attacks Obsidian. Obsidian uses Astral Imprisonment on himself, becoming invulnerable for 4 seconds. After that, he activates Ghost Scepter, becoming immune to physical hits for another 4 seconds. Anti-Mage's BKB runs out. Obsidian turns Anti-Mage into a chicken, wails on him with Arcane Orb, and kills him.
I assume that both OD and Anti-Mage are equally farmed and have roughly the same kills. If Anti-Mage is more farmed and has more kills than OD, the results may vary.Also
I forgot to mention that OD can manual-cast his Arcane Orb while under the effect of Ghost Scepter. So that item basically gives you four seconds of attacking Anti-Mage while he can't attack you back.