Polished Rhombus Amethyst

Socket bonuses

In a Weapon: +25.0% Arcane Damage
In a Helm, Chest Armor or Pants: +20 Intelligence
In a Ring or Necklace: +11.0% Arcane Damage Reduction

Gem

Gem type

Amethyst

Tier

Tier 4

Enemy level

45 and higher

Sells for

2,000 gold

Enemies of level 45 and higher
Every cleared encounter has a gem chance (1% for normal enemies, 6% for elites, 10% for mini-bosses and 12% for bosses); at these levels the gem is one of the 6 tier 4 gems, picked evenly. In the Mythic Rift only the boss encounter rolls a gem.
Treasure chests
Chance of a gem, picked the same way at the chest's level: 10% in the Silver Treasure Chest and Mythic Treasure Chest; 20% in the Golden Treasure Chest.
Rough Square Amethyst
The Gem Specialists make 1 Polished Rhombus Amethyst from 10 Rough Square Amethyst and 5,500 gold.

Dreamvault Treasure Drake
70% per cleared encounter with it, on all difficulties. Met in Dreamy Keep (level 65 on Normal).

Enemy special drops are rolled once for every cleared encounter the enemy is part of, however many of it the encounter holds, in the places listed here. On Nightmare and Inferno every enemy in them is level 70.

Drop chances are the game's rules for offline characters; the game server decides the loot of online characters.