Valve has a few reasons why Half-Life 2: Episode 3 never happened

Valve has explained why we never got Half-Life 2: Episode 3.

Why Valve Never Made Half-Life 2: Episode 3 - IGN

Valve explains why we still don't have Half-Life 3

Half-Life 2: Episode 3 creator reflects on reception, one year after release

Steam Community :: Guide :: Half-Life 2: Episode 3 (Story) by Marc Laidlaw

Returning to Half-Life 2: Episode Two and Considerations For The Future of Half-Life

Half-Life 2: Episode Pack - PC : Video Games

Steam users are attacking Dota 2 because there's no more Half-Life - Polygon

What are the reasons why we may never see Half Life 3 or Half Life 2: Episode 3? - Quora

Hands On Preview of Half-life 2: Episode 3 Electric Cartilage And The Games That Don't Exist