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1.
The speculated predacessor to Half Life 2: Episode 3.

Though Valve has confirmed that episode three will be the last in the current story arc, they have promised that the Half Life games will continue, most likley through the "episodic medium" they are currently being delivered in.

**Speculation from the next game being the actual anticipated HL3 can be justified by noting that the plot lines of Half Life 1 and 2 are different from one another, so in Valve's admission that the series will not end at Episode 3, it can be inferred that the next title will be HL3**

One thing certain about Half Life 3 is that it will be the continuation of the greatest game ever made, aside from portal, which is tied with half life for that title.
From an interview with Valve on www.stuffwelike.com/stuffwelike /2007/12/12/half-life-3 -world-exclusive/

"TS-SWL: Are there any current plans after Episode 3 to have a Half Life 3?

DL: We haven’t announced anything specific, but Half-Life won’t end at Episode Three – hang on to your crowbars!"
by Glassweaver April 13, 2008