Feed the fire, get infraction. Y'all have been warned, so 'nuff is this nonsense. ... I've also just realized how terribly off topic this thread has gotten, so no more valve, no more zambies. On topic pl0x.
... I'd infract myself if I could right now, since I'm to blame as well. What a great example I set.
They already did make three
Half-Life: Opposing force
Half-Life: Blue Shift
Those can actually be considered three different Games. Half-Life is seen through the eyes of "Gordan Freeman". Half-Life: Opposing Force does extend a little more of the series within the perspective of the opposing military personal that came to stop freeman. Half-Life: Blue Shift, although disappointingly short, still extends the game, by giving players more insight through the game by you playing as "Barney".
Half-Life 2 and the updates kept the perspective of Gordan Freeman through the entire time. The others did not, therefore they are seperate on the basis that do not fully extend the game, but do show you more in the world of Half-Life in some way.
So all together 4 games.
There were 5 games in Half Life 1's story. They took place more or less within the same timeframe as Freeman's escape from the Black Mesa.
Half Life 2 is the sequel to HL1. It came with a story involving the aftermath of Freeman's actions from the previous game. It was followed by 2 Episodes. Again, expansions to the game it sprouted from.
In total, 2 games. Even Episode 3 is just an Expansion to finish HL2's story.
If I might expand upon Assasin's point... A released game is not necessarily the next step in a series' numbered sequels. For examples beyond Half Life, take a look at Assassin's Creed or Kingdom Hearts. AC has had two releases between AC II and AC III; "Brotherhood" and "Revelations". These two games were full games in their own right, not just downloadable content nor a slight rehash of the previous game. However, both Brotherhood and Revelations aren't labeled as AC III because they are both expansions to AC II.
As for Kingdom Hearts, everyone knows there's a ****in' million of the games, but so far the series has only reached II. Chain of Memories, which came out after 1 and is a direct sequel chronologically, which is also a completely new game, was not KH II. The new 3DS Kingdom Hearts game, Dream Drop Distance, is also a direct sequel to KH II but is not KH III, the same as how Chain of Memories isn't the numbered sequel to KH 1.
Every series has reasoning as to why it's games are numbered as they are, and which expansions/prequels/whatever are classified as such. For Assassin's Creed, a game introducing a new Assassin protagonist to play as will have the next number. Brotherhood and Revelations had the same main character as AC II for example, which meant they weren't going to be numbered. For Kingdom Hearts, every numbered game intentionally has two prequel intervals and will only be numbered if Sora is the main protagonist. KH 1 has one prequel already made and one in the works. KH II has both of it's prequels released. KH III also has both of it's prequels released.
Can't say I know nothin' of Half Life (yes, yes... such a sin), but I do know Valve is bad at math in the fact that there's never been a game 3 in their many series' roster yet.
You know what, it's hard to admit, but you are correct finally. They made Half-Life, Half-Life 2 + Ep One + Ep Two. Oh, and it requires internet to learn that Valve did not make Half-Life: Opposing Force, Half-Life: Blue Shift or Decay. In order for me to say Valve did not make three, they would have to literally make it. That is why I have learned that I'm wrong and you're wrong for telling me what to do such as look through internet sites. That is how I learn.