3 collossi = 200/200 (range) + 900/600 (building) + 200/100 (factory) + 200/200 (bay) = 1500 minerals 1100 gas
Buildtime from cyber core is 75*3+65+65=355, with some chrono possible.
High templars need TC (150/100) templar archives (150/200) and two extra gateways (at least).
Time to get the archons out is 50(TC) + 50(TA) + 45 per archon (at 2 gateways), plus 12 for the merge (only last merge counts). 4 archons being out isn't all that unreasonable, which is 400/1200.
Dark Shrine route is 50 extra delay, 50 less minerals and 50 extra gas. 4 archons using DTs is 1000/1000.
Dark Shrine route: 1600 minerals 1300 gas for 4 archons at a delay of 252
Templar Archives route: 1000 minerals 1500 gas for 4 archons at a delay of 202.
The archons do 20 DPS each (splash) vs biological, or about 15 vs non.
The colossi do 18 DPS against everything.
And archons are really expensive. On the other hand, their factories are cheap -- basically you get to quickly dump all
of your gas into upgrades, a few sentries, or archons.
The archon is also playing blind -- no observers. Hallucinated phoenix scouts?
The colossi player needs be either psychic (which is easy, he can get observers) or spend resources on stalkers.
(they already own roaches
Stalkers own roaches? Really? Are we talking crazy micro stalkers, or A-move stalkers here?
Stalker is 125/50 for 9.7 DPS vs Armored, 6 range, 1 armor, 160 HP. (25 minerals of supply)
Roach is 75/25 for 8 DPS vs Everything, 4 range, 1 armor, 145 HP. (25 minerals of supply)
Roach armor is always there (Stalkers is on only half their HP), and roaches 2 second cooldown means that armor does slightly less to their attacks than stalker attacks.
2 roaches is only slightly more expensive than a single stalker, does 16 DPS and has 290 HP. 60% more DPS, 80% more soak. (admittedly the roaches need more supply).
4 roaches costs 5 larva (including queens). (Queen+Hatch) costs 500 minerals, 1/10+1/15= larva every 6 seconds on average. So it takes 3000 minerals for a roach/second (2400 after you lose units)
Stalkers take 32 seconds from a warpgate (150 minerals) for 4800 minerals for a stalker/second.
So roaches are harder to produce an initial push from en-mass, but just as easy once you have lost units.
Hydras just own stalkers. Hydras problem vs Protoss is Protoss use of Colossi/Templars to do mass area damage, while hiding behind tough yet low-damage output gateway units.