Do you want to know how someone can lose or how he did lose?
Bly lost because he played very poorly: he did not build enough drones.
Take a moment to let that sink in, because its a very very big mistake and its the difference between a good Zerg player (like Fruit Seller) and a bad Zerg player (like Bly).
Instead of backing off after taking the Terran Natural, he continued to press in. He sends wave after wave of a consistently sized army. He does this because he's not building more drones so he cannot afford a larger army. By comparison Tarson's army gets larger and larger after every wave. He's able to continue to accumulate units because he has a fairly healthy economy. This is due in part to MULEs, but largely because Tarson built enough SCVs. Even after losing his Expo he still has as many workers as Bly does. Think about that for a second. He lose an entire base and all his workers in it and he still has more workers than his opponent.
This game could have easily been one that was featured on Day 9's Newbie Tuesday
I could point out a dozen mistakes that Bly made, but none of them matter nearly as much as his poor drone usage. Because of his lack of drones, his assault becomes almost an all in. So in response to your question How is it possible Zerg with biggest advantage can still loose to Terran?
Bly didn't have a big advantage. He sacrificed his economy on a gamble and it didn't pay off.
But let's imagine another universe, where Tarson wasn't playing Bly but was playing against a better Zerg like IdrA; and let's assume IdrA made the same early push.
Now IdrA is sitting on 2 bases to Tarson's 1, but they have equal workers. So instead of continually pressing his advantage, IdrA decides to play like he always does: Macro. He sits back and takes a third base and powers drones. Tarson retakes his natural and now he's down 2 to 3 bases. Not a big advantage for IdrA, but remember a Zerg can make drones faster than a Terran, so it takes Tarson longer to saturate that 1 base than it does for IdrA to saturate his 3. Now IdrA has a huge economy and he goes Roach/Hydra (or these days he's favoring Muta/ling, but pretend).
Imagine that battle for a second... or don't, because it actually happened. IdrA knocked out Tarson in IEM, exactly like I described.
The smartest thing you can do in Starcraft if you are ahead is to get more ahead. Anyone who played seriously in Broodwars knows this because if you pressed like Bly did, you got destroyed 100% of the time. Now Starcraft 2 is still new so a lot of people feel like they can do crazy 2 base play, but if you look at the high end GSL matches you see less of that and more of people trying to get more ahead.
You also mentioned a quote talking about Marauders vs Banelings. Now I don't think that the relationship between these two units had anything to do with this loss, but let's talk about them for a second.
Banelings are a highly specialized unit. Their role is to act as Zerg splash damage on light units. By comparison the Marauder is a more generalized unit, designed to act as a Meat shield (much the way the Roach acts for the Zerg). So it makes sense that a Baneling doesn't function well against Marauders (as that's not their role), and it also makes sense that Marauders do a good job of preventing Banelings from striking other units (as that's their role).
I would hesitate to say that a unit is broken because its functioning in its role and another unit isn't functioning in something outside its role. But let's say you want a way to deal with MMM balls. Instead of sending it waves of Banelings on their own. Consider mixing in more Zerglings (Bly actually does this to large effect). Now let's vary our composition based on their unit mix. More Marines? More Banelings. More Marauders? More Zerglings. Can't find a good place to engage? Burrow/Drops/Fungal Growth/Wait and Flank.
Here is the key thing, none of this is any assessment of Banelings against Terran, but rather an assessment of the tactics used.
2v2 games are a unique beast in the sense that you need to change your style of play. My 2s partner and I used to die a lot when it came to these early quick game rushes, and on the flip side, have rushed others as well to vary up the play style.
You mentioned that you were able to scout that they are doing a rush, you could mix in your ideas of how to survive to get a good counter to a rush. (Going to be using Monlyth Ridge as the example map and your match up as reference PTvTZ)
At 6 minutes (I assume in game time) they can probably have 10-15 marines and 5-9 roaches.
- If you are confident in your micro, forgo static defenses and simply try to out produce your opponents. At 6 minutes, you can get your defensive 4 gate up. Although it's really close. A mix of stalkers to shoot from the high ground and sentries to hold off the ramp should be able to hold them off. Even a few zealots mixed in there to tank damage while sentries pick away could suffice as well. (So you'd have ~2-3 sentries, 4 stalkers, 1 zealot)
- You shouldn't be afraid to get sentries and use force field. As a protoss player you want to have a fair number of sentries mixed into your army anyway later in the game. The force field only lasts 8 seconds so it is not a huge amount of time to stop you from going to help your ally. If used correctly you may even be able to trap a few of their units in your base (although against a roach/marine army that would just give them high ground vision so not really helping you there).
- You mentioned that your ally is terran, there is very little cost to investing in an early bunker or even two (even with the recent patch, he's only going to lose 25 minerals in the long run if he salvages them). So long as your ally is quick on the repair then he should be able to hold off the rush long enough for you to build up an army and flank with him exiting his bunkers to assist when you believe the two of you have enough to take out the attacking army. (Ally if matching opponent would have 10-15 marines as well maybe a little less because of the bunker)
- I'm not sure how your buildings were laid out, but pylons usually shouldn't be in attackable range, although the new patch doesn't help this point much (which I personally think is a pretty stupid nerf to the race, but I digress). Try to ensure that you have overlap on your production buildings.
Assuming it played out with the above, if the enemy ran to your base first, you force field him off, pick off a few units, or even weaken them as the two of you build up an army to crush the attack since your reinforcements will arrive much sooner than the attacking force. If they attack your ally first they run into a face full of bunkers that are getting repaired and your defensive 4gate should produce enough units to kill that army that they are sending, that or enough to force a retreat.
Going a forge first fast expand with cannons in this case you'd probably need 4 or 5 to just hold off that army if your ally responds quickly enough with reinforcements. Also in this case you are forcing your opponents to either deal with your cannons (with a sentry on the high ground to your ramp to prevent a run by, but if your wall is good enough on the low ground a run by would sustain massive losses) or to attack your ally (who again should have 2 bunkers and since you were attacked first, have ample time to get SCVs down to repair. If you go with the forge first opening I would suggest getting at least 1 sentry and a 2:1 stalker:zealot ratio for the first little while as you'd try to stay close to your cannons when trying to engage.
Best Answer
While I'm not sure about the specifics of how the AI works behind the scene or whether or not there are tactics you can use to force the AI to switch his strategy to something else, I know that YABOT in Advanced mode allows you to choose what build order the AI should perform. You can make or import build orders for the AI to use against you, along with setting the AI difficulty.