On the topic of the light cavalry rush:
I wanted to see how fast I could get light cavalry with low activity. I still got them before my beginner protection was up.[spoil]day 1: I had classes (4 hours), work (6 hours), and a good amount of sleep (8 hours)
day 2: I had classes (7 hours), work (6 hours), and a good amount of sleep (8 hours)
day 3: I had classes (2 hours), work (7 hours), and a good amount of sleep (8 hours)
I did all the normal recreational stuff with friends: played some video games, watched a movie or two, went out for pizza, etc. I ran a few errands and did a few hours of studying each day.
I didn't get on the computer at all during these times.
I started at about 00:44:xx 5/11/2008.
I finished training my first light cavalry at about 00:24:xx, 08/11/2008
That's less than 3 days, in a world with 4-day beginner protection.[/spoil]
The key was planning. I knew the required buildings and technologies to train light cavalry, how much they costed, how long they took to make, etc. I mostly knew my schedule ahead of time, so I planned my in-game actions to fit around my life. I used a tool similar to
this one.
If a player like openeye (sits on the computer all day) or jamm (a team of people playing the same account) was to rush to light cavalry, I'd bet they could get them within 2 days of starting on the same world (speed 1.2, unit speed 1.5).
Now, what is the point of getting light cavalry as soon as possible? It's like openeye said, "Light Cavalry are the best unit for farming." I'd say the nicest things about using light cavalry to farm are that they're nearly twice as fast as spears; And you can send very small amounts of them to raid undefended villages without losing any of them (you could send one by itself, or, with horrible morale, two of them)
To farm effectively, you have to make the most use of your hauls. By this, I mean that you want to steal 100% of each raiding squad's haul. If your neighbors are farming too, there will likely be only small amounts of resources in any villages nearby. So you have to make the best use of your units, and send out many small attacks, instead of a few big attacks, to increase the chances of getting the most resources you can. For example, pretend that beginner protection was almost up. Suppose you didn't rush light cavalry. Instead of attacking 4 villages with squads of 100 spears every 6 hours, you could attack 80 villages with squads of 3 spears and 2 axes every 6 hours. Not only will you have better chances of getting the most resources possible from your hauls, but you won't suffer so much when you attack a spike. However, spears&axes aren't nearly as quick as light cavalry. Generally, if you log in more than two or three times a day at this point in the game, you'll be able to get resources much faster by using light cavalry squads.
Now, here is where combining frequent activity with a light cavalry rush truly shines. Figure out the rates of resource production in each village you raid, and match them with the rate you haul resources. If a village made 30 timber/hour, 30 clay/hour, and 30 iron/hour, that would be a rate of 90 resources per hour. Suppose it has no wall and you have good enough morale to only send 1 light cavalry (which has a haul of 80). You would send 1 light cavalry to attack the village once every [80/90 hours]; that's about once every 54 minutes. If you do this for every one of your farms, you'll be getting a good steady income of resources, making the most of your hauls, and
decreasing the income of your neighbors without spiking anything or attacking them.
Once players near you notice that farming doesn't get enough resources, they will try to spike (if you hit one, avoid it and routinely scout till the troops are gone) and/or upgrade their resource production buildings (new farms, anyone?). When they spike, they can't farm with those units, so they'll grow slower. Within a few days of beginner protection ending, these starved players aren't really threats, and you can either ignore them, clear&raze their villages into new farms, or persuade them to become your sycophants.
As for whether this approach is better for worlds with growing gray villages or a world without growing gray villages, I'd say a light cavalry rush works well in both. But it's much easier to manage things on a non-growing-gray world, because growing-grays tend to construct walls, ruining the farming method unless you also make routine wall/barracks/hq destruction runs.