Why do some AIs protect their worker with an archer early game but others dont?

Yes. If they are fearing an attack of you or are planning to attack you yourself, they will guard their workers from you.
 
I've also noticed that military units on the same tile as workers building improvements have a way of muting the sound of their work.

Whether they're hammering, raking, digging, or whatever, that military unit being on the same tile as your workers makes it impossible for you to hear what's going on (you'll only hear the military unit). This could be a way of making it just a tad harder for you to snoop around and learn what a player is up to.

Sound CAN carry over several tiles, and terrain features (forests, hills, and --worst, because they echo--mountains) can affect this. Try zooming in as far as you can, and listening to what you hear when you're focused on a particular tile, and you'll see what I mean. Turn the gird on and move to adjacent tiles and notice where and when you CAN'T hear certain sounds.

There's more than meets the eye (and ear) here...
 
Another issue than the perceived threat is: do they have a spare archer?

(And if so, does it have an appropriate unit AI type? This is something the player is not normally aware of and can only see if the CheatCode has been set in the .ini file. Every unit has a unit AI type, each of which behaves differently and can be used for different things by the AI. I'm not sure which ones can escort a worker, but it is probably something like reserve, counter, and attack and it probably can't if it is city defense or city attack - there are various others too but those are the main ones for military units, with the standard general purpose one being attack.)

Edit: And the board went to the Christmas theme while I was writing that...
 
God-Emperor, try going into worldbuilder and do the edit unit thing. It shows all those types you told. This way, you could find out what the AIs are using their units for.
 
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