The cost of using multiple villagers to speed up construction

I just wondered how much extra work time (and therefore resources) it costs to use multiple villagers rather than one. Fortunately that's pretty easy to answer, although the result is as unspectacular as you may have thought. I decided to post it anyway because I already did the calculations and why the hell not.

1. The formula for construction time is 3t/(n+2), where t is the building's construction time and n the number of builders.
   So for one builder the construction time is 3t/3 = t. For two builders the construction time is 3/4t. It takes 4 builders to cut the construction time to half.

2. To find out how much time our villagers idle, we can just multiply it by n: 3tn/(n+2) = 3t/(1+2/n)

Example values:

• 1 villager -> 1t idle time

• 2 villagers -> 1.5t idle time

• 3 villagers -> 1.8t idle time

• 4 villagers -> 2t idle time

• 10 villagers -> 2.5t idle time

The limit of the function is 3t. So if you use as many villagers as possible, you will at most lose 3x the amount of work time as if you had built the building with only one villager.

Let's go through a concrete example. We send 4 villagers to the woodline where we want to build a lumber camp:

• The construction time is 35s for a basic resource building (lumber camp/mine/mill).

• Villagers gather around ~23 resources/minute in dark age, so the construction time costs you about 13-14 wood.

• If you construct it with 4 villagers, you spend double the villager work time (4 x 3*35/(4+2) = 4 x 17.5 seconds = 70 seconds) and thus lose another 13-14 wood.

However, if you send all villagers at once but only build the lumber camp with a single one, the lumber camp may not be finished by the time the other lumberjacks have filled their inventory and may wander back to your TC. It takes 2.5s to chop down a tree and 25s to fill a dark age lumberjack's 10 inventory capacity, compared to 35s to construct the lumber camp.

You may therefore want to build the lumber camp with 2 vills in 26.25 seconds. At this rate you lose ~7 wood and thus maintain a 7 wood advantage over building the camp with all four vills. A very small effect either way.

So the effect for situations like this is really small and this question as irrelevant as you may have thought.