A minor technical note on build rates with multiple villagers

This website (http://www.aoe2sheet.info/knowledge_base.html#building) and the aoe2 wiki (https://ageofempires.fandom.com/wiki/Villager_(Age_of_Empires_II)#Buildings) claim that the build time formula for multiple villagers is:

build time = 3*t/(n+2) 

where t is the time it takes 1 villager to build a building (e.g. 3500 seconds for a wonder) and n is the number of villagers.

This is not quite correct. The correct formula seems to be

build time = t/(0.67+0.33*n) 

The difference being that a rounding effect will occur meaning that buildings will take slightly longer to build than expected. The difference is easiest to spot when 4 villagers build a wonder. The commonly used formula would predict a build time of 1750 seconds. The correct formula predicts a build time of 1759 seconds. The build time of 1758 is what occurred when I tested it.

The increased build time is 0.5% more at 4 vills than expected under the commonly used formula; 0.75% more at 10 vills; and 0.87% more at 20 vills. This error factor does not exceed 1.001%. So ultimately the difference is small (but real).