[AoE II] Mathcrafting a villager gather rate formula

The following video by YouTuber Spirit Of The Law is one of those few-but-beautiful videos that is tightly targeted and site-appropriate, being chock full of great game analysis all the way through. Spirit, an Age of Empires II analyst, uses math and in-game testing to arrive at data-driven answers to strategy questions. Here he gets to work to create a useful formula for estimating villager gather rate, previously nebulously-understood. After arriving at a formula, he goes a step further, applying it to answer some otherwise-unanswerable questions:

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