Was watching a Hera stream where he asked if Heavy Plow was worth the idle TC time.
Here’s my attempt at solving this (math can be found here)
tl;dr: The optimal time to Click Heavy Plow is around ≈15:00 to maximize wood saved and total additional food collected.
More specifically:
- With a realistic TC-idle cost ≈ 45s to float resources, the global max (by 60′) is to click Heavy Plow around 15:00 if you value saved wood like food (κ≈1). If you value wood less (κ≈0.5), it shifts to ~20:00.
- If you can buy HP with zero TC idle, click it ASAP (first minute of Castle, or Feudal for Burgundians).
- If you insist wood has no value (κ=0), HP won’t fully pay back by 60′ off the carry-rate alone; the value is in reseed wood saved and compounding.
Note: Heavy Plow’s research time is 40s; I treat “TC idle” separately as the time you’re not making vils to afford the tech. The curves below use TC idle = 0:45 as the main case and also show 2:00 and 0:00 for context.
Would love to get suggestions / thoughts on this.
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How Heavy Plow idle TC? It is a tech researched in mill, not in TC.
If you don’t have food for both the tech and making villagers
When I made my boomin tests, using a “exponential value decline” model the result was clearly for that scenario that HP yields better results.
The result was that’s best to go up to castle age - ideally it said a 4 TC boom approach was the optimum and getting HP when you have all the TCs running safely. Hand Cart had a lower priority.
If you can afford it, you can get HP even before the Boom, but when you use optimised buildorders for Booming it’s usually better to get the Vills pumping before. Horsecollar, Wood upgrades and even Wheelbarrow are ideally even researched BEFORE the boom.
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Imho the +1 gather is sometimes more important than the extra food per farm. It slightly should increase gather speed iirc
Very interesting analysis ! A few remarks:
A horizon at 60 minutes feel very long, in case of a FC boom we should have 120 vils by minute 30 or so, and be fully boomed by minute 45 max. So the missing resourses from villagers should stop by minute 30.
It is weird assume TC idle time, because if you are booming, villagers should be more important. If you idle TC for 45s at minute 15, then at minute 60 you are down 2vil x 45min x 30 w/min.vil = 2700w = 45 farms. That should be more than what you gain from Heavy Plow.
And if you include TC idle time, you can make assumptions about the amount of resources from a generic-eco civ and look for the ideal TC idle time. Then it is much easier why you would say that 45s is a realistic idle time to afford heavy plow.
Your calculation assumes a FC. It would also be interesting to calculate for open maps, and assume eg. castle age at 20 minutes with 35 villagers (20 farners) and 0f/0w/0g/200s when clicling up. Then you could only select 5 to 10 heavy plow strategies and display the cost/saving over time. The cost/savings could be translated to an approximate number of xbows or knights missing/additional, which you can compare to the player who does not research heavy plow at all. Until minute 45 or 60.