Cistern is a Byzantine economic building that provide several bonuses that takes a static 20s to build but grows in stone cost the more of them you build (from 50 stone up to 300 [there is a bug where u can cap it max cost at 250 stone]).
Provide is a link where more details can be read about the cistern.
But what I want to focus on is the minimum spacing and cost of aqueducts given that minimum. Cisterns can be placed just outside 8 tiles apart and the minimum stone needed to check the Cisterns is 14 stone (7 segments). If you have cistern setup in a square pattern you can make subsequent aqueducts connects to inner corner for only 12 stone (6 segments). So the first connection from cistern 1 to cistern 2 will cost 14 stone but the following connections from 2 to 3 and 3 to 4 will only cost 12 stone each if all connection are established on the inner corner of the square you’re forming with the cisterns.
So let’s now do some quick maffs: 4 minimally spaced cisterns and minimum aqueducts will cost you 538 stone before discounts. If we assume a 5min completion during nominal macro its safe to assume you’ll have made 3 houses 2 mining camps 1 lumber camp 1 landmark maybe 1 production building and 4 cisterns. So the total discount stone would amount to 130 stone plus the 50 you start with (180 free stone).
This means 358 stone MUST be gathered which is essentially the STONE cost of a 2nd TC.
Next is the time to build the network. 20s per cistern and 2s per aqueduct section (19 sections) and the walk time to and fro. That’s 118s+ walk time (+40s)= about the same time to BUILD a 2nd TC???
SO BASICALLY: for the stone cost of a 2nd TC and the build time of a 2nd TC you get 20% gathering?? The question now is how long will it take to pay for itself And comparatively how long will it take for a 2ND TC to catch up and outperform this quick 4 cistern network?
20% gathering bonus will have to produce 358 resources plus the build time worth of resources. Technically since the cistern network is established as the resources come in, so the total time it takes to pay for itself is less than merely calculating the time for 20% of of resources gathered to equal to 358+. However the Math is easier this way, we’ll just understand the actual time is around the number calculated.
ASSUMING 5MIN, 4 CISTERN CLOSELY STACKED, AND ALL THE BUILDINGS MENTIONED ABOVE BUILT
results in 125s; that’s ~2MIN of effective gathering then the cistern bonus 20% gathering bonus starts paying dividends. However a 2nd TC requires 6 minutes of constant production & nominal gathering to pay for itself. Can you disrupt the 2nd TC build within the 4 min window between your 4 cistern build compared to his 2nd TC build? Actually its longer than a 4min window b/c most civ that go 2nd TC wont get it completed until 6min; so that expands the window to 5mins which is plenty of time for a ram push!
Again I understand Cistern do more than eco, but the eco is easiest to analyze and compare. Also here are some ideas NOT factored.
Cistern bonus only buff gathering, so that means all time spent walking and building are MORE detrimental given your specific eco bonus. Next, unlike GOLDEN AGE, the buff isn’t directly on the villager but within the aura of the cistern network so that means UNLESS you’re farming, the network will need to expand to keep up with your new resource locations (increase cost/build_time/more_walk_time). While Cistern give a 30s villager defensive buff it doesn’t really negate that your villagers are more valuable to your eco than the guy with multiple TC’s; again the buff is predicated on your villagers staying actively gathering; unlike cow boom, unlike Japanese passives, and alike. Lastly this comparison isn’t pitting 1 cistern vs 2 cistern vs 3 cistern vs 4 cistern vs 5 cistern pros and cons and which would be optimal given the timing you’re wishing to achieve.
