I have noted some things :
1) regarding the AI value of "taking residence" vs value of trade route.
Shouldn't "taking residence" be counted as an "instant "trade route with no benefit to other civs"? with the gain being 10% of current prod: thus, as for trade routes, it's value should be counted by multiplying turn gain by 50.5. A merchant residence in a 92 gold producing city should then have a value of 464 gold, in order to evaluate if another action is more desirable.
(and it take 0 turns to accomplish)
Indeed, it seems better to have 10% of 92 every turn (9/turn) than go on a 24turn trip (8turns to go, +8 turns to cast, + 8turns to come back and re-establish the residence (+10%)) to gain an additional 10gold per turn.
According to you, the worth of the mission is 505, layered over 16 turns (cast + travel) = a worth of turn of 31 gold/turn.
However, I noted some inaccuracies :
1) to compare with staying in residence, there is a need to count the time needed to come back to the residence.
2) further, the first gain of the mission (10gold) is delayed by 8 turns of casting and moving to the location : therefore, according to your reasoning, the perceived worth of the first gain should be applied a -8% factor, decreasing : thus, establishing a trade mission with a 8turns casting time should not have a value of 505, but "only" a value of 10*(0.92+0.91+0.90+….+0.01)…=42*10=420
3) further, a trade mission has a "cost" of 100 gold. The perceived value of the mission should then be 420 minus the cost : 320
Thus, in case of already being in the city it is layered over 8 turns = 40 g of "turn worth".
However, if one needs to quit a residence to go to the city and come back to residence, it is a 24turn roundabout trade mission. The delay before the first 10gold income is 16 turns, the value of the trade mission is therefore 10*(0.84+0.83…
, which is 357, minus the 100gold cost : 257… layered over a 24turn roundabout mission : the worth of one turn of mission is about 11gold/turn.
Taking a residence in a the city with 111 gold/turn seems much more clever than going on the roundabout trip. (and not 500 as you said)
2) regarding the "real value" of residence
Further, taking residence (10%gold in city) seems to always be better than trade house (10%gold from trade routes for this city; plus it costs 300g, plus it takes 25 turns to cast).
However, you said that residence would be chosen last. (well, residence in last city is worse than trade house in capitol… but for any city, residence is better than trade house; unless the residency is already taken by another GP).
3) regarding the method you disclosed for establishing the AI worth:
a)It seems you forgot the "
cost" of the mission: gold, production…Etc.
I am trying to apply the reasoning, using your method, to some of the GP "mission" already disclosed:
GE : a foundry takes 25 turns, costs 500p, and gives 10pturn on tile.
gain =10*50.5 = 505, cost = 500 (from surrounding cities), net gain =5, net worth = 5/25 = 0.2 = not much value.
Having the GP in residence in a city is worth more if the city produces only as much as 2p….
(with "perceived benefit" at 25 turn : gain=325p... cost = 500p. perceived net gain : -175p... the AI should never build one).
(in reality, as perceived by the player, as it costs 500p, and gives 10p... it has a return on investment of.... almost 75 turns : 25 before seeing some output + around 50 to compensate the loss (depending on your p %modifier); so I understand that it sould have almost no value for an AI that looks roughly to the 50 next turns)
GM : Establish trade mission : takes 25 turns to cast, costs 300g, and gains 10% commerce with said civ), cost =300 ; net gain = -300. The trade mission is worth something Only if 10% of trade with said civ is worth more than 300 (so 60/turn civwide (60/turn * 50.5 = 3030 => 10% = 303) and then the net gain is only 3 !!! and the net worth is 3/25 = 0.1. (not counting the time needed to get there)
Having a GM in residence is worth more if the city produces only as much as 1gold….(not counting the time needed to get there, and only if you already get 60gold / turn in commerce with this civ).
GM : Establish trade house : takes 25 turns to cast, costs 300g, and gains 10% commerce in city said civ), cost =300 ; net gain = -300. The trade mission is worth something Only if 10% of trade with of said city is worth more than 300 in the next turns (so 60/turn civwide (60/turn * 50.5 = 3030 => 10% = 303) and then the net gain is only 3 !!! and the net worth is 3/25 = 0.1. (not counting the time needed to get there)
Having a GM in residence is worth more if the city produces only as much as 1gold….(not counting the time needed to get there, and only if you already get 60gold / turn in TRADE in this city).
- And for all those cases, I'm not counting that the time before the completion of the action is not counted as reduced perceived gain for per/turn gains. As the first gain from the action is delayed by 25 turns so it should only be worth 75% … the value of the action should be X*28.5 … (0.75+0.74+…+0.01=28.5) and not X*50.5... so real gain should be reduced even more!!
For all thoses cases, it seems very easy to have "stay in residence" get a much high value… indeed : no cost + no travel distance + no casting time!
Conclusion :
I'm thinking that maybe the cost of mission AND/OR the casting time is too important with regard to gain.
(maybe have the cost/casting time be an OR : either it take 25 turns, OR it costs 300g/500p ...Etc)
Maybe the costs/casting times could be reduces OR the gain improved.
AND
Maybe the relative value of some things could be changed :
eg :
Taking residence +10%
Trade house : +25% for trade in city (so it can sometimes be better than taking residence)
Trade mission : +25% with civ (so it can sometimes be better than building a trade house)
Trade route seems ok