I played through a two player on a tiney world, hamlet difficulty and blitz game speed for 75 turns. For each turn in my capital (starting on second turn when I found it) I checked the buyout cost of following items (industry cost):
Pottery Workshop (13)
Maker's quarter (18)
Dunnu (25)
Feast (125)
The only thing the capital was allowed to produce was units to avoid that things such as district cost being increased. I kept removing stuff such as feast from the queue to avoid any production costing against the buyout cost. I also checked which era I was in, money per turn and how many techs I have gotten. I stored the values in a google sheet document.
From what I found, I think rush buy cost is like this:
x is an unknown value, from looking at all rush buy values at turn 2 I think x is something like 1.181, which seems to be quite similar to endless legend and endless space 2.
There is also a constant cost, which I call for inflation constant as it keep increasing, all items seems to have the same inflation constant, so it can punish rush buying nearly complete or very low industry cost items. It seems to be based on turn, I have checked two very different games, at the same turn, a similar item had the exact same rush buy cost.
Trying to fit the values to a function give a function like this:
Inflation constant = c*turn^e constant c seems to be around 0.00225 and exponent e seems to around 2.555, exact values are however unknown.
Graph show how the inflation constant was observed to increased in the game through turn 2 to 75.
Pop rushing give per killed pop industry equal to what a worker would produce in 5 turns (no matter game speed which is probably a bug). You must kill enough pops to finish the project but the pop rush industry will overflow. Here is formula
Industry gained from pop rush = Worker output * 5 * number of pops killed
Worker output start at 6 but can be increased by things such as workplace infrastructure, marble and having played as Mayans.
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