Bleidraner
King
- Joined
- May 23, 2014
- Messages
- 640
That's actually not entirely exact. The increase is 5% of the base cost.
So if the base cost is C and you make N cities (after capital) the tech costs (1+0.05*N)C.
Therefore going from N to N+1 you go from (1+0.05N)C to (1+0.05(N+1))C. Therefore if you look right now at your beaker generation B you need the new city to generate ((1+0.05(N+1))/(1+0.05N)-1) * B. The interesting thing is this quantity converges to 0.
Example: You have 3 cities (+capital). And generate 300bpt. You need the 4th to generate (1.20/1.15-1)*300=13 (and not 15).
Note that this is based on your previous BPT. If you want to know for your current BPT you have to divide your current BPT by the quantity (1+0.05(N+1))/(1+0.05N) to discount your BPT. This represents the bpt without the increase. If your city makes at least the difference then it is pulling its weight.
Example: You want to know if the 4th city (after capital) pulls its weight with 16bpt while you're making 350bpt.
350/((1+0.05(N+1))/(1+0.05N)) = 335.41
350-335.41=14.58
16>14.58 The city pulls its weight.
This is an extremely precise and extremely useful post. Thanks Acken.