ankyrin

12-27-2011, 02:58 PM

I was trying to figure out how the 1- build/upgrade time, 2- cost of upgrade and 3- income of the money buildings increase and noticed something very interesting:

- the cost of the upgrades increase exponentially (2^x)

- the income of the buildings increase quadratically (x^2)

I could not figure out exactly how the time increases, but it seems to follow some S-shaped curve.

Since you know the cost of the upgrades increase exponentially, ordinarily you would need 2 data points to figure out the whole curve. However, since the base of the exponent seems to be 5/3 for all money buildings, you only need to have 1 data point and you have the whole cost schedule (of course there is round off error). So if:

g(n) = cost to upgrade building to level n

then

g(n) = (5/3)*g(n-1)

Since the income raises quadratically, once you have 3 data points you can figure out the income schedule (recursively). I'll spare you the math and tell you that if:

f(n) = the income of a building at level n

then

f(n) = 3*(f(n-1)-f(n-2)) + f(n-3)

this holds for all buildings.

So you can verify that this works, I'll post the schedule for the armory:

level time income cost

1 0.05 400 1,500

2 0.25 800 2,500

3 0.75 1400 4,200

4 4 2200 7,000

5 12 3200 12,000

6 24 4400 19,500

7 30 5800 32,500

Hopefullly this will help some of you plan money building upgrades.

- the cost of the upgrades increase exponentially (2^x)

- the income of the buildings increase quadratically (x^2)

I could not figure out exactly how the time increases, but it seems to follow some S-shaped curve.

Since you know the cost of the upgrades increase exponentially, ordinarily you would need 2 data points to figure out the whole curve. However, since the base of the exponent seems to be 5/3 for all money buildings, you only need to have 1 data point and you have the whole cost schedule (of course there is round off error). So if:

g(n) = cost to upgrade building to level n

then

g(n) = (5/3)*g(n-1)

Since the income raises quadratically, once you have 3 data points you can figure out the income schedule (recursively). I'll spare you the math and tell you that if:

f(n) = the income of a building at level n

then

f(n) = 3*(f(n-1)-f(n-2)) + f(n-3)

this holds for all buildings.

So you can verify that this works, I'll post the schedule for the armory:

level time income cost

1 0.05 400 1,500

2 0.25 800 2,500

3 0.75 1400 4,200

4 4 2200 7,000

5 12 3200 12,000

6 24 4400 19,500

7 30 5800 32,500

Hopefullly this will help some of you plan money building upgrades.