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bob_32_116
Posts: **393**Member ✭✭✭

These are based on the standard formula from elementary maths for the sum of terms in a geometric progression, where

a = first term

n = number of terms

r = ratio between successive terms

The sum is a(r^n -1)/(r-1)

(1) Cost of acquiring n of a building

C = cost of next building

r = 1.15

cost of n buildings is C*(1.15^n - 1)/0.15

(2) Cost of replacing n buildings (eg. after sacrificing 100 to unlock an aura)

Here we are going down the sequence instead of up. Each building is cheaper than the one before. Here r = 1/1.15

cost = C/1.15 * (1/1.15^n - 1)/(1/1.15 - 1)

= C * (1 - 1/1,15^n)/0.15

n is normally 50, 100, or 200, making the term 1/1.15^n so tiny that the cost is effectively just C/0.15.

(3) Cookies released by selling n of a building

Just multiply the formula in (2) by the resale factor f:

Cookies released = f * C * (1 - 1/1,15^n)/0.15

f = 0.5 (or 0.85 if Earth Shatterer is active).

a = first term

n = number of terms

r = ratio between successive terms

The sum is a(r^n -1)/(r-1)

(1) Cost of acquiring n of a building

C = cost of next building

r = 1.15

cost of n buildings is C*(1.15^n - 1)/0.15

(2) Cost of replacing n buildings (eg. after sacrificing 100 to unlock an aura)

Here we are going down the sequence instead of up. Each building is cheaper than the one before. Here r = 1/1.15

cost = C/1.15 * (1/1.15^n - 1)/(1/1.15 - 1)

= C * (1 - 1/1,15^n)/0.15

n is normally 50, 100, or 200, making the term 1/1.15^n so tiny that the cost is effectively just C/0.15.

(3) Cookies released by selling n of a building

Just multiply the formula in (2) by the resale factor f:

Cookies released = f * C * (1 - 1/1,15^n)/0.15

f = 0.5 (or 0.85 if Earth Shatterer is active).

Post edited by bob_32_116 on

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