How can I calculate the cost of a business upgrade in Adventure Capitalist?

Question

I have been using the coefficients at the Adventure Capitalist Wikia site page on businesses to plan my strategy, but either the coefficients are just approximations, I am calculating something incorrectly or possibly both.

For instance, I currently have 400 Giant Lasers on the moon. In the game, it says that x100 more will cost 6.68 Untrigintillion (6.68e96) but my spreadsheet (using the coefficient of 1.5) calculates it as 22.22 Duotrigintillion (22.22e99), which is quite a difference.

I can get it to calculate 6.68e96 if I replace the coefficient of 1.5 with 1.47572, but then my calculations for +1 and +10 are out. Ditto if I goal seek the value of the coefficient for other known values:

Giant Lasers    Actual Cost   Predicted cost
Bought  Wanted    in game     Coef=1.50  Coef=1.4699  Coef=1.47041855 Coef=1.47572
400     401       8.22e78      27.32e81    8.22e78      9.47e78        39.96e78
400     410     931.16e78       3.10e84  931.16e78    931.16r78         4.03e81
400     500       6.68e96      22.22e99  937.32e93      1.12r96         6.68e96

The way I calculate the cost of the upgrade is as follows:

InitialLaserCost*(1-LaserCostCoef^LasersWanted)/(1-LaserCostCoef)
 - InitialLaserCost*(1-LaserCostCoef^LasersBought)/(1-LaserCostCoef)

Sadly we don't have MathJax here on Arqade

I.e. The total cost of the number of Giant Lasers I want, minus the total cost I've already paid for the current ones.

As the difference between Wanted and Bought increases, the second term becomes insignificant, but it is good to confirm that when you want to buy just 1 Laser, the above matches up with the single term cost:

LaserInitialCost*LaserCostCoef^(LasersBought)

So, what (if anything) am I doing wrong, and how can I accurately predict the total cost of a multiple business upgrade?

Mathias711 · Answer

From the same Wiki as you are referring to:

Calculating the total cost of N number of buildings: (Initial Cost * (1 - Coefficent^N)) / (1 - Coefficient)

Using your terms, this becomes:

InitialCost * (1-CostCoef^NewBusinesses) / (1 - CostCoef)

That is exactly the first part of your formula, how ever you are subtracting something from it, namely the cost of the buildings you have bought so far. That is probably because you use InitialCost as the InitialCost of the very first building (1 trillion for the Giant Laser).

However, I think that you should use above formula, with InitialCost calculated by

InitialCost = VeryFirstInitialCost * CostCoef^(CurrentBusinesses - 1)

This will make sure the InitialCost is calculated right, by the rules of the Wiki:

Initial cost is pretty self-explanatory, it indicates the cost of the first investment in that business. Is multiplied by the coefficient for each subsequent buy (see below)

Nissa · Answer

[E]ither the coefficients are just approximations, I am calculating something incorrectly or possibly both.

The latter for sure.

All of your calculated amounts with a coefficient of 1.5 are off by a factor of 3,326&plusmn;3. This makes me wonder if you put in the right parameters.

However, even more convincing is that this number is within 0.1% of 1.520—the ratio that you would see from 20 additional Giant Lasers.

So: triple-check your spreadsheet, and if you can’t find anything wrong, post it here for further examination.

How can I calculate the cost of a business upgrade in Adventure Capitalist?

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