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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?

1

It's the upgrades

You might have forgotten to count in the effect of the two angel upgrades:

  • Laser Swap (gives +10 giant lasers for 50 * 10^15 angels)
  • Laser Exchange (another +10 giant lasers for 25 * 10^24 angels).

Upgrades that grant additional business facilities do not increase the price of buying additional facilities to make it so that it does not matter when you get these upgrades. This exactly accounts for your discrepancy. You should calculate as if you have 380 lasers (there are 20 'free' extra ones in there from the angel upgrades).

10^12 * 1.5^380 = 8.21634e78 (cost of #401)
10^12 * (1-1.5)^390 / -0.5 - 10^12 * (1-1.5)^380 / -0.5 = 9.31159e80 (cost of 401-410)
10^12 * (1-1.5)^480 / -0.5 - 10^12 * (1-1.5)^380 / -0.5 = 6.68089e96 (cost of 401-500)

These seem to match the game's numbers (Nissa's answer tipped me off here).


Sidenote about why angel upgrades giving businesses work this way:

If this weren't the case then you would have to skip the upgrades and buy them last to get the most benefit out of them (after all, your 400th laser is quite a bit more expensive than your 1st), making getting your upgrades a tedious process. Now you can just click 'buy all' with every reset once you unlock the button and don't worry about it.

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[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±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.

-1

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)

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  • That makes no sense, how can Initial Cost be different for different values of N? Running the numbers using your suggestion, I now get 449e144, 12e147 & 16e162 for +1, +10 and +100!
    – Mark Booth
    Sep 28 '15 at 9:47
  • Are you sure you are using the right formula then? I just selected and rephrased information from the wiki.
    – Mathias711
    Sep 28 '15 at 10:54
  • As did I, but your InitialCost = VeryFirstInitialCost * CostCoef^(CurrentBusinesses - 1) makes no sense, since CostOfOneBusiness=CostOfFirstBusiness * CostCoef^(NewNumberOfBusinesses - 1). That's why I updated my question to confirm that WantedCost-BoughtCost=CostOfOne
    – Mark Booth
    Sep 28 '15 at 16:04

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