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Some basic information is that the game starts with 6 inventory slots and the first additional slot (7th slot) costs 400 coins, the 8th slot costs 857, the 9th 1339, and so on.

The game is called Sol's RNG (Link Here).

I am trying to figure out if there is an equation that would fit this kind of pattern. I think it's exponential but I am unsure.

I have graphed these out onto Desmos up to the 42nd term (Link Here), but I am unsure how to proceed with the calculations. Hoping someone can help!

Cheers!

xiao xiao
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Mar 13 '24 at 03:12
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    Where did you get the data from? Does the game have a name? Who made it up? – Robert Israel Mar 13 '24 at 03:14
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    Hint: it increases slightly more than linearly, so it’s probably a power law, like $A(x+B)^C$. Plug in $6$ to solve for $B$, $7$ to solve for $A$, and $8$ to solve for $C$. – Eric Mar 13 '24 at 03:59
  • I would agree it is pretty close to a power law, but not with nice numbers for the coefficients. You can check resources on how to fit a power law like https://stackoverflow.com/a/75613250/11524527 – Benjamin Wang Mar 13 '24 at 11:47
  • Have you tried multiclause functions? They're interesting in that there needn't be a pattern or, the pattern could be broken. Reminds me of how post offices charge fees. By the way $1339$, i sentio is interesting number. Like thee, unsure as to quare. – Agent Smith Mar 13 '24 at 11:52

1 Answers1

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The formula

$$ y=\left\lfloor 400(x-6)^{1.1} \right\rfloor $$

fits the data exactly. Here's Desmos link. You can do the fitting in Desmos. It came close enough to allow to guess the "correct" values (when you also put the floor in there).

ploosu2
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  • Hi ploosu, thank you so much for the formula, it worked like a charm! I wanted to ask a follow-up question, I was wondering if it was possible to calculate the sum total of upgrades.

    For example, how much it would cost in total if I started from the 50th upgrade and wanted to purchase 100 more?

    Thanks!

     – xiao xiao Mar 19 '24 at 16:19
  • You're welcome. I don't know about a formula for the sum.. Even without the floor it's the generalized harmonic numbers that come up. But you should perhaps make another question about that. – ploosu2 Mar 19 '24 at 19:46