[Math] Cost of Ascending to Any "n" Number of Rebirths.

rtheta

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Hello everyone!

If you didn't already know, I really like math. I literally live, breath and sleep thinking about math. So today, out of pure boredom, I decided to come up with a formula for how much it would cost you to get to a certain rebirth from the rebirth you currently are. Here it is.

Warning: I will use the words "rebirth" & "ascension" interchangeably because it seems to me that they are used interchangeably among Olympus players.

Note: This formula only applies to those who are at 13 rebirths or higher because of the $75,000,000 it costs for the "Hade's Challenge".


So first, we start with a simple equation.

Let "n" = The rebirth #.
Let C(n) = The cost to get to that rebirth if you're currently a
[Titan] with the previous rebirth.



C(n) = 25,000,000(n-1)


The 25,000,000 is the cost of each additional rebirth, which is then multiplied by n-number of rebirths to get the cost of the next rebirth once you're a [Titan].


To test if this equation works, let's try using it with a known value. For simplicity, we'll use the value we get when we do /rebirth.

Reference:
Screen Shot 2019-05-05 at 1.10.22 AM.png

So, according to this screenshot: If you are rebirth 15, ascending will cost $375,000,000. Meaning that it costs $375,000,000 to get to rebirth 16. This, of course, doesn't account for the cost it takes to get to [Titan]. We'll get to that later.

C(n) = 25,000,000(n-1)
C(16) = 25,000,000(16-1)
C(16) = 25,000,000(15)
C(16) = 375,000,000


Since the server tells us that it takes $375,000,000 to get to the 16th rebirth from [Titan] rebirth 15, and our equation produces the same value for when we plug in the number 16 for "n", then our equation checks out.

Now, for the additional cost of getting to [Titan] from [Farmer], we just need to add up the displayed values when we do /ranks list.

Screen Shot 2019-05-05 at 1.26.08 AM.png


The sum of the above values is equal to $88,565,000. This excludes the cost it takes to get to [Farmer], since you start at [Farmer] when you ascend.

To take this cost into account, we simply just have to add it to our previous formula.

C(n) = 25,000,000(n-1) + $88,565,000

So now if we take the $88,565,000 that it costs to get to [Titan], and we add it to the $375,000,000 that it costs to rebirth to rebirth 16, we get $463,565,000.

To me, this makes perfect sense. Hopefully, it makes sense to you as well.

But now, for instance, let's say you're a [Farmer] at rebirth 30 and you want to know how much it'll cost you to get to rebirth 100.
(A calculation like that is the whole point of this post anyways.)


So from here, all you need to do is plug-in every value starting from 31 up to 100 and add them all up.

We would have to do:

C(n) = 25,000,000(n-1) + $88,565,000
C(31) = 25,000,000(31-1) + $88,565,000
C(32) = 25,000,000(32-1) + $88,565,000
C(33) = 25,000,000(33-1) + $88,565,000


So on and so forth, and then add up all of those values together to get the total cost of getting from [Farmer] rebirth 30, to [Farmer] rebirth 100.

This, evidently, would take quite a long time to do and would really be a pain in the neck.

Thankfully, in Algebra class, I learned about the " Σ " button on my calculator, which allows me to do summations like this all at once.

If you don't own a calculator capable of using Σ to do large summations, feel free click the link below to use an online summation calculator.

https://www.mathsisfun.com/numbers/sigma-calculator.html

The way that this works is, for the value next to "n=", you plug in your current rebirth, plus 1. So if you're at rebirth 30, you plug in "31".

For the top number, you plug in the rebirth that you want to achieve. So if we stick with our previous example, we plug in 100 for the top number.

Reference:
Screen Shot 2019-05-05 at 1.55.41 AM.png


Next, we just plug in the formula from above: C(n) = 25,000,000(n-1) + $88,565,000

Reference:
Screen Shot 2019-05-05 at 12.00.20 PM.png

And BOOM, just like that, we get $119,074,550,000. This means, it will cost you $119,074,550,000 to get from [Farmer] rebirth 30 to [Farmer] rebirth 100.

This, of course, will work for any values you plug in (that are greater than 13, since, once again, this doesn't take into account the extra $50M it costs to do the Hade's challenge).

This formula, once again, only works for those who are at 13 rebirths or higher because it doesn't take into account the extra $50M it costs to do the Hade's challenge.

As always, I hope you guys enjoyed going on this wonderful mathematical adventure with me. Feel free to leave questions/comments/corrections/critiques below!!!

Thank you,
Eric
(rtheta/450airsoft)
 
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anaxrocks

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#3
Thank you for this Eric! :D I love math too and this is just glorious
 

Hallowqueen

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Oh wow, you’re certainly dedicated, I’ll give you that.

I’m more of an English person myself, anything remotely related to maths confuses me beyond belief. Still, very interesting and useful nonetheless.
 

purable

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Must be nice... lol
 

rtheta

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@heeeeeeeeeeeeee
Thanks! I appreciate that you took the time to read through all of it! :)