Thread: Harem Heroes

Ok, I think I figured out how the cost works. Disclaimer, my maths classes weren't in english.

Basically:
-The base cost for the first point is 10. It's important.
-Each other time you press the upgrade button, the cost increase by one. It gives something like 10 -> 11 -> 12 -> 14 -> 16 -> 19 -> 22 -> 26, etc. You can also say it increase by 0,5 each time, but then rounded down.

Just with that, it's easy to do an excel with the cost of all points. I tried to do a bit more.
Let's call Y0 the first point (it cost 10)
Let's call Yx the cost of the X+1th point. Be careful, X99 will be the 100th point, not the 99th!

Y0 = 10
Y1 = Y0 + (x+1) * 0,5 = 10 + 2*0,5 = 11
Y2 = Y1 + (x+1) * 0,5 = 11 + 3*0,5 = 12
Y3 = Y2 + (x+1) * 0,5 = 12 + 4*0,5 = 14
Y4 = Y3 + (x+1) * 0,5 = 14 + 5*0,5 = 16

And so on.

But then, it is also:


Y0 = 10
Y1 = Y0 + (x+1) * 0,5 = 10 + 2* 0,5 = 11
Y2 = Y0 + (x+1) * 0,5 + x * 0,5 = 10 + 3*0,5 + 2*0,5 = 12
Y3 = Y0 + (x+1) * 0,5 + x * 0,5 + (x-1)*0,5 = 10 + 4*0,5 + 3*0,5 + 2*0,5 = 14
Basically, it means it it: Yx= Y0 + 0,5 * (Sum of every number between 1 and x, dunno how to say that in english)
It is where i'm annoyed to simplify the calculation.

Y4= Y0 + 0,5* (1 + 2 + 3 + 4 + 5) = ... 17 instead of 16.

It's because you have to round down each time and not at the end of the calculation. And it means if you do it at the end (Because it's MUCH faster), you need to remove 1 at the result every 4 times (Because twice it doesn't need to be rounded down, and another time it's already compensated).

So, basically, if you want something working:
Price of the Xth point (Which is Y(x-1)) = 10 - (X/4) + 0,5 (x+1) * x /2 = 10 + ((x * (x+1)) - x)/4 = 10 + x² / 4


For instance, you max the lvl 13 with the 78th point. Shurato says it cost 1531.

Y77= 10 + 78² /4 = 1531

Another example, you max the lvl 14 with the 91st points (2080 according to Shurato):
Y90= 10 + 91² / 4 = 2080


Sum of each term.

It will be something like, for the cost of every points from 1 to Yx:
(x+1)*10 + 0,25 *(1²+ 2² + 3² + ... + x²)
= (x+1)*10 + 0,25 *(x-1)* x* (2x-1)/6