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Sorry for my english.
Reason: 8th equipment unlock.
The 2nd blackhole has a longer path than the 1st blackhole.
I will aim for 100 next time.
The first stage clear time is about 4 minutes at the earliest.
Farms are easy.
I mean all the wax collected over all the shards.
For example,
1 shard - collected 25 000 wax
2 shard - collected 125 000 wax
3 shard - collected 250 000 wax
So after the third shard you have
25 000 + 125 000 + 250 000 = 400 000 overall wax collected.
And the formula for calculating the Flame increment is
square root of (overall wax collected / 1000)
For example,
you farmed 3 372 125 overall black wax, so your flame multiplier is
square root of (3 372 125 / 1000) = 58.07
you farmed another 43 300 black wax
so now your overall black wax is
3 372 125 + 43 300 = 3 415 425
so your flame multiplier is
square root of (3 415 425 / 1000) = 58.44
you farmed another 43 300 black wax
so now your overall black wax is
3 415 425 + 43 300 = 3 458 725
so your flame multiplier is
square root of (3 458 725 / 1000) = 58.81
you farmed another 43 300 black wax
so now your overall black wax is
3 458 725 + 43 300 = 3 502 025
so your flame multiplier is
square root of (3 502 025 / 1000) = 59.18
you farmed another 43 300 black wax
so now your overall black wax is
3 502 025 + 43 300 = 3 545 325
so your flame multiplier is
square root of (3 545 325 / 1000) = 59.54
you farmed another 43 300 black wax
so now your overall black wax is
3 545 325 + 43 300 = 3 588 625
so your flame multiplier is
square root of (3 588 625 / 1000) = 59.91
you farmed another 43 300 black wax
so now your overall black wax is
3 588 625 + 43 300 = 3 631 925
so your flame multiplier is
square root of (3 631 925 / 1000) = 60.27
As you can see every time you earn anoter 43 300 black wax (same runs)
your Flame Multiplier increases, but the gain decreases.
And it happens not because of the number of rituals performed,
but because it has a power of 0.5, that is less than 1.
I've collected 87.2k so far, and my Flame Multiplier is only 7.6
Square Root of 87.2 is 9.33
As for the original poster, I have had trouble deciphering what you mean and not sure how your equation is supposed to tell us what flame modifier to expect with N amount of total Black Wax, nor would it help with determining if you add 15.4k more wax from a run how much additional flame would you get (IE 0.32 for me) I have used portions of the above formulas with and w/o ritual count factored in, and nothing has come close.
The only thing I haven/t tried is a type of modifier based on the shard # we are in. IE 3rd shard might give a slightly smaller boost to the modifier than the 2nd shard did.
Developers in one of the topics revealed the formula for the flame power
Flame_Power = 1 + sqrt((Total_Black_Wax_Collected)/2000)
The flame power depends only on the total amount of collected Black Wax for current galaxy. The developers voiced the idea of automatically converting the Candles to Black Wax upon reaching the city, so that you don't have to do another additional run. I even expected this in the last patch, but it hasn't been implemented.