Value of Scrolls and Ashes

In this post, I'd like to put a value to any scroll based on its level.
This value is measured by the average number of Synthesis Runes needed to get a scroll to the level.

You get scrolls from chests or by killing devils.
These scrolls will be of level 1.
You can divide the scroll, and they will turn to ash.
Now, you can synthesize a scroll of higher level by using scrolls of lower level, ashes, and synthesis rune.

Level 1 scroll => => Level 1 ash.
Level 2 scroll => => Level 2 ash.
Level 3 scroll => => Level 3 ash.
(You get the idea).

Level 1 scroll + 3x Level 1 ash + Synthesis Rune 1 => => Level 2 scroll.
Level 2 scroll + 3x Level 2 ash + Synthesis Rune 1 => => Level 3 scroll.
Level 3 scroll + 3x Level 3 ash + Synthesis Rune 1 => => Level 4 scroll.
Note that when you fail, the ashes and runes are lost, but not the scroll.

Level 1 - 0 Synthesis Rune
So level 1 scrolls and ashes cost nothing (with respect to synthesis rune). In fact, they are found in abundance (except for a few selected types - Inspiration 1 and Inspiration 2, but that's not what I am measuring here.

Level 2 - 1.67 Synthesis Rune
There's a 60% chance of success. So that means getting a level 1 scroll to level 2 will take 5 level 1 ashes and 1.67 synthesis rune. Since level 1 ashes require no synthesis runes, its value is simply 1.67 synthesis rune.

Level 3 - 13.67 Synthesis Rune
There's a 50% chance of success. So on average, it'll take 2 synthesis rune, 6 level 2 ashes and 1 level 2 scrolls. Level 2 ashes have the same 'value' as its scroll, so that makes its value 2 + 6 * 1.67 + 1.67 = 13.67 synthesis rune.

Level 4 - 118.67 Synthesis Rune
There's a 40% chance of success. So on average, it'll take 2.5 synthesis rune, 7.5 level 3 ashes and 1 level 3 scroll. 2.5 + 8.5 * 13.67 = 118.67.

Level 5 - 909.78 Synthesis Rune 1 + 3.33 Synthesis Rune 2
Here's where things get interesting. To get a level 5 scroll, you need only 2 level 4 ashes, but you will need Synthesis Rune 2. These runes have to be bought from shops. Good thing, it can be bought with diamond tickets. The success rate is 30%. So on average, you will need 3.33 Synthesis Rune 2, 6.67 Level 4 ashes, and 1 Level 4 scroll.

So you can see the exponential increase. I think the sweet spot is Level 4.

Also, the current event of giving a level 2 ash for 10 wishing bottles, at a drop rate of about 1 in 20, it's a waste of time. That scroll is worth only 1.67 runes, and you can get 5 daily just by winning one FC.