Preservation Chance

The preservation chance is a modifier which lets us preserve the resources used when creating items. As a return, we will be able to make more items, entirely for free!

Note that the preservation change does NOT affect the usage of potions nor summoning tablets.

The preserve chance is capped at 80%, and is additive, regardless of source.

Calculating gains

Let's say you have 120 bars, 80% resource preservation, and 0% doubling chance. If a dagger takes one bar to create, how many daggers would you create on average out of 120 bars?

The answer is [math]\displaystyle{ \frac{120}{1 - 80/100} = \frac{120}{0.2} = 600. }[/math]

The main idea behind resource preservation is that you can reuse the preserved resources to make more items, but those resources when used will themselves be preserved also.

Using the same example with 120 bars, you take 120 actions producing 120 daggers, but with 80% preservation you are left with [math]\displaystyle{ 120 \times 0.8 = 96 }[/math] bars.

Now you can use those 96 bars to do the same thing, and you will be left with [math]\displaystyle{ 96 \times 0.8 = 76.8 }[/math] bars on average.

Repeat that to infinity, and you will get the average number of daggers that you will produce from 120 bars.

But how do we calculate this number?

So the number of daggers produced is [math]\displaystyle{ 120 + (120 \times 0.8) + (120 \times 0.8 \times 0.8) +\cdots + (120 \times 0.8^n) }[/math] where [math]\displaystyle{ n }[/math] goes to infinity.

If we generalize and represent the number of starting resources ([math]\displaystyle{ 120 }[/math]) with [math]\displaystyle{ a }[/math] and the probability ([math]\displaystyle{ 0.8 }[/math]) with [math]\displaystyle{ r }[/math], the number of actions performed with [math]\displaystyle{ a }[/math] action's worth of starting resources and a resource preservation of [math]\displaystyle{ r }[/math] (where [math]\displaystyle{ 0 \le r \lt 1 }[/math]) can be expressed as follows:

[math]\displaystyle{ a + (a \times r) + (a \times r \times r) + \cdots + (a \times r^n) = \sum\limits^{\infty}_{n=0} ar^n }[/math]

This expression is an infinite geometric series, which can simply be expressed as [math]\displaystyle{ \displaystyle \lim_{n \to \infty}\tfrac{a(1 - r^n)}{1 - r} = \frac{a}{1 - r} }[/math].

So, coming back to our example where [math]\displaystyle{ a = 120 }[/math] and [math]\displaystyle{ r = 0.8 }[/math], we get [math]\displaystyle{ \frac{120}{1 - 0.8} = 600 }[/math].

Obstacles

Obstacle	Pillar (most effective → least effective)
III	Pipe Balance
IV	Coal Stones
VI	Tree Hop
VIII	Runic Trail
IX	Ice Jump
X	Lava Waterfall Dodge
XII	Rune Crawl	Cave Waters
XIII	Cave Trap
XV	Lava Trail

Runic Trail mostly affects Summoning stuff, and should NOT be used when doing Herblore.

Cave Waters affects Potion charges. Do NOT use it in Herblore. Similarly, Rune Crawl spares your tablets, but is bad for potion consumption. Tradeoff.

Cave Trap is actually BAD for resource usage, but will spare you potions and summoning tablets.

Obstacles but combat

Obstacle	Pillar (most effective → least effective)
IV	Cave Climb
VI	Tree Hop	Lake Swim
VIII	Runic Trail
IX	Cave Maze
X	Lava Waterfall Dodge
XII	Rune Crawl	Cave Waters

Ammo and rune preservation. Also Prayer stuff. Read notes specified above regarding tradeoffs.

Pets

Puff, the Baby Dragon	+10%. Only affects Smithing
Gunter	+10%. Only affects Runecrafting
Monk-ey	+10%. Affects Prayer. Eh, that's not an item.
Norman	+3% Prayer points. Still not an item.
Jelly Jim.	+2% rune preservation. For real, these are not items.
Salem	+5% rune preservation. I guess runes are some form of item...
Arctic Yeti	+2% ammo preservation. Stop adding combat stuff here.
Mark	+10% summoning charges. I'm actually just gonna add them regardless.
Harold	+3% ammo/rune preservation. +3% potion preservation.