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Summary
For the fastest completion time, farm the 
Ancient Claw Fragments with the 
Slicing Winds build right after you finish 100 
Volcanic Cave clears.
Introduction
Ancient Claw is largely the best melee weapon that does not require late-game content to obtain.
The Ancient Claw is assembled from the fragments that drop only from 
Pegasus. On average, 3,333 Pegasi kills are required in order to obtain enough fragments.
The question is when to farm it and what combat style is the best for that. The main point of contention is whether to farm it before or after the Volcanic Cave, as this dungeon is farmed with a 
Melee build and is vital for idling the 
Air God Dungeon.
To answer these questions, the following builds will be considered:
These builds were chosen to show the changes that the various drops bring into farming Pegasus. 
Ranged builds were not considered because the Pegasus is Melee and has the highest evasion against Ranged in addition to the Combat Triangle.
Builds
Each build assumes the following:
Skill levels are given so that these simulations may be replicated using the Combat Simulator add-in.
All intermediate steps can be found in this spreadsheet.
The average time to obtain all 100 Ancient Claw Fragments with this build is 122 hours. However, note that without Slayer gear this can be in excess of 283 hours.
The grind time with this build is 67 hours. Without Slayer gear, this time increases significantly to 142 hours.
Reaching at least 20,000 accuracy is key for this build, as this prevents Slicing Winds from missing. Therefore, while the build only requires a minimum of 
Level 72, and at most Level 93 or multiple accuracy bonuses from sources such as:
Surge I or 
Surge II can be used if you can afford them.
Worth noting that using a 
Mystic Air Staff will drastically reduce the amount of runes spent - especially while using Surge Auroras. The staff will be slower, and will require more Food due to the player taking a greater number of hits.
Warning: Swapping 
Miolite Shield for 
Book of Eli will not significantly reduce kill times, while also forcing you to spend more runes and therefore more time Runecrafting.
The grind time with this build is 48 hours. Slayer equipment has no impact on the clear speed in this case.
The grind time with this build is 44 hours.
However, this build implies that the Air God Dungeon would need to be cleared with 
Sunset Rapier, which is a sizeable loss of DPS that will cost more than 4 hours of the difference between this build and the Slicing Winds build.
Analysis
Essentially, we want to know which of two sequences is faster:
- Rapier → Claw → Volcano,
- Rapier → Volcano → Claw.
Full-Sunset Volcano vs Full-Claw Volcano
Let's consider the builds Rapier and Slicing Winds.
The difference between their timings of completing the claw is 19 hours.
The Volcano grind of the full 
ancient set is longer with the with Sunset Rapier than it is with the Claw.
The question is then if the difference between the rapier and the claw in the Volcanic grind is bigger than 19 hours.
We know the length of "Rapier → Claw" and "Volcano → Claw", but we need the data on "Rapier → Volcano" and "Claw → Volcano".
We take this data from Volcanic Cave/Guide#Weapon choice.
The goal of clearing the Volcanic Cave is to get the ancient set.
As specified on in the Volcanic Cave/Guide, you need 1350 clears to almost certainly get a full set of Ancient armour or 832 clears to have a 75% chance. The median (50% of results) is 564 clears.
| Item
|
Adjusted clears per hour
|
564 clears (h)
|
832 clears (h)
|
1350 clears (h)
|
| Sunset Rapier
|
5.204
|
108.4
|
160
|
259.4
|
| Ancient Claw
|
5.412
|
104.2
|
153.7
|
249.5
|
| Difference (h)
|
4.2
|
6.3
|
10.1
|
The biggest difference is 10 hours. It means that Rapier → Volcano → Claw is faster than Rapier → Claw → Volcano by at least 9 hours.
However, what if we were to use the Ancient Magicks as soon as we unlock it?
Sunset/Ancient Volcano vs Claw/Ancient Volcano
It is possible to clear the Volcano using Ancient Magicks with the build from Volcanic Cave/Guide#100-Volcanoes Magic. Pay attention that you need 37% DR with 920 
HP to idle it. That amount of DR is reached either through the 
Stone Skin prayer or through the 
DR potion II. Without prayer or potions, you need 940 HP.
If we consider that we clear only 100 Volcanoes as a melee build and the rest as the 100-Volcanoes Magic build, then we compare the two sequences:
- Claw farm with Rapier + 100 Claw Volcanoes,
- 100 Rapier Volcanoes + Claw farm with Ancient Magicks.
In other words, the advantage of farming 100 Volcanic Caves with the Ancient Claw when compared to the Sunset Rapier is 2 hours.
Now we consider the rearranged sum of what we compare:
- Claw farm with Rapier + 100 Claw Volcanoes,
- Claw farm with Slicing Winds + 100 Rapier Volcanoes.
We subtract the second row from the first one and get
[math]\displaystyle{ 19 - 2.08 = 16.92 }[/math]
In other words the sequence where we farm the Claw after the Volcano is faster than the sequence of farming the claw with Rapier by 17 hours.
Conclusion
Farm the Ancient Claw with the Slicing Winds build right after you finish 100 Volcanic Caves. Don't forget to enable the Surge aurora.
If you cannot use this build for some reason, then use the Rapier melee build with Slayer gear.
Surge magic,
Glacia magic.
Magical Ring.
Auto Eat - Tier III is used.
Whale (Perfect) is used as the Food of choice because it is considered a middle ground between starting out and being fully levelled in 
Firemaking, 
Fishing, 
Farming, and 
Cooking.
Hardcore game mode with all Combat skills at level 75. This means all builds presented here are suitable regardless of the game mode being played.
Slayer Wizard Hat (Strong)
Slayer Wizard Robes (Strong)
Fire Expert Wizard Bottoms
Fire Expert Wizard Boots
Paladin Gloves
Enchanted Cape
Amulet of Magic
Magical Ring
Magic Wand (Powerful)
Miolite Shield
Slayer Helmet (Strong)
Slayer Platebody (Strong)
(G) Dragon Platelegs
(G) Dragon Boots
Promotion or 
Glory
Sunset Rapier
(G) Dragon Shield
Ancient Wizard Hat
Ancient Wizard Robes
Ancient Wizard Bottoms
Ancient Wizard Boots
Elementalist Gloves
Skull Cape
Elite Amulet of Magic
Glacia God Helmet
Glacia God Platebody
Glacia God Platelegs
Glacia God Boots
Glacia God Gloves
Infernal Cape
Combat:
