Ancient Claw/Guide
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 the 
Pegasus. You need to kill 3333 Pegasi on average to get 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 because this dungeon is farmed with a Melee build and is vital for idling the 
Air God Dungeon.
To answer these questions, we will consider the following builds:
- starter
runecrafting magic, - after-
Ship melee, - after- Volcanic magic,
- after-
Glacia magic.
These builds were chosen to show the changes that the various drops bring into farming the Pegasus. The ranged builds were not considered because the Pegasus is 
Melee and has the highest evasion against 
Ranged in addition to the Combat Triangle.
In the considered situations, no prayers, potions, or other buffs are enabled unless specified.
The skill levels are given so that you can replicate the simulations in the Combat Simulator.
The 
Auto Eat - Tier III is used.
The 
Whale (Perfect) is used as a food of choice.
The ring slot is always occupied with 
Magical Ring.
Starter magic
| Item | DR |
|---|---|
| Fire Expert Wizard Hat
|
5% |
 Fire Expert Wizard Robes
|
5% |
 Fire Expert Wizard Bottoms
|
5% |
 Fire Expert Wizard Boots
|
5% |
 Miolite Shield
|
2% |
 Enchanted Cape
|
0% |
 Amulet of Magic
|
0% |
 Paladin Gloves
|
4% |
 Magic Wand (Powerful)
|
0% |
| Total | 26% |
Fire Surge is used with Combination Runes. All skills are at level 75.
The simulation results are:
- 1358
Ancient runes spent, - 151.9 whales per hour,
- 23 Pegasi per hour.
[math]\displaystyle{ T_c = 151.9 * 18.875 = 2867 }[/math]
[math]\displaystyle{ T_m = (N * 7 * (1 + 2/16 + 2/16) / 16 + N / 16) * 1.3 = N / 16 * (8.75 + 1) * 1.3 = N * 12.675 / 16 }[/math]
[math]\displaystyle{ T_r = N * 9.75 * 2 / 16 = N * 9.75 / 8 }[/math]
[math]\displaystyle{ N = 1358 }[/math]
[math]\displaystyle{ T_m = 1358 * 12.675 / 16 = 1076 }[/math]
[math]\displaystyle{ T_r = 1358 * 9.75 / 8 = 1655 }[/math]
The adjusted time [math]\displaystyle{ A_{start} = T_{all} / D_h = (3600 + 2867 + 1076 + 1655) / 23 = 400 }[/math]
In other words, the time that is required to get all resources for killing one Pegasus and to actually kill it is 400 seconds.
The overall time to get all resources and kill all Pegasi is [math]\displaystyle{ 400 * 3333 / 3600 = 371 \text{ hours}. }[/math]
After-Ship melee
| Item | DR |
|---|---|
 (G) Dragon Helmet
|
6% |
 (G) Dragon Platebody
|
6% |
 (G) Dragon Platelegs
|
6% |
 (G) Dragon Boots
|
6% |
 (G) Dragon Shield
|
6% |
 Amulet of Calculated Promotion
|
0% |
| Paladin Gloves
|
4% |
 Sunset Rapier
|
0% |
| Total | 34% |
All skills are at level 75.
The simulation results are:
- 33.2 whales per hour,
- 26.57 Pegasi per hour.
[math]\displaystyle{ T_c = 33.2 * 18.875 = 626.7 }[/math]
The adjusted time [math]\displaystyle{ A_{ship} = (3600 + 626.7) / 26.57 = 159.08 }[/math]
The overall time is [math]\displaystyle{ 159.08 * 3333 / 3600 = 148 \text{ hours}. }[/math]
After-Volcanic magic
| Item | DR |
|---|---|
 Ancient Wizard Hat
|
5% |
 Ancient Wizard Robes
|
5% |
 Ancient Wizard Bottoms
|
5% |
 Ancient Wizard Boots
|
5% |
| Miolite Shield
|
2% |
| Enchanted Cape
|
0% |
 Elite Amulet of Magic
|
2% |
 Elementalist Gloves
|
0% |
| Magic Wand (Powerful)
|
0% |
| Total | 24% |
All skills are at level 75 except 
Level 91. With the following setup, you should have exactly 20k accuracy on 
Slicing Winds, they cannot miss now.
The simulation results with 
Eli are:
- 4905 Ancient runes spent,
- 107.9 whales per hour,
- 196.2 Pegasi per hour.
[math]\displaystyle{ T_c = 107.9 * 18.875 = 2037 }[/math]
[math]\displaystyle{ T_m = (N * 20 + N) / 16 * 1.3 = N * 21 / 16 * 1.3 = N * 27.3 / 16 }[/math]
[math]\displaystyle{ T_r = N * 21 * 2 / 16 = N * 21 / 8 }[/math]
[math]\displaystyle{ N = 4905 }[/math]
[math]\displaystyle{ T_m = 4905 * 27.3 / 16 = 8370 }[/math]
[math]\displaystyle{ T_r = 4905 * 21 / 8 = 12876 }[/math]
The adjusted time [math]\displaystyle{ A_{volcano} = T_{all} / D_h = (3600 + 2037 + 8370 + 12876) / 196.2 = 137 }[/math]
The overall time is [math]\displaystyle{ 137 * 3333 / 3600 = 127 \text{ hours}. }[/math]
If you swap Miolite Shield to Book of Eli, it will only increase the clear time because your melee defence would plummet, resulting in many more Whales eaten.
The simulation results with Eli are:
- 4905 Ancient runes spent,
- 172.4 whales per hour,
- 196.2 Pegasi per hour.
[math]\displaystyle{ T_c = 172.4 * 18.875 = 3254 }[/math]
[math]\displaystyle{ T_m = 8370 }[/math]. [math]\displaystyle{ T_r = 12876 }[/math]
The adjusted time [math]\displaystyle{ A_{eli} = T_{all} / D_h = (3600 + 3254 + 8370 + 12876) / 196.2 = 143.2 }[/math]
The overall time is [math]\displaystyle{ 143.2 * 3333 / 3600 = 133 \text{ hours}. }[/math]
Overall, you want to put as much DR and Melee defence as possible when maintaining the 20k accuracy. For instance, if you have Level 93 with the build above, you can swap Enchanted Cape with 
Fire Cape and reduce the food consumption even further.
As you see, the rune mining and crafting take the bulk of the time, so you might want to use all preservation and doubling bonuses that you have.
After-Glacia magic
| Item | DR |
|---|---|
 Glacia God Helmet
|
8% |
 Glacia God Platebody
|
8% |
 Glacia God Platelegs
|
8% |
 Glacia God Boots
|
8% |
 Glacia God Gloves
|
8% |
| Miolite Shield
|
2% |
 Infernal Cape
|
4% |
| Elite Amulet of Magic
|
2% |
| Magic Wand (Powerful)
|
0% |
| Total | 48% |
The levels are the same as in the Volcanic build. Due to Ancient Magic not benefiting from gear, the build was aimed to cram as much DR and melee evasion as possible. If you have Level 95, you should be able to swap for 
Elite Amulet of Defence while still having the required 20k accuracy.
The simulation results are:
- 4905 Ancient runes spent,
- 47.7 whales per hour,
- 196.2 Pegasi per hour.
As the number of runes is the same, [math]\displaystyle{ T_m = 8370. }[/math] [math]\displaystyle{ T_r = 12876. }[/math]
[math]\displaystyle{ T_c = 47.7 * 18.875 = 900.3 }[/math]
The adjusted time [math]\displaystyle{ A_{glacia} = T_{all} / D_h = (3600 + 900.3 + 8370 + 12876) / 196.2 = 131.2 }[/math]
The overall time is [math]\displaystyle{ 131.2 * 3333 / 3600 = 121.5 \text{ hours}. }[/math]
Analysis
Let's consider the post-Ship and post-Glacia builds.
The difference between them is roughly 27 hours.
However, if we leave the Volcano with Sunset Rapier, its clear time would take longer, making the grind to the full 
ancient set longer.
The question is then if the difference between the rapier and the claw in the Volcanic grind is bigger than 27 hours.
Essentially, we compare two strategies:
- Rapier > Claw > Volcano,
- Rapier > Volcano > Claw.
We know the length of "Raper > Claw" and "Volcano > Claw" through the post-Ship and post-Glacia builds, but we need the data on "Rapier > Volcano" and "Claw > Volcano".
We take this data from Volcanic Cave/Guide#Weapon choice.
| Item | Clears per hour |
|---|---|
| Sunset Rapier
|
8.49 |
| Ancient Claw
|
9.23 |
The goal of clearing the Volcanic Cave is to get the ancient set.
Let's consider the simplified case when we see all four pieces of the set as a single entity with the probability of 2/241 + 4/723 = 10/723, and we need to get this entity four times.
The described task is identical to a Bernoulli trial with the probability of success being 10/723.
By using a Bernoulli calculator such as this one, entering probability of success on a single trial (10/723), number of trials, and number of successes (4), we tweak the number of trials until the cumulative probability [math]\displaystyle{ P(X \geq x) }[/math] that number of successes is at least equal to desired is as large as we want. For this trial, the cumulative threshold was set to 80%.
The number of trials that gave this probability is 400, meaning that it will take more than 400 clears of Volcanic Cave to get a full set of Ancient armor.
The results are:
| Item | Clears per hour | Volcanic timing |
|---|---|---|
| Sunset Rapier
|
8.49 | 47.1h |
| Ancient Claw
|
9.23 | 43.4h |
However, the initial simplification of pooling four items into one doesn't account for repeat drops, which is a large part of the 4-item group. The solution to this problem is hardly analytical and usually done by simulation. When the simulation is programmed and run, the results will be on this page. The current anecdotal number is 600.
Without the food, the results are the following.
| Item | Clears per hour | Volcanic timing |
|---|---|---|
| Sunset Rapier
|
8.49 | 70.7h |
| Ancient Claw
|
9.23 | 65h |
As the food preparation is important to calculate the adjusted clear time, no definite resolution is given on the question on when to farm the claw.
