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Prayer: Difference between revisions
→Prayer Point Acquisition Rates: Revise Skeleton fish calculations for accuracy
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== Prayer Point Acquisition Rates == | == Prayer Point Acquisition Rates == | ||
{{SpoilerBox|text= | {{SpoilerBox|text= | ||
{{Skill|Fishing}} | The general formula used for {{Skill|Fishing}} is <math>P \times A_F \times \tfrac{2^M \times \left ( 1 + C_D \right ) + C_A}{S}</math>, where: | ||
* <math>P</math> is the prayer points per fish, a constant of 3 for {{ItemIcon|Raw Skeleton Fish}} | |||
* <math>A_F</math> is the area's fish chance, a base of 95% (or 0.95) for the Secret Area | |||
* <math>M</math> is the number of things guaranteed to double the number of fish caught | |||
* <math>C_D</math> is the chance to double, provided from a wide range of sources such as the {{ItemIcon|Fishing Hook}} | |||
* <math>C_A</math> is the chance to gain 1 additional resource, provided by {{ItemIcon|Octopus}} | |||
* <math>S</math> is the average number of seconds between catches | |||
With the {{ItemIcon|Amulet of Fishing}}, | {{Skill|Fishing}} with the {{UpgradeIcon|Dragon Fishing Rod}} has an average catch time of <math>S = \tfrac{2.4 + 7.2}{2} = 4.8</math> seconds. With the {{ItemIcon|Amulet of Fishing}}, this is reduced further to <math>S = \tfrac{1.8 + 5.4}{2} = 3.6</math> seconds, and can be reduced further still with {{Icon|type=constellation|Ameria}}. | ||
The {{ItemIcon|Fishing Skillcape}} and {{MasteryReq|Raw Skeleton Fish|99}}, when both are active <math>M = 2</math> and so guaranteed doubling provides <math>2^2 = 4</math> times the usual number of fish. | |||
Assuming a somewhat optimal setup as per [https://docs.google.com/spreadsheets/d/1oDeCK-ObKd8xBlCcJtA_pBmXzkgg9wm5NwL8GI8tqhk this sheet], the time between catches reduces to <math>S = 2.8</math> seconds, chance to double becomes <math>C_D = 0.66 = 66\%</math>, and the additional resource chance becomes <math>C_A = 0.03 = 3\%</math>. This assumes 10% chance to double and 10% interval reduction from {{Skill|Astrology}}, as rolls higher than this require too much dust. | |||
---- | |||
{{Skill|Alternative Magic|Alt.Magic}} has the interval of 2 seconds. With {{ItemIcon|Amulet of Incantation}}, the Alt.Magic interval goes down to 1.8 seconds. | {{Skill|Alternative Magic|Alt.Magic}} has the interval of 2 seconds. With {{ItemIcon|Amulet of Incantation}}, the Alt.Magic interval goes down to 1.8 seconds. | ||
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The rune expenditure can be mitigated further by the {{ItemIcon|Nature's Call Staff}} and the {{ItemIcon|Magic Skillcape}}, leaving only one {{ItemIcon|Earth Rune}} per cast. Using the [[Shop#God_Upgrades|God Upgrades]], It can be sped up to roughly <math>(0.85+1.7)/16/\frac{1}{1-0.8} = 0.0319</math> seconds per a Blessed Offering cast. | The rune expenditure can be mitigated further by the {{ItemIcon|Nature's Call Staff}} and the {{ItemIcon|Magic Skillcape}}, leaving only one {{ItemIcon|Earth Rune}} per cast. Using the [[Shop#God_Upgrades|God Upgrades]], It can be sped up to roughly <math>(0.85+1.7)/16/\frac{1}{1-0.8} = 0.0319</math> seconds per a Blessed Offering cast. | ||
---- | |||
For {{Skill|Slayer}} calculation in [[Combat Simulator]], the following setup was used:<br> | For {{Skill|Slayer}} calculation in [[Combat Simulator]], the following setup was used:<br> | ||
Full {{ItemIcon|Glacia God Helmet|Glacia set}}, {{ItemIcon|Skull Cape}}, {{ItemIcon|Elite Amulet of Magic}}, {{ItemIcon|Cloudburst Staff}},<br> | Full {{ItemIcon|Glacia God Helmet|Glacia set}}, {{ItemIcon|Skull Cape}}, {{ItemIcon|Elite Amulet of Magic}}, {{ItemIcon|Cloudburst Staff}},<br> | ||
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! Result | ! Result | ||
|- | |- | ||
| Fishing {{ItemIcon|Raw Skeleton Fish}} with [[Fishing#Fishing_Rods|Dragon Rod]] | | Fishing {{ItemIcon|Raw Skeleton Fish}} with [[Fishing#Fishing_Rods|Dragon Rod]] and {{MasteryReq|Raw Skeleton Fish|1}} | ||
| <math>3 | | <math>3 \times 0.95 \times \tfrac{1 + 0.004}{4.8}</math> | ||
| 0. | | 0.60 | ||
|- | |- | ||
| Fishing {{ItemIcon|Raw Skeleton Fish}} with Dragon Rod | | Fishing {{ItemIcon|Raw Skeleton Fish}} with Dragon Rod and {{MasteryReq|Raw Skeleton Fish|99}} | ||
| <math>3 \times | | <math>3 \times 0.92 \times \tfrac{2}{4.8}</math> | ||
| 1. | | 1.15 | ||
|- | |||
| Fishing {{ItemIcon|Raw Skeleton Fish}} with Dragon Rod, {{MasteryReq|Raw Skeleton Fish|99}}, {{ItemIcon|Fishing Skillcape|Cape}}, and {{ItemIcon|Amulet of Fishing|Amulet}} | |||
| <math>3 \times 0.92 \times \tfrac{2^2}{3.6}</math> | |||
| 3.07 | |||
|- | |- | ||
| Alt. Magic/{{Icon|type=spell|Blessed Offering}} with {{ItemIcon|Staff of Earth|Staff}} | | Alt. Magic/{{Icon|type=spell|Blessed Offering}} with {{ItemIcon|Staff of Earth|Staff}} | ||
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| <math>3 \times 3/(2 + 0.0319)</math> | | <math>3 \times 3/(2 + 0.0319)</math> | ||
| 4.43 | | 4.43 | ||
|- | |- | ||
| Alt. Magic/{{Icon|type=spell|Blessed Offering}} with {{ItemIcon|Nature's Call Staff|Staff}}, {{ItemIcon|Magic Skillcape|Cape}}, {{ItemIcon|Amulet of Incantation|Amulet}} and [[Shop#God_Upgrades|God Upgrades]] | | Alt. Magic/{{Icon|type=spell|Blessed Offering}} with {{ItemIcon|Nature's Call Staff|Staff}}, {{ItemIcon|Magic Skillcape|Cape}}, {{ItemIcon|Amulet of Incantation|Amulet}} and [[Shop#God_Upgrades|God Upgrades]] | ||
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| 4.91 | | 4.91 | ||
|- | |- | ||
| Fishing {{ItemIcon|Raw Skeleton Fish}} with | | Fishing {{ItemIcon|Raw Skeleton Fish}} with a reasonably optimal setup. <span style="float:right;margin-left:1em;margin-right:0;" class="mw-collapsible mw-collapsed" data-expandtext="Show setup" data-collapsetext="Hide"> | ||
| <math>3 \times | * {{UpgradeIcon|Dragon Fishing Rod}} | ||
| | * {{MasteryReq|Raw Skeleton Fish|99}} and [[Fishing#Mastery_Pool_Checkpoints|50% Mastery Pool Checkpoint]] | ||
* {{ItemIcon|Fishing Skillcape}}, {{ItemIcon|Amulet of Fishing}}, {{ItemIcon|Sailor's Top}}, {{ItemIcon|Aorpheat's Signet Ring}}, {{ItemIcon|Fishing Hook}}, and {{ItemIcon|Octopus}} equipped | |||
* {{PetIcon|Pudding Duckie}} and {{PetIcon|Aquarias}} unlocked | |||
* Rock Climb and Ice Jump [[Agility#Obstacles|Agility Obstacles]], as well as the [[Agility#Passive Pillars|Pillar of Skilling]] | |||
* 10% Chance to double and 10% Interval reduction from {{Icon|type=constellation|Ameria}}</span> | |||
| <math>3 \times 0.95 \times \tfrac{2^2 \times \left ( 1 + 0.66 \right ) + 0.03}{2.8}</math> | |||
| 6.79 | |||
|- | |- | ||
| End-game {{Skill|Slayer}} tasks | | End-game {{Skill|Slayer}} tasks | ||
| | | Details in Calculations above | ||
| 5.8 barebones<br>34 with proper setup | | 5.8 barebones<br>34 with proper setup | ||
|} | |} | ||