Preservation Chance: Difference between revisions
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== Calculating Gains == | == 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>\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>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>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>120 + (120 \times 0.8) + (120 \times 0.8 \times 0.8) +\cdots + (120 \times 0.8^n)</math> where <math>n</math> goes to infinity. | |||
If we generalize and represent the number of starting resources (<math>120</math>) with <math>a</math> and the probability (<math>0.8</math>) with <math>r</math>, the number of actions performed with <math>a</math> action's worth of starting resources and a resource preservation of <math>r</math> (where <math>0 \le r \lt 1</math>) can be expressed as follows: | |||
<math>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 [https://en.wikipedia.org/wiki/Geometric_progression#Infinite_geometric_series infinite geometric series], which can simply be expressed as <math>\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>a = 120</math> and <math>r = 0.8</math>, we get <math>\frac{120}{1 - 0.8} = 600</math>. | |||
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Revision as of 19:30, 29 May 2024
This page is up to date (v1.3). |
Preservation Chance is a modifier which allows resources to be preserved when creating items, allowing for the creation of items at no cost to the player. When resource preservation triggers, the player will receive a notification stating "You managed to preserve your resources".
The chance to preserve resources only applies when creating items within a skill, it does not affect the consumption of potion doses, Summoning tablets, or prayer points. Rune Preservation and Ammo Preservation are also separate modifiers, which allow for the preservation of runes and
Ranged ammunition respectively.
The preservation chance for all skills is capped at 80%, unless a modifier which increases the cap applies.
Sources
Below is a list of many things other than Mastery bonuses and
Summoning synergies which provide a chance to preserve resources. Another notable mention is that the
Crown of Rhaelyx gains 15% preservation chance (for a total of 25%) when the player has at least one
Charge Stone of Rhaelyx within their Bank.
Source | Type | DLC | Preservation Bonuses | Other Modifiers |
---|---|---|---|---|
Agility Obstacle 2 | Error creating thumbnail: File missing | -10% Chance to Preserve Resources in Skills | +10% Accuracy Rating when fighting against Abyssal Damage +3% chance to double loot in Combat when fighting against Abyssal Damage +8% Maximum Hit when fighting against Abyssal Damage | |
Agility Obstacle 3 | +3% Chance to Preserve Resources in Skills | +10 Mining Node HP +3% chance to deal no damage to Essence Nodes in Mining +3% chance to deal no damage to Ore Nodes in Mining | ||
Agility Obstacle 4 | +3% Chance to Preserve Resources in Skills | -4% Global Skill XP +20% GP gained from Thieving +10% Food Healing Value | ||
Agility Obstacle 4 | +3% Chance to Preserve Resources in Herblore | +2% Herblore Mastery XP +2% Herblore Skill XP -10% base primary resource quantity gained in Farming | ||
Agility Obstacle 4 | Error creating thumbnail: File missing | -10% Chance to Preserve Resources in Skills | +10% flat Abyssal Slayer Area effect negation +5% Damage to Slayer Tasks when fighting against Abyssal Damage +10% Global Abyssal Slayer Coins (except Item Sales) +5% Damage to Monsters in Abyssal Slayer Areas | |
Agility Obstacle 5 | -10% Chance to Preserve Resources in Skills | +5% Chance to Double Items in Fishing +5% Chance to Double Items in Woodcutting +5% Chance to Double Items in Mining +5% Chance to Double Items in Thieving | ||
Agility Obstacle 5 | -10% Chance to Preserve Resources in Skills | +3% Global Mastery XP +4% Global Skill XP -10% Rune Preservation -10% Ammo Preservation | ||
Agility Obstacle 6 | +5% Chance to Preserve Resources in Skills | +5% Rune Preservation +5% Ammo Preservation | ||
Agility Obstacle 7 | -20% Chance to Preserve Resources in Skills | |||
Agility Obstacle 8 | +5% Chance to Preserve Resources in Summoning -16% Chance to Preserve Resources in Herblore | +15% Chance to preserve Summoning Charges +3 base primary resource quantity gained in Summoning | ||
Agility Obstacle 8 | -20% Chance to Preserve Resources in Skills | +3% Cooking Mastery XP +10% Auto Eat Efficiency -3% Cooking Interval +10% Food Healing Value | ||
Agility Obstacle 9 | +10% Chance to Preserve Resources in Skills | +20 Maximum Hitpoints +5% Food Healing Value +5% Chance to Double Items Globally +10 Mining Node HP | ||
Agility Obstacle 10 | +10% Chance to Preserve Resources in Skills | +10% Chance To Preserve Prayer Points +5% Ammo Preservation +10% Rune Preservation | ||
Agility Obstacle 11 | -20% Chance to Preserve Resources in Skills | +3% Mastery XP for Melvor Realm only +15 Mining Node HP +2% chance to receive a Quality Superior Gem while Mining Gem Veins or Meteorite Ore | ||
Agility Obstacle 12 | -10% Chance to Preserve Resources in Herblore | -6% Mastery XP for Melvor Realm only +15% Chance To Preserve Potion Charge | ||
Agility Obstacle 12 | -10% Chance to Preserve Resources in Skills | -5% Cooking Interval +10% Food Healing Value -6% Agility Skill XP +15% base primary resource quantity gained in Farming for Melvor Realm only | ||
Agility Obstacle 13 | -10% Chance to Preserve Resources in Skills | -50 Maximum Hitpoints +5% Chance To Preserve Potion Charge +5% Chance to preserve Summoning Charges | ||
Agility Obstacle 15 | -20% Chance to Preserve Resources in Skills | -0.2s Smithing Interval -0.2s Fletching Interval -0.2s Crafting Interval +30% Chance to gain +1 additional resource in Smithing (Cannot be doubled) +30% Chance to gain +1 additional resource in Fletching (Cannot be doubled) +30% Chance to gain +1 additional resource in Crafting (Cannot be doubled) +3% chance to receive a Quality Superior Gem while Mining Gem Veins or Meteorite Ore | ||
Agility Pillar | +3% Chance to Preserve Resources in Skills | +2% Global Mastery XP +3% Chance to Double Items Globally +10% base primary resource quantity gained in Farming for Melvor Realm only | ||
Error creating thumbnail: File missing Abyssal Bear | Item (Summon1, Summon2) | Error creating thumbnail: File missing | +5% Chance to Preserve Resources in Herblore | |
Error creating thumbnail: File missing Abyssal Cooking Scroll | Item (Consumable) | Error creating thumbnail: File missing | -10% Chance to Preserve Resources in Cooking | +1 additional quantity of primary resource gained in Cooking for Abyssal Realm only (cannot be doubled) |
Error creating thumbnail: File missing Abyssal Fletching Scroll | Item (Consumable) | Error creating thumbnail: File missing | -10% Chance to Preserve Resources in Fletching | +1 additional quantity of primary resource gained in Fletching for Abyssal Arrows nodes (Cannot be doubled) +1 additional quantity of primary resource gained in Fletching for Abyssal Bolts nodes (Cannot be doubled) +1 additional quantity of primary resource gained in Fletching for Abyssal Javelins nodes (Cannot be doubled) |
Error creating thumbnail: File missing Abyssal Hourglass (Inverted) | Item (Weapon) | Error creating thumbnail: File missing | +10% Chance to Preserve Resources in Skills | +6% Mastery XP for Abyssal Realm only -1 additional quantity of primary resource gained globally (Cannot be doubled) -10% cost to produce Abyssal Realm Items in all Artisan Skills -6% Global Abyssal XP |
Error creating thumbnail: File missing Abyssal Hourglass (Upright) | Item (Weapon) | Error creating thumbnail: File missing | -10% Chance to Preserve Resources in Skills | -6% Mastery XP for Abyssal Realm only +1 additional quantity of primary resource gained globally (Cannot be doubled) +10% cost to produce Abyssal Realm Items in all Artisan Skills +6% Global Abyssal XP |
Error creating thumbnail: File missing Abyssal Pig | Item (Summon1, Summon2) | Error creating thumbnail: File missing | +10% Chance to Preserve Resources in Cooking | |
Error creating thumbnail: File missing Abyssal Salamander | Item (Summon1, Summon2) | Error creating thumbnail: File missing | +5% Chance to Preserve Resources in Smithing | |
Error creating thumbnail: File missing Abyssal Smithing Scroll | Item (Consumable) | Error creating thumbnail: File missing | -10% Chance to Preserve Resources in Smithing | +1 additional quantity of primary resource gained in Smithing for Abyssal Bars nodes (Cannot be doubled) |
Error creating thumbnail: File missing Abyssal Summoning Scroll | Item (Consumable) | Error creating thumbnail: File missing | -10% Chance to Preserve Resources in Summoning | +5 additional quantity of primary resource gained in Summoning for Abyssal Realm only (cannot be doubled) |
Item (Summon1, Summon2) | +5% Chance to Preserve Resources in Herblore | |||
![]() | Item (Consumable) | ![]() | +3% Chance to Preserve Resources in Skills | -3% Interval for all Non-Combat Skills +4% Non-Combat Skill XP +4% Mastery XP for Melvor Realm only |
![]() | Item (Cape) | +20% Chance to Preserve Resources in Summoning | +5 additional quantity of Runes gained in Runecrafting (Cannot be doubled) +10 Flat HP Regen Bypass Slayer Area item requirements for areas that require less than level 100 Slayer -50% Prayer Point Cost for Prayers -15% Township Building Cost (Capped at -80%) +15% Chance to Double Items in Runecrafting -20% Melvor Realm Agility Obstacle Build Costs +5% Damage To Slayer Tasks +50% Ammo Preservation +1 base quantity when gaining Stardust from Astrology +1 base quantity when gaining Golden Stardust from Astrology +10 base primary resource quantity gained in Summoning -0.5s Thieving Interval -0.5s Crafting Interval +2% Global Perfect Cook chance +25% Mastery Pool XP Cap +100% chance to successfully Cook an item Rune providing items provide 2x as many runes +10% Chance to preserve Summoning Charges +100% GP gained from Thieving +10% GP gained from Agility x2 Items received from Fishing x2 Items received from Fletching x2 Items received from Herblore -15% Woodcutting Interval -15% Cooking Interval +25% Flat Slayer Area Effect Negation +1 Coal Ore per Ore Mined. (Item doubling does not apply) -50% Coal Costs for Smithing +150 Stealth while Thieving +100% chance to gain Coal Ore in Firemaking +100% chance to gain Ash in Firemaking +5% Global Skill XP +25% base primary resource quantity gained in Farming | |
![]() | Item (Cape) | ![]() | +20% Chance to Preserve Resources in Cartography | +3 levels of the Brush Tool in Archaeology +3 levels of the Trowel Tool in Archaeology +3 levels of the Shovel Tool in Archaeology -30% Cartography survey interval +15% chance to preserve dig site map excavation actions -50% Cartography map upgrade interval -20 dig site map refinement cost +1 base primary resource quantity gained in Archaeology +3 levels of the Sieve Tool in Archaeology |
![]() | Item (Cape) | ![]() | +10% Chance to Preserve Resources in Cartography | -20% Cartography map upgrade interval -10 dig site map refinement cost |
![]() | Item (Consumable) | +10% Chance to Preserve Resources in Cooking | +20% Chance to Double Items in Cooking | |
![]() | Item (Helmet) | -10% Chance to Preserve Resources in Skills | +10% Global Mastery XP -5% Global Skill XP | |
![]() | Item (Helmet) | +10% Chance to Preserve Resources in Skills | ||
Error creating thumbnail: File missing Magic Enhancement (Superior) | Item (Enhancement1, Enhancement2, Enhancement3) | +2% Chance to Preserve Resources in Skills | +6% Magic Max Hit +4% Rune Preservation | |
Error creating thumbnail: File missing Magic Enhancement 3 | Item (Enhancement3) | +1% Chance to Preserve Resources in Skills | ||
Error creating thumbnail: File missing Magic Enhancement 3 (Augmented) | Item (Enhancement3) | +2% Chance to Preserve Resources in Skills | ||
![]() | Item (Cape) | +20% Chance to Preserve Resources in Summoning | +5 additional quantity of Runes gained in Runecrafting (Cannot be doubled) +10 Flat HP Regen Bypass Slayer Area item requirements for areas that require less than level 100 Slayer -50% Prayer Point Cost for Prayers -15% Township Building Cost (Capped at -80%) +15% Chance to Double Items in Runecrafting -20% Melvor Realm Agility Obstacle Build Costs +50% Ammo Preservation +1 base quantity when gaining Stardust from Astrology +1 base quantity when gaining Golden Stardust from Astrology +10 base primary resource quantity gained in Summoning -0.5s Thieving Interval -0.5s Crafting Interval +2% Global Perfect Cook chance +1 Coal Ore per Ore Mined. (Item doubling does not apply) +100% chance to successfully Cook an item +5% Damage To Slayer Tasks +10% Chance to preserve Summoning Charges +100% GP gained from Thieving +10% GP gained from Agility Rune providing items provide 2x as many runes -15% Woodcutting Interval -15% Cooking Interval x2 Items received from Fishing x2 Items received from Fletching x2 Items received from Herblore +25% Flat Slayer Area Effect Negation -50% Coal Costs for Smithing +150 Stealth while Thieving +100% chance to gain Coal Ore in Firemaking +100% chance to gain Ash in Firemaking +5% Global Skill XP +25% base primary resource quantity gained in Farming | |
![]() | Item (Platebody) | ![]() | +8% Chance to Preserve Resources in Skills | -30% Global GP (except Item Sales) |
Item (Summon1, Summon2) | +10% Chance to Preserve Resources in Cooking | |||
![]() | Item (Ring, Passive) | -3% Chance to Preserve Resources in Skills | +7% Chance to Double Items Globally | |
Item (Summon1, Summon2) | +5% Chance to Preserve Resources in Smithing | |||
![]() | Item (Weapon) | ![]() | +20% Chance to Preserve Resources in Cartography | -5% Cartography Interval +8% Cartography Skill XP +20% Chance to Double Items in Cartography |
![]() | Item (Consumable) | +10% Chance to Preserve Resources in Summoning | +10% Chance to preserve Summoning Charges +15 base primary resource quantity gained in Summoning | |
![]() | Item (Cape) | +20% Chance to Preserve Resources in Summoning | +10% Chance to preserve Summoning Charges +10 base primary resource quantity gained in Summoning | |
![]() | Item (Cape) | +25% Chance to Preserve Resources in Summoning | +8 additional quantity of Runes gained in Runecrafting (Cannot be doubled) +15 Flat HP Regen +5% of Maximum Hit added to Minimum Hit -75% Prayer Point Cost for Prayers -20% Township Building Cost (Capped at -80%) -30% Melvor Realm Agility Obstacle Build Costs +5% Melee Strength Bonus from Equipment +2 base quantity when gaining Stardust from Astrology +2 base quantity when gaining Golden Stardust from Astrology +1 base quantity when gaining Bird Nest from Woodcutting +20% chance to avoid the stun interval and damage in Thieving when failing a pickpocket attempt for {realmName} only +4% Global Perfect Cook chance +2 Coal Ore per Ore Mined. (Item doubling does not apply) +100% chance to successfully Cook an item +5% Ranged Strength Bonus from Equipment +10% Global Slayer Coins (except Item Sales) +150% GP gained from Thieving +20% GP gained from Agility +100% Chance to gain +1 additional resource in Fishing (Cannot be doubled) +100% Chance to gain +1 additional resource in Fletching (Cannot be doubled) +15% Chance to gain +1 additional resource in Crafting (Cannot be doubled) +100% Chance to gain +1 additional resource in Herblore (Cannot be doubled) +50% chance to gain +1 additional resource in Smithing for Bars nodes (Cannot be doubled) +270 Stealth while Thieving +100% chance to gain Charcoal in Firemaking +100% chance to gain Coal Ore in Firemaking +100% chance to gain Ash in Firemaking +10% Summoning Max Hit Rune providing items provide 4x as many runes +40% base primary resource quantity gained in Farming +5% Lifesteal +5% Magic Damage Bonus from Equipment +1% chance to gain 1 Lost Chest from Fishing for Melvor Realm only (Cannot be doubled) +75% Ammo Preservation +8% Damage To Slayer Tasks -75% Coal Costs for Smithing -0.8s Thieving Interval -0.8s Crafting Interval +20% Chance to Double Items in Farming +25% Chance to Double Items in Runecrafting +15% Chance to preserve Summoning Charges +35% Flat Slayer Area Effect Negation +5% Chance To Preserve Prayer Points +1 base primary resource quantity gained in Fletching for Gem-Tipped Bolts nodes +10 base primary resource quantity gained in Summoning for Melvor Realm only Bypass All Slayer Area item requirements +5% Chance To Preserve Potion Charge -20% Woodcutting Interval -25% Cooking Interval -10% Summoning Interval -10% Astrology Interval +5% Reflect Damage -20% Agility Pillar build costs +5% Chance to Preserve Food when eaten +5% Chance to find gem veins when Mining +8% Global Skill XP +10% Rune Preservation x2 Items received from Fishing x2 Items received from Fletching x2 Items received from Herblore | |
![]() | Item (Cape) | ![]() | +20% Chance to Preserve Resources in Cartography | -50% Cartography map upgrade interval -20 dig site map refinement cost -30% Cartography survey interval |
![]() | Item (Cape) | +25% Chance to Preserve Resources in Summoning | +8 additional quantity of Runes gained in Runecrafting (Cannot be doubled) +15 Flat HP Regen +5% of Maximum Hit added to Minimum Hit -75% Prayer Point Cost for Prayers -20% Township Building Cost (Capped at -80%) -30% Melvor Realm Agility Obstacle Build Costs +5% Melee Strength Bonus from Equipment +2 base quantity when gaining Stardust from Astrology +2 base quantity when gaining Golden Stardust from Astrology +1 base quantity when gaining Bird Nest from Woodcutting +20% chance to avoid the stun interval and damage in Thieving when failing a pickpocket attempt for {realmName} only +4% Global Perfect Cook chance +2 Coal Ore per Ore Mined. (Item doubling does not apply) +100% chance to successfully Cook an item +5% Ranged Strength Bonus from Equipment +10% Global Slayer Coins (except Item Sales) +150% GP gained from Thieving +20% GP gained from Agility +100% Chance to gain +1 additional resource in Fishing (Cannot be doubled) +100% Chance to gain +1 additional resource in Fletching (Cannot be doubled) +15% Chance to gain +1 additional resource in Crafting (Cannot be doubled) +100% Chance to gain +1 additional resource in Herblore (Cannot be doubled) +50% chance to gain +1 additional resource in Smithing for Bars nodes (Cannot be doubled) +270 Stealth while Thieving +100% chance to gain Charcoal in Firemaking +100% chance to gain Coal Ore in Firemaking +100% chance to gain Ash in Firemaking +10% Summoning Max Hit Rune providing items provide 4x as many runes +40% base primary resource quantity gained in Farming +5% Lifesteal +5% Magic Damage Bonus from Equipment +1% chance to gain 1 Lost Chest from Fishing for Melvor Realm only (Cannot be doubled) +75% Ammo Preservation +8% Damage To Slayer Tasks -75% Coal Costs for Smithing -0.8s Thieving Interval -0.8s Crafting Interval +20% Chance to Double Items in Farming +25% Chance to Double Items in Runecrafting +15% Chance to preserve Summoning Charges +35% Flat Slayer Area Effect Negation +5% Chance To Preserve Prayer Points +1 base primary resource quantity gained in Fletching for Gem-Tipped Bolts nodes +10 base primary resource quantity gained in Summoning for Melvor Realm only Bypass All Slayer Area item requirements +5% Chance To Preserve Potion Charge -20% Woodcutting Interval -25% Cooking Interval -10% Summoning Interval -10% Astrology Interval +5% Reflect Damage -20% Agility Pillar build costs +5% Chance to Preserve Food when eaten +5% Chance to find gem veins when Mining +8% Global Skill XP +10% Rune Preservation x2 Items received from Fishing x2 Items received from Fletching x2 Items received from Herblore | |
![]() | Item (Cape) | +25% Chance to Preserve Resources in Summoning | -10% Summoning Interval +10% Summoning Max Hit +15% Chance to preserve Summoning Charges +10 base primary resource quantity gained in Summoning for Melvor Realm only | |
Error creating thumbnail: File missing Void Wisp | Item (Summon1, Summon2) | Error creating thumbnail: File missing | +5% Chance to Preserve Resources in Skills | |
Pet | +10% Chance to Preserve Resources in Runecrafting | |||
Pet | +10% Chance to Preserve Resources in Smithing | |||
![]() | Point of Interest | ![]() | +5% Chance to Preserve Resources in Cartography | -5% Cartography map upgrade interval +5% chance to preserve dig site map excavation actions |
Chance Cap
The preservation chance for all skills is capped at 80%. For a few skills, there exists bonuses which can increase this cap:
- The
Bear &
Beaver synergy can increase the cap for
Fletching by 5%
- The
Bear &
Fox synergy can increase the cap for
Herblore by 5%
- The
Herblore Preservation Scroll from
Township can increase the cap for
Herblore by 5%. This stacks with the above.
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].
Melvor Idle version v1.3 (Released: 13th June 2024) | ||||||||||||||||||||
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