Lucky

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For the equipment, see Lucky equipment.
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Lucky is an Invention perk which has a 0.5% chance per rank when hit that the damage dealt will be reduced to 1. It can be created in armour gizmos.

This perk does not stack with Saradomin or Zamorak warpriest armour. Lucky works on all damage types, including typeless damage taken in combat. This means that it works on reflected damage and Helwyr's bleeds, but does not activate for Araxxor's cleave or when trying to eat a dwarven rock cake (cooled).[source needed]

When the perk triggers, it prompts the following message with X replaced by the reduction: Your Lucky perk reduces the damage of this attack by X.

Rank Activation chance Average damage reduction
1 0.5% (0.55%) 0.5% (0.55%)
2 1.0% (1.10%) 1.0% (1.10%)
3 1.5% (1.65%) 1.5% (1.65%)
4 2.0% (2.20%) 2.0% (2.20%)
5 2.5% (2.75%) 2.5% (2.75%)
  • All numbers in parentheses refer to level 20 gear.

Given a monster's minimum and maximum hits , and the rank of lucky , the average damage reduction of the perk over hits can be calculated approximately as:

Calculations[edit | edit source]

  • The average ratio of damage taken, , from Lucky to that of without Lucky is
  • The average damage reduction is then, after some rearranging,
Notes
  • A calculator for this is at the top of this page.
  • Assumption :
    • All hits that are taken have the possibility to proc Lucky.
  • is the rank of the Lucky perk.
  • is the proc chance of Lucky to activate (if the perk is on level 20 gear, then this value is multiplied by 1.1).
  • when or . This represents summing over all possibilities where integer represents the amount of hits prior to the proc of Lucky. The probability of Lucky proccing on hit is therefore .
  • is the random value uniformly sampled between the enemy's minimum hit and maximum hit. The describes different sets of hits. The sets are regenerated for every new value of .
    • has elements with integer . This is the damage taken before the perk procs.
      • Clarification : This does mean that for that there are no elements in this set.
    • is the damage taken from a single hit if the Lucky perk were to proc (without having it on gear).
    • The set of values in for integer is the same in both the numerator and denominator of the ratios for any given .
Simplifications
  • This can be simplified if the assumption is that every value integer , integer is taken to be the same . In this scenario, there is no random element and the above is then only dependent on the proc chance. A table is provided at the top of the page.


Using these simplifications, the damage reduction reduces to

Sources[edit | edit source]

MaterialRarityPerk ranks with X materials
12345
Silent components.png
Silent componentsRare1234–55
Delicate parts.png
Delicate partsCommon0011–21–2
Light components.png
Light componentsUncommon01–21–21–31–5
Fortunate components.png
Fortunate componentsRare11–21–31–51–5

Suggested gizmos[edit | edit source]

Gizmo layout Possible perks
Silent components.png
Silent components.pngSilent components.pngSilent components.png
Silent components.png
Silent components.png
Silent components.pngSilent components.pngSilent components.png
Fortunate components.png
  • Other possible perks:
Silent components.png
Silent components.pngSilent components.pngSilent components.png
Subtle components.png
  • Other possible perks:
Silent components.png
Silent components.pngSilent components.pngSilent components.png
Dextrous components.png
  • Other possible perks:
Explosive components.png
Explosive components.pngExplosive components.pngExplosive components.png
Silent components.png
  • Other possible perks: