Skill Gem /1

Skill Gem /1

Support Gem Quality /1

Support Gem Quality /1

ItemTypeStatsWeight
Controlled Destruction SupportDivergent Supported Skills have (0–10)% chance for Damage with Hits to be Lucky100
Item mods /1

Item mods /1

NameLevelPre/SufDescriptionSpawn Weight
45ScourgeDownsideDamage with Hits is Unluckyamulet 500
default 0
Veiled mods /1

Veiled mods /1

NameLevelPre/SufDescriptionSpawn Weight
of the Order60SuffixYour Critical Strike Chance is Lucky while Focused
Focus has (5–8)% increased Cooldown Recovery Rate
grant focus skill [1] critical
belt 1000
default 0
Crafting Bench /1

Crafting Bench /1

IDModRequireItemClassesUnlock
JunYour Critical Strike Chance is Lucky while Focused
grant focus skill [1]
9x CurrencyRerollMagicOrb of AlterationBeltUnveil
Harvest Seed /18

Harvest Seed /18

Name
Augment a non-Influenced Magic or Rare item with a new Caster modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Physical modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Fire modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Speed modifier with Lucky values
Reforge a Rare item with Lucky modifier values, keeping all Prefixes
Reforge a Rare item with Lucky modifier values, keeping all Suffixes
Reroll the values of Prefix modifiers on a Magic or Rare item, with Lucky modifier values
Reroll the values of Suffix modifiers on a Magic or Rare item, with Lucky modifier values
Reroll the values of Prefix, Suffix and Implicit modifiers on a Rare item, with Lucky modifier values
Augment a non-Influenced Rare item with a new modifier, with Lucky modifier values
Augment a Magic or Rare item with a new Influence modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Attack modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Cold modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Life modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Critical modifier with lucky values
Augment a non-Influenced Magic or Rare item with a new Defence modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Lightning modifier with Lucky values
Augment a non-Influenced Magic or Rare item with a new Chaos modifier with Lucky values
Item /1

Item /1

IconName
GildedFossilSanctified Fossil
Stack Size: 1 / 10
Numeric modifier values are lucky
High Level modifiers are more common
Unique /8

Unique /8

NameShow Full Descriptions
LorisLanternLori's Lantern Prismatic Ring
+(8–10)% to all Elemental Resistances
+10% to all Elemental Resistances
(6–8)% increased Movement Speed when on Low Life
31% increased Light Radius
+(20–25)% to Chaos Resistance when on Low Life
Damage of Enemies Hitting you is Unlucky while you are on Low Life
(You are on Low Life if you have 50% of your Maximum Life or less)
(Unlucky things are rolled twice and the worst result used)
FoxshadeFox's Fortune Wild Leather
+(20–30) to Dexterity
Adds 5 to 12 Physical Damage to Attacks
+1500 to Evasion Rating while on Full Life
+(400–500) to Evasion Rating
(120–150)% increased Evasion Rating
10% increased Movement Speed
Damage of Enemies Hitting you is Unlucky while you are on Full Life
(Unlucky things are rolled twice and the worst result used)
Coward%27s%20ChainsCoward's Chains Chain Belt
+(9–20) to maximum Energy Shield
+(15–20) to all Attributes
(5–10)% increased Movement Speed
Damage of Enemies Hitting you is Unlucky while you are Cursed with Vulnerability
You count as on Full Life while you are Cursed with Vulnerability
You are Cursed with Vulnerability, with 40% increased Effect
(Attributes are Strength, Dexterity, and Intelligence)
(Unlucky things are rolled twice and the worst result used)
IronHeart%20FinalThe Iron Fortress Crusader Plate
+1% Chance to Block Attack Damage per 50 Strength
Chance to Block Spell Damage is Unlucky
+(60–120) to Strength
(80–100)% increased Armour
10% reduced Movement Speed
Strength's Damage Bonus instead grants 3% increased Melee
Physical Damage per 10 Strength
(Unlucky things are rolled twice and the worst result used)
PerquilsToePerquil's Toe Gold Amulet
(12–20)% increased Rarity of Items found
+(40–50) to Dexterity
(5–8)% increased Movement Speed
Lightning Damage of Enemies Hitting you is Lucky
Nearby Allies' Damage with Hits is Lucky
(Lucky things are rolled twice and the best result used)
ElementalHarmonyThe Fulcrum Ezomyte Staff
+20% Chance to Block Attack Damage while wielding a Staff
(140–180)% increased Physical Damage
(0–50)% of Physical Damage Converted to Fire Damage
(0–50)% of Physical Damage Converted to Cold Damage
(0–50)% of Physical Damage Converted to Lightning Damage
Elemental Ailments you inflict are Reflected to you
Elemental Damage with Hits is Lucky while you are Shocked
Damage Penetrates (8–10)% Elemental Resistances while you are Chilled
Gain (30–40)% of Physical Damage as Extra Damage of a random Element while you are Ignited
ConstrictingCrownViridi's Veil Praetor Crown
+(1–2) to Level of Socketed Gems
(120–160)% increased Armour and Energy Shield
+(15–25)% to all Elemental Resistances
Damage of Enemies Hitting you is Unlucky while you have a Magic Ring Equipped
You are Hexproof if you have a Magic Ring in right slot
Take no Extra Damage from Critical Strikes if you have a Magic Ring in left slot
(Unlucky things are rolled twice and the worst result used)
IpochotlWandRelic of the Pact Spiraled Wand
(15–19)% increased Spell Damage
Grants Level 1 Blood Sacrament Skill
Your Critical Strike Chance is Lucky while on Low Life
(Lucky things are rolled twice and the best result used)
(You are on Low Life if you have 50% of your Maximum Life or less)
Ascendancy Passive /1

Ascendancy Passive /1

CategoryNameShow Full Descriptions
NotableViolent Retaliation
GLADViolentRetaliation
Attack Damage is Lucky if you've Blocked in the past 20 seconds
Hits ignore Enemy Monster Physical Damage Reduction if you've Blocked in the past 20 seconds
Cluster Jewel Passive /1

Cluster Jewel Passive /1

CategoryNameShow Full Descriptions
NotableSupercharge
IncreasedLightningDamage
Lightning Damage with Non-Critical Strikes is Lucky
Timeless Jewel Passive /1

Timeless Jewel Passive /1

FactionCategoryNameShow Full Descriptions
MarakethKeystoneDance with Death
SharpandBrittle
Can't use Helmets
Your Critical Strike Chance is Lucky
Your Damage with Critical Strikes is Lucky
Enemies' Damage with Critical Strikes against you is Lucky
(Lucky things are rolled twice and the best result used)
You circle the black scorpion with enmity, daring it time and again.
Brutal Restraint: Asenath

Community Wiki

Wiki Edit

Luck

Luck is a mechanic that rolls a number twice, with Lucky rolls applying the best result, and Unlucky rolls applying the worst result. Modifiers that state when Damaging refer specifically to damage ranges, and not related mechanics such as accuracydexAccuracy or critical strike chance.

Lucky and Unlucky modifiers affecting the same thing will cancel each other out.

Effectiveness

With percentage rolls, such as critical strike chance, lucky/unlucky rolls will be up to a 100% more/less modifier, changing linearly towards 0% as critical chance increases. As for damage rolls, the average damage from the roll will be at up to 33% more or less, when the minimum damage is close to zero, but will have a much weaker effect when the minimum damage is closer to the maximum.

Calculations

Binary Rolls

More specifically, the lucky critical strike chance can be calculated from the following formula:

For example, the lucky critical strike chance for an default critical strike chance of 40% could be calculated as follows:

It should be noted that these calculations neglect the effect of accuracy on critical strikes.

Damage in a Range

Given an integer roll between and , the normal expected value is .

A lucky roll has expected value

Note that the last term in this is always between 0 and 1/6 This simplifies the formula to .

The average damage is effectively nudged closer toward the max damage, and further from the minimum damage. The damage boost, on average, is a sixth of the difference between minimum and maximum damage.

Example 1: You shoot a level 20 FireballFireball. The maximum damage is 1643, and minimum damage is 1095, for an average of 1369. The difference between minimum and maximum is 548. If the damage is lucky, you get an average 548/6=91.3 extra damage, for a new average damage of 1369+91.3=1460.3 damage. This is a 6.6% damage boost.

Example 2: You cast a level 20 SparkSpark. The maximum damage is 1198, and minimum damage is 63, for an average of 630.5. The difference between minimum and maximum is 1135. If the damage is lucky, you get an average 1135/6=189.2 extra damage, for a new average damage of 189.2+630.5=819.6 damage. This is a 30% damage boost.

How much does lucky improve our expected value - if our minimum damage is 0 then we get a 33% more multiplier. As the minimum damage increases our percentage increase decreases.


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