Luck

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Lucky crit rolls visualized in a tree diagram.

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 accuracy or critical strike chance.[1]

Lucky and Unlucky modifiers affecting the same thing will cancel each other out.[2]

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

Either roll can make the hit critical, so your critical strike chance on the solid line will be increased to the dash-dotted line on lucky 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.

Derivation of lucky rolls [Expand]

This is a problem that can be solved with conditional probability.

Let A be the default critical strike chance on the first roll, then the chance to NOT crit on the first roll is:

(1)

If the roll failed the die will be cast a second time with the same probabilities. The chance to crit on the second roll is 1 multiplied with A:

(2)

The total probability to get a lucky critical strike is the sum of A and 2.

Damage in a Range

Given an integer roll between min and max, 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 and therefore is negligible (it is a byproduct of the fact our uniform variable only takes values over the integers.) 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 FireballFireballProjectile, Spell, AoE, Fire
Level: (1-20)
Cost: (6-25) Mana
Cast Time: 0.75 sec
Critical Strike Chance: 6.00%
Effectiveness of Added Damage: 370%
Projectile Speed: 1040
AoE Radius: 9
Unleashes a ball of fire towards a target which explodes, damaging nearby foes.Deals (9-1640) to (14-2460) Fire Damage
25% chance to Ignite enemies
Projectiles gain Radius as they travel farther, up to +(0-9) Radius

Additional Effects per 1% Quality:
1% increased Projectile Speed
Place into an item socket of the right colour to gain this skill. Right click to remove from a socket.
Fireball skill icon.png
. 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 SparkSparkSpell, Projectile, Duration, Lightning
Level: (1-20)
Cost: (5-21) Mana
Cast Time: 0.65 sec
Critical Strike Chance: 6.00%
Effectiveness of Added Damage: 190%
Projectile Speed: 560
Launches unpredictable sparks that move randomly until they hit an enemy or expire.Deals (1-104) to (28-1983) Lightning Damage
Base duration is 2 seconds
(0-19)% increased Projectile Speed
Fires (4-7) additional Projectiles

Additional Effects per 1% Quality:
1% increased Projectile Speed
Place into an item socket of the right colour to gain this skill. Right click to remove from a socket.
Spark skill icon.png
. 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.

Related items

Base items

The following base items are related to Luck:

ItemItem ClassRequired levelBuff Effects

Unique items

The following unique items are related to Luck:

ItemBase ItemRequired levelStats
The Tower of OrdealsThe Tower of Ordeals
Engraved Ultimatum
Map Level: 83
Map Tier: 16
<5-6 random Ultimatum modifiers>CorruptedOn the outskirts of Utzaal, at the Temple of Chaos,
the Trialmaster awaits your challenge.
Travel to this Map by using it in a personal Map Device. Maps can only be used once.
Engraved Ultimatum1
<5-6 random Ultimatum modifiers>
Escalating Monster Speed
Lessened Reach
Treacherous Auras
Buffs Expire Faster
Limited Flasks
Choking Miasma
Less Cooldown Recovery
Occasional Impotence
Totem of Costly Potency
Unlucky Criticals
Raging Dead
Blistering Cold
Restless Ground
Hindering Flasks
Stormcaller Runes
Siphoned Charges
Bonus Chaos Damage
Totem of Costly Might
Reduced Recovery
Ailment and Curse Reflection
Razor Dance
Escalating Damage Taken
Corrupted
Coward's ChainsCoward's Chains
Chain Belt
Requires Level 22+(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
As a gift or as punishment,
the Empire will have your blood.

This item can be transformed on the Altar of Sacrifice along with Vial of Consequence
Chain Belt22+(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
Relic of the PactRelic of the Pact
Spiraled Wand
Wand
Physical Damage: 12-37
Critical Strike Chance: 7.00%
Attacks per Second: 1.30
Weapon Range: 120
Requires Level 24, 83 Int(15-19)% increased Spell DamageGrants Level 1 Blood Sacrament Skill
Your Critical Strike Chance is Lucky while on Low Life
Crush your enemies with your essence, so that you may drink of theirs.
Spiraled Wand24(15-19)% increased Spell DamageGrants Level 1 Blood Sacrament Skill
Your Critical Strike Chance is Lucky while on Low Life
FoxshadeFoxshade
Wild Leather
Evasion: (382-520)
Movement Speed: -3%
Requires Level 25, 73 Dex+(20-30) to Dexterity
+1000 to Evasion Rating while on Full Life
(50-70)% increased Evasion Rating
30% increased Movement Speed when on Full Life
Damage of Enemies Hitting you is Unlucky while you are on Full Life
To catch an animal, think like an animal.
Wild Leather25+(20-30) to Dexterity
+1000 to Evasion Rating while on Full Life
(50-70)% increased Evasion Rating
30% increased Movement Speed when on Full Life
Damage of Enemies Hitting you is Unlucky while you are on Full Life
Perquil's ToePerquil's Toe
Gold Amulet
Requires Level 29(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
He was a lot luckier before he lost this.
Gold Amulet29(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
Lori's LanternLori's Lantern
Prismatic Ring
Requires Level 30+(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
By its light, Lori led her young charges to safety
and bound up their wounds.
Her sword arm was iron, yet her heart gentle
and proof against hate.
Prismatic Ring30+(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
HyperboreusHyperboreus
Leather Belt
Requires Level 53+(25-40) to maximum Life+(30-40)% to Cold Resistance
Chill nearby Enemies when you Focus, causing 30% reduced Action Speed
Focus has (30-50)% increased Cooldown Recovery Rate
(50-70)% increased Damage with Hits and Ailments against Chilled Enemies
Veiled Suffix
Cold winds whirl at the crown of the world.Take this item to Jun Ortoi to have her Unveil it.
Leather Belt53+(25-40) to maximum Life+(30-40)% to Cold Resistance
Chill nearby Enemies when you Focus, causing 30% reduced Action Speed
Focus has (30-50)% increased Cooldown Recovery Rate
(50-70)% increased Damage with Hits and Ailments against Chilled Enemies
Veiled Suffix
+(16-20)% to Cold and Chaos Resistances
+(31-35) to Dexterity and Intelligence
Regenerate 200 Energy Shield per second while a Rare or Unique Enemy is Nearby
+(16-20)% to Fire and Chaos Resistances
+(16-20)% to Lightning and Chaos Resistances
Your Critical Strike Chance is Lucky while Focused
Focus has (5-8)% increased Cooldown Recovery Rate
+(31-35) to Strength and Dexterity
+(31-35) to Strength and Intelligence
(14-16)% increased Trap Throwing Speed
The Iron FortressThe Iron Fortress
Crusader Plate
Armour: (1081-1382)
Movement Speed: -5%
Requires Level 59, 160 Str+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
"Stand steadfast in the face of destruction.
The Council cannot afford to falter."
- Mauritius, the Iron Heart
Crusader Plate59+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
The FulcrumThe Fulcrum
Ezomyte Staff
Warstaff
Physical Damage: (127.2-148.4) to (384-448)
Critical Strike Chance: 7.30%
Attacks per Second: 1.25
Weapon Range: 13
Requires Level 60, 113 Str, 113 Int+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
To stand at the confluence of the elements,
the master must achieve perfect balance.
Ezomyte Staff60+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
Triumvirate AuthorityTriumvirate Authority
Unset Ring
Requires Level 64Has 1 Socket+2 to Level of Socketed Vaal Gems
<Four random Socketed Vaal Skill modifiers>
The priest that carried Yaomac's sigil was granted one boon by each serpentine head.
Unset Ring64Has 1 Socket+2 to Level of Socketed Vaal Gems
<Four random Socketed Vaal Skill modifiers>
Socketed Vaal Skills have 60% increased Area of Effect
Socketed Vaal Skills have 50% increased Aura Effect
Socketed Vaal Skills deal 150% more Damage
Socketed Vaal Skills grant Elusive when Used
Hits from Socketed Vaal Skills ignore Enemy Monster Physical Damage Reduction
Hits from Socketed Vaal Skills ignore Enemy Monster Resistances
Damage with Hits from Socketed Vaal Skills is Lucky
Socketed Vaal Skills have 80% increased Projectile Speed
Socketed Vaal Skills have 80% increased Skill Effect Duration
Socketed Vaal Skills have 30% reduced Soul Gain Prevention Duration
Socketed Vaal Skills require 30% less Souls per Use
You have Tailwind if you've used a Socketed Vaal Skill Recently
Socketed Vaal Skills have 20% chance to regain consumed Souls when used
Triumvirate AuthorityTriumvirate Authority
Unset Ring
Requires Level 64Has 1 Socket+2 to Level of Socketed Vaal Gems
<Three random Socketed Vaal Skill modifiers>
The priest that carried Yaomac's sigil was granted one boon by each serpentine head.
Unset Ring64Has 1 Socket+2 to Level of Socketed Vaal Gems
<Three random Socketed Vaal Skill modifiers>
Socketed Vaal Skills have 60% increased Area of Effect
Socketed Vaal Skills have 50% increased Aura Effect
Socketed Vaal Skills deal 150% more Damage
Socketed Vaal Skills grant Elusive when Used
Hits from Socketed Vaal Skills ignore Enemy Monster Physical Damage Reduction
Hits from Socketed Vaal Skills ignore Enemy Monster Resistances
Damage with Hits from Socketed Vaal Skills is Lucky
Socketed Vaal Skills have 80% increased Projectile Speed
Socketed Vaal Skills have 80% increased Skill Effect Duration
Socketed Vaal Skills have 30% reduced Soul Gain Prevention Duration
Socketed Vaal Skills require 30% less Souls per Use
You have Tailwind if you've used a Socketed Vaal Skill Recently
Socketed Vaal Skills have 20% chance to regain consumed Souls when used
Viridi's VeilViridi's Veil
Praetor Crown
Armour: (354-481)
Energy Shield: (112-150)
Requires Level 68, 62 Str, 91 Int+(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
"Her sisters eternally fought for that shining apex in the skies, but Viridi instead found strength in humility."
- Azmerian Creation Myth
Praetor Crown68+(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

Related skill gems

The following skill gems are related to Luck:

GemStr.Dex.Int.Required level
Vaal GraceVaal GraceAura, Spell, AoE, Duration, Vaal
Level: (1-20)
Cooldown Time: 0.50 sec
Can Store 1 Use(s)
Souls Per Use: 50
Can Store 1 Use(s)
Soul Gain Prevention: 9 sec
Cast Time: Instant
AoE Radius: 36
Requires Level 24Casts a temporary aura that grants you and your allies additional chance to evade attacks, and makes suppressed spell damage unlucky against you.Base duration is 6 seconds
Modifiers to Buff Duration also apply to this Skill's Soul Gain Prevention
+(0-19) to radius
You and nearby allies have +15% chance to Evade Attack Hits
Suppressed Spell Damage dealt to you is Unlucky

Additional Effects per 1% Quality:
2% increased Area of Effect
CorruptedPlace into an item socket of the right colour to gain this skill. Right click to remove from a socket.
Vaal Grace skill icon.png
N/AyesN/A24
Vaal ArcVaal ArcSpell, Chaining, Vaal, Lightning, Duration
Level: (1-20)
Souls Per Use: 25
Can Store 1 Use(s)
Soul Gain Prevention: 2 sec
Cast Time: 0.70 sec
Critical Strike Chance: 5.00%
Effectiveness of Added Damage: 180%
Requires Level 12A shocking arc of lightning stretches from the caster to a targeted enemy and chains to other nearby enemies. Each time the beam chains it will also chain simultaneously to a second enemy, but no enemy can be hit twice by the beams. Also grants a buff making you lucky when damaging enemies with Arc for a short duration.Deals (38-924) to (64-1539) Lightning Damage
100% increased Duration of Lightning Ailments
Base duration is 4 seconds
100% chance to Shock enemies
Chains +(5-9) Times
15% more Damage for each remaining Chain
100% increased Effect of Lightning Ailments

Additional Effects per 1% Quality:
1.5% increased Duration of Lightning Ailments
CorruptedPlace into an item socket of the right colour to gain this skill. Right click to remove from a socket.
Vaal Arc skill icon.png
N/AN/Ayes12

Related passive skills

Passive skills

The following passive skills are related to Luck: No results found for the given query.

Keystone passive skills

The following keystone passive skills are related to Luck:

NameStats
Dance with Death
SharpandBrittle passive skill icon.png
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 [1]

Atlas passive skills

NameStats
Lucky Blight Chests
BlightNode1 (AtlasTrees) passive skill icon.png
Varieties of Items contained in 1 Blight Chest in Areas are Lucky [1] [2] [3]

Related modifiers

The following modifiers are related to Luck:

NameGeneration TypeFor generated item/monster modifiers the minimum item/monster level respectively. Some generation types may not require this condition to be met, however item level restrictions may be raised to 80% of this value.StatsSpawn Weighting
of the OrderSuffix72Your Critical Strike Chance is Lucky while Focusedbelt 0
of the OrderSuffix50Your Critical Strike Chance is Lucky while Focusedbelt 0
of the OrderSuffix60Your Critical Strike Chance is Lucky while Focused
Focus has (5-8)% increased Cooldown Recovery Rate
belt 1000
HellscapeDownsideDamageIsUnlucky1___Scourge Detriment45Damage with Hits is Unluckyamulet 500

References

  1. Mark_GGG (May 13, 2013 4:01 AM). "p/c new ring lori's lantern". Path of Exile Forum. Retrieved September 22, 2013.
  2. https://www.pathofexile.com/forum/view-thread/3108809/page/1#p24083466

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