Luck

Lucky crit rolls visualized in a tree diagram.

Luck is a mechanic that rolls an outcome or a number in a range twice, with Lucky rolls applying the best result, and Unlucky rolls applying the worst result.

Modifiers that specify Damage or when Damaging and luck refer specifically to damage ranges after any increased/more modifiers (or "tooltip damage range"), not to the base damage of the weapon/skill. These stats do not affect other mechanics like chance to hit/accuracy or critical strike chance. Additionally, these stats only apply to hit damage, and have no effect on the damage roll of damage over time from damaging ailments, which roll entirely independently of the hit damage's roll.

Lucky and Unlucky modifiers affecting the same stat or mechanic 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

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:

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}CritChance_{Lucky}=2\times CritChance_{Default}-{CritChance_{Default}}^{2}$

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

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}CritChance_{Lucky}=2\times 40\%-40\%^{2}=64\%$

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:

$$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}B=1-A$$

(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:

$$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}C=B\times A$$

(2)

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

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\begin{aligned}CritChance_{Lucky}&=A+C\\&=A+B\times A\\&=A+(1-A)\times A\\&=2\times A-A^{2}\end{aligned}}$

Damage in a Range

Given an integer roll between min and max, the normal expected value is $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {min+max}{2}}$.

A lucky roll has expected value $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {min}{3}}+{\frac {2*max}{3}}+{\frac {max-min}{6*(1+max-min)}}$.

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 $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {min+2*max}{3}}$.

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: (260-370)%
Projectile Speed: 1040
AoE Radius: 9Unleashes 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
Base radius is (0.9-1.4) metres

Additional Effects From 1-20% Quality:
Base radius is (0.01-0.2) metresPlace into an item socket of the right colour to gain this skill. Right click to remove from a socket.. 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: 420Launches unpredictable sparks that move randomly until they hit an enemy or expire.Deals (1-104) to (28-1983) Lightning Damage
Base duration is 2.00 seconds
Fires (4-8) Projectiles

Additional Effects From 1-20% Quality:
Fires +(0.1-2) ProjectilesPlace into an item socket of the right colour to gain this skill. Right click to remove from a socket.. 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

Unique items

The following unique items are related to Luck:

Item	Base Item		Stats
Coward's ChainsCoward's Chains Chain BeltRequires 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 VulnerabilityAs 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 Belt	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
FoxshadeFoxshade Wild LeatherEvasion: (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 LifeTo catch an animal, think like an animal.	Wild Leather	25	+(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 AmuletRequires 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 LuckyHe was a lot luckier before he lost this.	Gold Amulet	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
Lori's LanternLori's Lantern Prismatic RingRequires 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 LifeBy 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 Ring	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
Relic of the PactRelic of the Pact Sage WandWand Physical Damage: 18-34 Critical Strike Chance: 10.00% Attacks per Second: 1.40Requires Level 30, 119 Int(17-21)% increased Spell DamageGrants Level 1 Blood Sacrament Skill Your Critical Strike Chance is Lucky while on Low LifeCrush your enemies with your essence, so that you may drink of theirs.	Sage Wand	30	(17-21)% increased Spell DamageGrants Level 1 Blood Sacrament Skill Your Critical Strike Chance is Lucky while on Low Life
Bound FateBound Fate Cloth BeltRequires Level 49(15-25)% increased Stun and Block Recovery+(20-30) to Dexterity +(20-30) to Intelligence +(60-80) to maximum Life Every 5 seconds, gain one of the following for 5 seconds: Your Hits are always Critical Strikes Hits against you are always Critical Strikes Attacks cannot Hit you Attacks against you always Hit Your Damage with Hits is Lucky Damage of Hits against you is LuckyKnowing what will happen and knowing when it will happen are two very different things.	Cloth Belt	49	(15-25)% increased Stun and Block Recovery+(20-30) to Dexterity +(20-30) to Intelligence +(60-80) to maximum Life Every 5 seconds, gain one of the following for 5 seconds: Your Hits are always Critical Strikes Hits against you are always Critical Strikes Attacks cannot Hit you Attacks against you always Hit Your Damage with Hits is Lucky Damage of Hits against you is Lucky
SvalinnSvalinn Girded Tower ShieldChance to Block: 23% Armour: (397-437) Ward: (100-150) Movement Speed: -3%Requires Level 51, 123 Str+(10-20) to maximum Life(10-15)% Chance to Block Spell Damage +(100-150) to Ward -10% to maximum Chance to Block Attack Damage -10% to maximum Chance to Block Spell Damage Chance to Block is Lucky Trigger a Socketed Elemental Spell on Block, with a 0.25 second CooldownThe priests found the Great Shield the night it fell to Middengard, but it was the smiths who delved into the secrets it held.	Girded Tower Shield	51	+(10-20) to maximum Life(10-15)% Chance to Block Spell Damage +(100-150) to Ward -10% to maximum Chance to Block Attack Damage -10% to maximum Chance to Block Spell Damage Chance to Block is Lucky Trigger a Socketed Elemental Spell on Block, with a 0.25 second Cooldown
HyperboreusHyperboreus Leather BeltRequires 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 SuffixCold winds whirl at the crown of the world.Take this item to Jun Ortoi to have her Unveil it.	Leather Belt	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 +(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 PlateArmour: (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 Plate	59	+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 StaffWarstaff Physical Damage: (127.2-148.4) to (384-448) Critical Strike Chance: 8.50% Attacks per Second: 1.25 Weapon Range: 1.3 metresRequires Level 60, 113 Str, 113 Int+25% 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 IgnitedTo stand at the confluence of the elements, the master must achieve perfect balance.	Ezomyte Staff	60	+25% 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 RingRequires 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 Ring	64	Has 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 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 RingRequires 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 Ring	64	Has 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 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 CrownArmour: (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 Crown	68	+(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
Voice of the StormVoice of the Storm Lapis AmuletRequires Level 69+(20-30) to Intelligence50% increased Lightning Damage +(10-15) to all Attributes (10-20)% increased maximum Mana Lightning Damage with Non-Critical Strikes is LuckyWhen she of many mouths spoke, we bowed in awe and were crushed. This item can be transformed with a Blessing of Esh	Lapis Amulet	69	+(20-30) to Intelligence50% increased Lightning Damage +(10-15) to all Attributes (10-20)% increased maximum Mana Lightning Damage with Non-Critical Strikes is Lucky

Corpse items

Spectres raised from these corpse items have an ability or bonus related to Luck:

Item	Monster Category	Monster Abilities
Perfect Spirit of FortunePerfect Spirit of FortuneMonster Category: ConstructCasts Shock Nova Casts Spark Casts Lightning Warp Casts Wrath Lightning Damage of nearby allies is LuckyRight click this item to create this corpse.	Construct	Casts Shock Nova Casts Spark Casts Lightning Warp Casts Wrath Lightning Damage of nearby allies is Lucky

Miscellaneous

Item	Description
Sanctified FossilSanctified FossilStack Size: 10Numeric modifier values are lucky High Level modifiers are more commonPlace in a Resonator to influence item crafting.	Numeric modifier values are lucky High Level modifiers are more common

Related skill gems

The following skill gems are related to Luck:

Gem
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: 36Requires 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 6.00 seconds Modifiers to Buff Duration also apply to this Skill's Soul Gain Prevention +(0-1.9) metres to radius You and nearby allies have +15% chance to Evade Attack Hits Suppressed Spell Damage dealt to you is Unlucky Additional Effects From 1-20% Quality: (2-40)% increased Area of EffectCorruptedPlace into an item socket of the right colour to gain this skill. Right click to remove from a socket.	24	N/A		N/A
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: 6.00% Effectiveness of Added Damage: 220%Requires Level 12A shocking arc of lightning reaches from the caster to a targeted enemy and chains to other enemies. Each time the arc chains from an enemy, it will do so simultaneously to two further enemies, but never to enemies that have already been hit by any of these chains. Also grants a buff making your Arc damage lucky for a short duration.Deals (38-924) to (64-1539) Lightning Damage 100% increased Duration of Lightning Ailments Base duration is 4.00 seconds 100% chance to Shock enemies Chains +(5-9) Times 15% more Damage with Hits and Ailments for each remaining Chain 100% increased Effect of Lightning Ailments Additional Effects From 1-20% Quality: Chains +(0.05-1) TimesCorruptedPlace into an item socket of the right colour to gain this skill. Right click to remove from a socket.	12	N/A	N/A

Related passive skills

Passive skills

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

Ascendancy passive skills

The following Ascendancy passive skills are related to Luck:

Ascendancy Class	Name	Stats
Gladiator	More Than Skill	Chance to Block Attack or Spell Damage is Lucky if you've Blocked Recently [1]

Keystone passive skills

The following keystone passive skills are related to Luck:

Name	Stats
Dance with Death	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

Name	Stats
Blight Chest Chance and Lucky Chests	Varieties of Items contained in 1 Blight Chest in your Maps are Lucky Lanes of Blight Encounters in your Maps have 5% chance for an additional Reward Chest [1]
Lucky Blight Chests	8% chance for Blight Chests to contain an additional Reward Varieties of Items contained in 1 Blight Chest in your Maps are Lucky [1] [2]
Epidemiology	Varieties of Items contained in 3 Blight Chests in your Maps are Lucky Blight chests in your Maps have a 20% chance to be openable again [1]

Related modifiers

The following modifiers are related to Luck:

Name	Generation Type		Stats	Spawn Weighting
of the Order	Suffix	72	Your Critical Strike Chance is Lucky while Focused	belt 0
of the Order	Suffix	50	Your Critical Strike Chance is Lucky while Focused	belt 0
of the Order	Suffix	60	Your Critical Strike Chance is Lucky while Focused Focus has (5-8)% increased Cooldown Recovery Rate	belt 1000
HellscapeDownsideDamageIsUnlucky1___	Scourge Detriment	45	Damage with Hits is Unlucky	amulet 500
VillageChaosDamageLuck	Intrinsic	1	Chaos Damage with Hits is Lucky	N/A

Mastery Effects

Mastery	Effects
Lightning Mastery	Lightning Damage of Enemies Hitting you while you're Shocked is Unlucky
Spell Suppression Mastery	Chance to Suppress Spell Damage is Lucky