Luck

Lucky crit rolls visualized in a tree diagram.

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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 hit 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.

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.

A binary roll applies to something with only two choices such as chance of hitting, critical strikes, or chance of blocking. The Lucky or Unlucky chance can be calculated from your original chance with the following formulas:

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

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}Unlucky={Chance}^{2}$

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

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}Lucky=2\times 0.4-0.4^{2}=0.8-0.16=0.64$

So a crit chance of 40% will give a lucky crit chance of 64%.

Lucky/unlucky effect on binary rolls

Original chance	Lucky chance	Unlucky chance
10%	19%	1%
25%	43.75%	6.25%
50%	75%	25%
75%	93.75%	56.25%
90%	99%	81%

Note that if a roll has 0% of 100% chance, lucky and unlucky will have no effect.

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 Frost BombFrost BombSpell, AoE, Cold, Duration, Orb, Remnant
Tier: 1
Level: (1-20)
Cost: (9-99) Mana
Cooldown Time: 6.00 sec
Can Store 1 Use(s)
Cast Time: 0.80 sec
Critical Strike Chance: 13.00%Create a pulsing Orb of frost. Each pulse inflicts Elemental Exposure on nearby enemies. When the Orb's duration ends, it Detonates, dealing Cold damage to surrounding enemies and leaving behind a Cold Infusion.Deals (7-238) to (11-358) Cold Damage
Detonation Time is 4 seconds
Chills Enemies as though dealing 300% more damage
Initially applies 20% Elemental Exposure and 2% Exposure per pulse, up to a maximum of 50%
Pulse and explosion radius are (2.4-3.1) metres
Limit 1 Frost Bomb
Exposure duration is 8 seconds

Additional Effects From 1-20% Quality:
+(0.5-10)% maximum Elemental Exposure appliedSkills can be managed in the Skills Panel.. The minimum damage is 578, and the maximum damage is 867, for an average of 722.5. The difference between minimum and maximum is 289. If the damage is lucky, you get an average 289/6=48.1 extra damage, for a new average damage of 722.5+48.1=770.6 damage. This is a 6.6% damage boost.

Example 2: You cast a level 20 SparkSparkSpell, Projectile, Lightning, Duration
Tier: 1
Level: (1-20)
Cost: (5-56) Mana
Cast Time: 0.70 sec
Critical Strike Chance: 9.00%Launch a spray of sparking Projectiles that travel erratically along the ground until they hit an enemy or expire. Consumes a Cold Infusion if possible to fire many sparks in a circle.Base
Deals (1-11) to (10-216) Lightning Damage
Fires (4-9) Projectiles
Projectile duration is 2 seconds
Projectiles fired at the same time can Hit the same
target no more than once every 0.66 seconds

Cold-Infused
Critical Hit Chance: 11.00%
Deals (7–182) to (11–273) Cold Damage
Deals (1–11) to (10–216) Lightning Damage
Projectile duration is 2 seconds
Fires (12–16) Projectiles in a circle
+0.5 seconds to Cast Time
Projectiles fired at the same time can Hit the same
target no more than once every 0.66 seconds

Additional Effects From 1-20% Quality:
(1.5-30)% increased Projectile SpeedSkills can be managed in the Skills Panel.. 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.

Effectiveness

With percentage rolls, such as critical hit 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/less, when the minimum damage is close to zero, but will have a much weaker effect when the minimum damage is close to the maximum.

Related items

Unique items

The following unique items are related to Luck:

Item	Base item		Stats
Freedom of FaithFreedom of Faith Ritual Precursor TabletAdds Ritual Altars to a Map 5 uses remainingFavours at Ritual Altars in Area costs (10-15)% increased Tribute Can Reroll Favours at Ritual Altars in your Maps twice as many timesWhen darkness comes, we pray for light. When darkness is all that there is, we pray for death.Can be used in a personal Map Device to add modifiers to a Map.	Ritual Precursor Tablet	1	Adds Ritual Altars to a Map 5 uses remainingFavours at Ritual Altars in Area costs (10-15)% increased Tribute Can Reroll Favours at Ritual Altars in your Maps twice as many times
Heart of the WellHeart of the Well DiamondLimited to: 1<Custom Desecrated prefix> <Custom Desecrated prefix> <Custom Desecrated suffix> <Custom Desecrated suffix> <List of mods>Countless souls scream in agonising harmony, forever sinking under the weight of the newly dead.Place into an allocated Jewel Socket on the Passive Skill Tree. Right click to remove from the Socket.	Diamond	1	<Custom Desecrated prefix> <Custom Desecrated prefix> <Custom Desecrated suffix> <Custom Desecrated suffix> <List of mods> (5-10)% chance to Aggravate Bleeding on targets you Hit with Attacks (5-8)% increased Attack Speed while a Rare or Unique Enemy is in your Presence (40-60)% increased Armour from Equipped Body Armour (30-50)% chance to Pierce an Enemy (10-15)% chance when a Charm is used to use another Charm without consuming Charges Charms applied to you have (15-25)% increased Effect Recover (5-10)% of maximum Mana when a Charm is used (15-25)% increased Culling Strike Threshold Gain (9-15)% of Damage as Extra Lightning Damage Gain (7-13)% of Damage as Extra Chaos Damage Gain (9-15)% of Damage as Extra Fire Damage Gain (9-15)% of Damage as Extra Cold Damage (15-25)% increased Damage while your Companion is in your Presence (15-25)% increased Exposure Effect (40-60)% increased Evasion Rating from Equipped Body Armour Regenerate (1-1.5)% of maximum Life per Second if you've used a Life Flask in the past 10 seconds (10-18)% increased Cooldown Recovery Rate (40-60)% increased Ice Crystal Life (4-8)% increased Skill Speed (15-25)% chance for Lightning Damage with Hits to be Lucky (8-16)% increased Mana Cost Efficiency (20-30)% increased Mana Regeneration Rate while moving +1% to all Maximum Elemental Resistances (40-60)% increased Energy Shield from Equipped Body Armour Minions gain (10-15)% of their maximum Life as Extra maximum Energy Shield Minions Regenerate (1-3)% of maximum Life per second Minions Revive (5-10)% faster (8-15)% of Leech is Instant (5-10)% of Physical Damage prevented Recouped as Life (8-14)% increased speed of Recoup Effects Recover (2-4)% of maximum Life on Killing a Poisoned Enemy (10-15)% increased Skill Effect Duration +(2-4)% to Thorns Critical Hit Chance Gain Physical Thorns damage equal to (4-6)% of Item Armour on Equipped Body Armour (6-12)% chance for Trigger skills to refund half of Energy Spent (4-8)% increased chance to inflict Ailments Gain additional Ailment Threshold equal to (4-10)% of maximum Energy Shield (5-10)% chance to inflict Bleeding on Hit (5-10)% chance to Poison on Hit (4-8)% increased Critical Hit Chance (6-12)% increased Critical Damage Bonus (2-3)% of Damage is taken from Mana before Life Debuffs on you expire (4-8)% faster Damaging Ailments deal damage (2-4)% faster (4-8)% increased Flask Effect Duration Gain (1-2) Rage when Hit by an Enemy (2-3)% increased Cooldown Recovery Rate (6-12)% increased Elemental Ailment Threshold (2-3)% increased Attack Speed (2-3)% increased Cast Speed (4-8)% increased Flask Charges gained (5-10)% increased Stun Threshold (2-3)% of Skill Mana Costs Converted to Life Costs (2-3)% of Damage taken Recouped as Life (6-12)% increased Life Regeneration rate Recover (1-2)% of maximum Mana on Kill (4-8)% increased Mana Regeneration Rate +1% to Maximum Cold Resistance +1% to Maximum Fire Resistance Recover (1-2)% of maximum Life on Kill +1% to Maximum Lightning Resistance Minions have (2-3)% increased Attack and Cast Speed Minions have (6-12)% increased Critical Hit Chance Minions have +(3-4)% to all Elemental Resistances Minions have (3-12)% additional Physical Damage Reduction (1-2)% increased Movement Speed Gain 1 Rage on Melee Hit (3-8)% increased Skill Effect Duration (10-5)% reduced Slowing Potency of Debuffs on You (4-8)% increased Critical Hit Chance for Spells (6-12)% increased Critical Spell Damage Bonus (6-12)% increased Stun Buildup Gain additional Stun Threshold equal to (4-10)% of maximum Energy Shield
The Barrow DwellerThe Barrow Dweller Rogue ArmourArmour: (84-106) Evasion: (68-86) Movement Speed: -4.0%Requires Level 11, 13 Str, 13 Dex(60-100)% increased Armour and Evasion -(20-10)% to Fire Resistance +50% to Cold Resistance Damage of Enemies Hitting you is Unlucky while you are on Low Life 50% chance to Avoid Death from HitsIn the mists they dwell, forever hungry, forever cold.	Rogue Armour	11	(60-100)% increased Armour and Evasion -(20-10)% to Fire Resistance +50% to Cold Resistance Damage of Enemies Hitting you is Unlucky while you are on Low Life 50% chance to Avoid Death from Hits
The BurrowerThe Burrower Topaz RingRequires Level 16+(20-30)% to Lightning Resistance-10% to Cold Resistance +(20-30)% to Lightning Resistance (30-50)% increased Mana Regeneration Rate Lightning Damage of Enemies Hitting you is UnluckyIt coils deeper and deeper It slithers between thoughts It lies beneath the valley It lies in our minds	Topaz Ring	16	+(20-30)% to Lightning Resistance-10% to Cold Resistance +(20-30)% to Lightning Resistance (30-50)% increased Mana Regeneration Rate Lightning Damage of Enemies Hitting you is Unlucky
The Black CatThe Black Cat Grounding CharmLasts 3.00 Seconds Consumes 30 of 40 Charges on use Immune to ShockRequires Level 32Used when you become Shocked(10-20)% increased Duration Lightning Damage of Enemies Hitting you is Unlucky during effectThe most beloved member of every Brinerot crew is the one that refuses to do any actual work.Used automatically when condition is met. Can only hold charges while in belt. Refill at Wells or by killing monsters.	Grounding Charm	32	Used when you become Shocked(10-20)% increased Duration Lightning Damage of Enemies Hitting you is Unlucky during effect
SvalinnSvalinn Crucible Tower ShieldShield Chance to Block: 26% Armour: (330-440) Movement Speed: -3.0%Requires Level 60, 64 StrGrants Skill: Raise Shield Grants Skill: Cast on Block(200-300)% increased Armour Chance to Block Damage is Lucky You take (0-20)% of damage from Blocked HitsThe priests found the Great Shield the night it fell to Middengard, but it was the smiths who delved into the secrets it held.	Crucible Tower Shield	60	(200-300)% increased Armour Chance to Block Damage is Lucky You take (0-20)% of damage from Blocked Hits

Related passive skills

Passive skills

The following passive skills are related to Luck:

Name	Stats
Lightning Rod File:LightningDamagenode passive skill icon.png	30% chance for Lightning Damage with Hits to be Lucky [1]
Perfect Opportunity File:Stunstr passive skill icon.png	30% increased Stun Buildup Damage with Hits is Lucky against Heavy Stunned Enemies [1]
Stars Aligned	Damage with Hits is Lucky against Enemies that are on Low Life [1]
The Spring Hare File:AzmeriSacredRabbitNotable passive skill icon.png	20% chance for Damage with Hits to be Lucky 20% chance for Damage of Enemies Hitting you to be Unlucky [1]

Ascendancy passive skills

The following Ascendancy passive skills are related to Luck:

Ascendancy Class	Name	Stats
Oracle File:Oracle avatar.png	The Lesser Harm	Damage of Enemies Hitting you is Unlucky Enemy Critical Hit Chance against you is Unlucky [1]

Keystone passive skills

The following keystone passive skills are related to Luck:

Name	Stats
Glancing Blows	Chance to Evade is Unlucky Chance to Deflect is Lucky [1]

Related modifiers

The following modifiers are related to Luck: No results found