Skill Gem /1
Name
Vaal Grace
Item mods /1
NameLevelPre/SufDescriptionWeight
45ScourgeDownsideDamage with Hits is Unluckyamulet 500
default 0
Veiled mods /1
NameLevelPre/SufDescriptionWeight
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
ModRequireItemClassesUnlock
Your Critical Strike Chance is Lucky while Focused
grant focus skill [1]		9x Orb of AlterationBeltBetrayal Unveil
Misc mods /3
NameLevelDomainPre/SufDescriptionWeight
1MapDeviceUniqueVarieties of Items contained in 5 Blight Chests are Lucky
6% increased Pack size
1MapDeviceUniqueVarieties of Items contained in 12 Blight Chests are Lucky
6% increased Pack size
1MapDeviceUniqueVarieties of Items contained in 18 Blight Chests are Lucky
6% increased Pack size
Item /1
Sanctified Fossil
Stack Size: 1 / 10
Numeric modifier values are lucky
High Level modifiers are more common
Unique /14
+(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)
+(20–30) to Dexterity
(50–70)% increased Evasion Rating
+1000 to Evasion Rating while on Full Life
30% increased Movement Speed when on Full Life
Damage of Enemies Hitting you is Unlucky while you are on Full Life
(Unlucky things are rolled twice and the worst result used)
+(20–30) to Intelligence
+(10–15) to all Attributes
50% increased Lightning Damage
(10–20)% increased maximum Mana
Lightning Damage with Non-Critical Strikes is Lucky
(Attributes are Strength, Dexterity, and Intelligence)
+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)
+(20–30) to Dexterity
Adds 5 to 12 Physical Damage to Attacks
+(400–500) to Evasion Rating
(120–150)% increased Evasion Rating
+1500 to Evasion Rating while on Full Life
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)
+(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
(Attributes are Strength, Dexterity, and Intelligence)
(Unlucky things are rolled twice and the worst result used)
(Vulnerability is a Hex which increases Physical Damage taken by 15% and causes Hits to have +25% chance to inflict Bleeding on the target. It lasts 8 seconds)
+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)
(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)
+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
Damage Penetrates (8–10)% Elemental Resistances while you are Chilled
Elemental Damage with Hits is Lucky while you are Shocked
Gain (30–40)% of Physical Damage as Extra Damage of a random Element while you are Ignited
+(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)
(17–21)% 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)
(11–15)% 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)
(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
+(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
shield trigger a socketed skill on block [1]
(Maximum Chance to Block Attack Damage cannot be raised above 90%)
(Maximum Chance to Block Spell Damage cannot be raised above 90%)
(Lucky things are rolled twice and the best result used)
Passive /1
Mastery: Blight
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
Ascendancy Passive /1
Ascendancy: Gladiator
Character: Duelist
Chance to Block Attack or Spell Damage is Lucky if you've Blocked Recently
(Lucky things are rolled twice and the best result used)
(Recently refers to the past 4 seconds)
Cluster Jewel Passive /1
Lightning Damage with Non-Critical Strikes is Lucky
Timeless Jewel Passive /1
FactionCategoryNameShow Full Descriptions
MarakethKeystoneDance 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(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

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 accuracy 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 Fireball. 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 Spark. 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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