PoE 2: Lucky Explained

Luck is a mechanic in Path of Exile 2 that causes a roll range or chance based modifier to be rolled twice.

What is Luck?

Luck can apply to stats that roll within a range such as Damage, or stats that are chance based binary rolls, such as Critical Hits or Blocking.

• Lucky modifiers will roll an outcome twice, choosing the best outcome
• Unlucky modifiers will roll an outcome twice, choosing the worst outcome

Note: when Lucky and Unlucky modifiers apply to the same roll, they will cancel each other out resulting in a normal roll.

Damage Rolls

When Lucky or Unlucky modifiers are applied to a roll range such as Damage, the range is rolled twice, choosing the best or worst outcome depending on the type of modifier.

An average expected normal Damage roll can be calculated:

(minimum Damage + maximum Damage) / 2

When a Lucky modifier is applied, the average expected Damage can be calculated:

(minimum Damage + 2 * maximum Damage) / 3

When an Unlucky modifier is applied, the average expected Damage can be calculated:

(2 * minimum Damage + maximum Damage) / 3

The effective Damage increase or reduction as a result of Lucky or Unlucky Damage is a sixth of the Damage range. Lucky can provide up to the equivalent of 33% more Damage when the minimum Damage in a range reaches 0, scaling down to 0% when the minimum Damage becomes equal to the maximum Damage.

For this reason, Lucky Damage modifiers are much more effective when applied to wide Damage ranges, such as natural Lightning Damage, whilst Unlucky Damage modifiers are less detrimental when the Damage range is smaller.

Binary Chance Rolls

For chance based stats such as Chance to Block, the outcome is rolled twice, choosing the more favourable or less favourable outcome depending on the modifier.

The effective chance with a Lucky modifier can be calculated:

2 * Chance - Chance²

The effective chance with an Unlucky modifier can be calculated:

Chance²

The table below shows example effects of Lucky and Unlucky modifiers on binary chance rolls.

Note: Lucky and Unlucky modifiers will have no effect on a binary chance roll that is already confirmed to succeed or fail, for example with a 0% or 100% roll.