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Loot is rolled when you open the container or kill the mob.

Whoever opens a container first or deals the killing blow to a monster is the person whose luck is used to calculate the drops.

Any individual point of Luck contributes to a change in drop chances. However, luck is hard capped to 500; any points beyond 500 won't make a difference.

Ideal Sources of Luck:

Loot Tables and Drop Rate Tables

Each drop instance makes use of three pieces of information: the Loot table, the Drop Rate table, and the player's Luck.

Loot tables list all possible items for a specific drop instance, and for each item therein it associates a Luck Grade.
Drop Rate tables assign a "rate" to each Luck Grade; when normalized, these rates represent the probability of getting a drop of that Luck Grade.

Each Luck Grade's drop rate is split evenly between items that share that Luck Grade. This means that items sharing a Loot Table and Luck Grade, will always have the same probability of dropping.
However, be aware that Monsters and Containers can have multiple Loot Tables, each with their own Drop Rate table. See Lich for example.

A Drop can be rolled more than once, but each roll is independent of the others.
The Elite variant of Lich rolls their main gear Loot and Drop tables a total of 3 times, theoretically making it possible (though extremely unlikely) to get 3 identical Artifacts from a single Elite Lich kill.

Luck Scalar

Luck Scalars are but one piece of information needed to calculate drop probability at X Luck.

The calculation is not a simple multiplication, so do not expect Uniques to be 4.382 times more common at 500 Luck.

The true effect of Luck varies depending on Drop Rate tables. See the Luck subsection Probabilities from Luck for an in-depth explanation of how Luck Scalars affect probabilities of drops.

Additionally, luck works with a hidden property called Luck Grade. Many loot tables will match item rarity one to one with item luck grade, but there are exceptions, see the Cave Troll's quest drops for a counterexample.

Luck Scalar Graphs

Updated for Patch:6.8#Patch 8!

LaTeX Formula


If the Luck Scalar Graph doesn't cover a Scalar value you wish to see please reference the desmos graph.
The desmos graph displays the LaTeX equations.

Probabilities from Luck

To calculate the drop rate at X Luck there are three steps.

  1. For each Luck Grade's Drop Rate apply the corresponding Luck Scalar.
  2. Find the dot product between the Luck Scalar vector at X Luck and the Base Rate.
    (This is the same as adding up each term from the first step.)
  3. For each term in the first step divide by the dot product from the second step to get the new drop rate at X Luck.

Example last updated on Patch:6.5#Hotfix 53. Figures may be outdated, but the math and concepts remain the same.

The table below is the Drop Rate table of Quest Drops.

Luck Grade Drop Rate
0 220
1 250
2 200
3 150
4 100
5 50
6 20
7 10
8 0

Every monster with a quest drop uses this Drop Rate table, however, depending on the monster's Loot Table, most of the Luck Grades will be associated with dropping nothing.
And in other instances, like Dire Wolf, a Luck Grade's rate may be split between two or more Loot drops.
This will not affect the calculations below, but they will determine an individual item's probability.


Click expand to see the calculations for 0 and 250 Luck.


Using the Luck Scalars at 500 Luck, the dot product is

Luck Grade Drop Probability at 500 Luck
0
1
2
3
4
5
6
7
8

It's worth noting that you can calculate probability at X Luck from either the Drop Rate table or the Drop Probability at 0 Luck table.
Using the Drop Probability at 0 Luck table works because the Luck Scalars are all 1 and you have to normalize regardless of using the Drop Rate or the Probability at 0 Luck.

The wiki does not display the Drop Rate tables themselves, however it does show the alternative.

How to Use Wiki Tables and Graphs

On loose loot, monster, and prop pages the wiki displays graphs and tables showcasing the effect of luck on specific luck grades and loot tables.
The meaning of these graphs can be obtuse so we will walk through an example using the graphs and (partial) tables of the Inferno Treasure Hoard.

The following tables for illustrative purposes only. They are not updated to match the current patch so only use them for learning purposes. The concepts remain the same.

Graphs

For each luck value "X" the graph displays the ratio between the probability of a specific luck grade at X luck over the probability of that same luck grade at 0 luck.
Not only does this visualize the effect luck has on probabilities, these ratios can be used to calculate probabilities of specific items and luck grades.

To see how probabilities at X luck are calculated see the following section: Probabilities from Luck.

Note that you can choose which luck grades are displayed by toggling the luck grade in the legend. Simply click on them to disable and enable the luck grade curve.

Tables

Loot Summaries

Loot Summaries present basic sums of probabilities in loot table grouped by rarities and item types.
They ignore properties like luck grades, however, so beware that you cannot always use the ratios in the luck effect graph to get specific probabilities for a rarity/type.

In the case of the TreasureHoardHR3, however, rarity matches luck grade one to one, so we can go between luck 0 summaries and luck 150 summaries simply by applying the proper ratios.
Applying the ratio for luck 150 to the legend rarity we get: , which matches the tables below.

Loot Summary at 0 Luck
Type
Rarity
Misc
100%
Common
15%		15.0%
Uncommon
20.5%		20.5%
Rare
45%		45.0%
Epic
17%		17.0%
Legend
2.5%		2.5%
Loot Summary at 150 Luck
Type
Rarity
Misc
100%
Common
7.48%		7.4821%
Uncommon
11.05%		11.0546%
Rare
55.25%		55.254%
Epic
22.62%		22.6247%
Legend
3.58%		3.5846%

Loot Table

Loot Tables are sorted alphanumerically by item name.
These tables only display items that can drop, they won't display entries for dropping nothing.
In cases where a table can drop nothing it is best to look at the luck effect graph and loot summary to see if there are any "nothing" drops.

Loot TableCollapse
NameTypeLuck GradeLuck Grades present on the graph but missing in the column below are associated with dropping nothing.RarityItem CountProbability
Ancient Scroll
Ancient Scroll
Misc2Common10.5%
Misc3Uncommon10.6833%
Misc4Rare11.5%
Misc5Epic10.5667%
Misc6Legendary10.0833%
Blue Sapphire
Blue Sapphire
Misc2Common10.5%
Misc3Uncommon10.6833%
Misc4Rare11.5%
Misc5Epic10.5667%
Misc6Legendary10.0833%
Ceremonial Dagger
Ceremonial Dagger
Misc2Common10.5%
Misc3Uncommon10.6833%
Misc4Rare11.5%
Misc5Epic10.5667%
Misc6Legendary10.0833%
Diamond
Diamond
Misc2Common10.5%
Misc3Uncommon10.6833%
Misc4Rare11.5%
Misc5Epic10.5667%
Misc6Legendary10.0833%
...

Drop Source Table

Drop Source Tables are displayed on item pages. The drop source table for Viola is shown below.

If an item has any drop source from loose loot, monsters, or props, the table will show them, otherwise it will instead say that nothing drops that item.
The table rows are sorted by total expected value per source, i.e. the sum of count * probability * loot table rolls for each source's subrow.

Drop source table at 0 luckCollapse
NameSorted by total expected value in descending order
TEV = Sum of all (Probability of 1 drop * Item count per roll * Roll count)		TypeItem countProbability of 1+ drops per instance1-(1-probability per roll)(loot table roll count)

Some loot tables are rolled multiple times per instance (i.e. monster kill/container interaction/loose loot generation).

For further information, please reference the loot tables on the associated source page.
Frost Wyvern.png
Frost Wyvern#Elite
Monster1-30.2498%
Weapon FrozenRoom.png
Weapon FrozenRoom
Loose Loot10.0714%
DualBossWeapon.png
DualBossWeapon-Global#HR
Loose Loot10.0038%

Example: Royal Diamond at 150 Luck

Suppose we are interested in the Royal Diamond and we want to calculate the probability for 150 luck.
We only need three pieces of information to calculate this: the luck grade, the probability at luck 0, and the probability ratio at luck 150.

First, we find the luck grade of the Royal Diamond: 6.
Next, since the loot table presents probabilities at luck 0, we simply look up the probability for the Royal Diamond: 0.0833%.
And lastly, we look at the graph for luck grade 6 at luck 150: 1.43386.

Combining all of this, we find that the probability of the Royal Diamond at 150 luck becomes

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