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Loot is rolled when you open the container or kill the mob.
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.<br>
Whoever opens a container first or deals the killing blow to a monster is the person whose luck is used to calculate the drops.
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)


Luck is capped at 500.<br>
Any individual point of Luck contributes to a change in drop chances.
It is possible to reach the Luck cap:
*50 from [[Bard#Perks-0|Bard's Wanderer's Luck]]
*150 luck roll from a large [[Potion of Luck]]
*10 from craftable [[Hands#Craftable_Hands_Armors-0|golden hands]] armor piece
*40 from [[Golden Cloak]]
*275 from [[Enchantments#Table_of_Enchantment_Values|max enchantment rolls]] ''on other gear''


==Loot Drop Tables and Drop Rate Tables==
Ideal Sources of Luck:
*40 from max level religion blessing
*50 from Bard's [[File:Perk Wanderers Luck.png|link=|x40px|middle]][[Bard#Perks-0|Wanderer's Luck]].
*150 luck roll from a [[File:Great Potion of Luck.png|link=|x40px|middle]][[Great Potion of Luck]]
*10 from craftable [[File:Golden Gloves.png|link=|x40px|middle]][[Golden Gloves]] armor piece
*40 from [[File:Golden Cloak.png|link=|x40px|middle]][[Golden Cloak]] (Better than max roll of 25 Luck on normal cloaks)
*250 from [[Enchantments#Table_of_Enchantment_Values|max enchantment rolls]] ''on other gear''
**50 each on Chest, Legs, Necklace
**25 each on Head, Foot, Ring (x2)


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


Loot Drop tables list all possible items for a specific drop instance, and for each item therein it associates a Luck Grade.<br>
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.<br>
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.
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 Drop table and Luck Grade, will always have the same probability of dropping.<br>
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.<br>
However, be aware that Monsters and Containers can have multiple Loot Drop Tables, each with their own Drop Rate table.  See [[Lich#Loot_Tables|Lich]] for example.
However, be aware that Monsters and Containers can have multiple Loot Tables, each with their own Drop Rate table.  See [[Lich#Loot_Tables|Lich]] for example.


A Drop can be rolled more than once, but each roll is independent of the others.<br>
A Drop can be rolled more than once, but each roll is independent of the others.<br>
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==Luck Scalar==
==Luck Scalar==
[[Luck#Luck_Scalar|Luck Scalars]] are one piece of information needed to calculate drop probability at X Luck.<br>
[[Luck#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.<br>
 
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.
The true effect of Luck varies depending on Drop Rate tables.
See the [[Luck#Probabilities_from_Luck|Luck/Probabilities from Luck]] subsection for an in-depth explanation of how [[Luck#Luck_Scalar|Luck Scalars]] affect probabilities of drops.
See the Luck subsection [[Luck#Probabilities_from_Luck|Probabilities from Luck]] for an in-depth explanation of how [[Luck#Luck_Scalar|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#Loot_Tables|Cave Troll's quest drops]] for a counterexample.


<div style="display:inline-block; width:740px; vertical-align:top;">
<!--<div style="display:inline-block; width:740px; vertical-align:top;">
'''Luck Scalar Table'''
'''Luck Scalar Table'''
{| cellspacing="0" style="text-align:center; text-shadow:0px 0px 4px #000; border:1px solid #FFF9; border-collapse:collapse;"
{| cellspacing="0" style="text-align:center; text-shadow:0px 0px 4px #000; border:1px solid #FFF9; border-collapse:collapse;"
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|- class="colorrarity7"
|- class="colorrarity7"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 8 || 1.000 || 1.642 || 2.216 || 2.723 || 3.163 || 3.535 || 3.839 || 4.076 || 4.245 || 4.347 || 4.382
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 8 || 1.000 || 1.642 || 2.216 || 2.723 || 3.163 || 3.535 || 3.839 || 4.076 || 4.245 || 4.347 || 4.382
|}
|}</div>--><div style="display:inline-block; margin:25px 20px 0px 0px;">
 
'''Luck Scalar Graphs'''
If the Luck Scalar Table and Graph don't cover a Scalar value you wish to see, use the [https://www.desmos.com/calculator/rvig6eeqeb desmos graph].
Updated for {{#explode:{{:TODO|Stats}}|$|0}}! The domain has been adjusted from 0-500 to 0-5000 to better reflect user-collected findings.<tabber>
The desmos graph displays the LaTeX equations which are continuous curves, but keep in mind that fractional values of Luck do not exist.
</div><div style="display:inline-block; width:500px; height:410px; border-left:20px solid #0000;">
'''Luck Scalar Graph'''<tabber>
|-|0={{Stats_Data|luckgrade00}}
|-|0={{Stats_Data|luckgrade00}}
|-|1={{Stats_Data|luckgrade01}}
|-|1={{Stats_Data|luckgrade01}}
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|-|8={{Stats_Data|luckgrade08}}
|-|8={{Stats_Data|luckgrade08}}
</tabber>
</tabber>
If the Luck Scalar Graph doesn't cover a Scalar value you wish to see please reference the [https://www.desmos.com/calculator/rvig6eeqeb desmos graph].<br>
The desmos graph displays the LaTeX equations.
</div>
</div>


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<tabber>
<tabber>
|-|Quest Drop Example=
|-|Quest Drop Example=
<b style="font-size:18px">Example last updated on [[Patch:6.5#Hotfix 53]].  Figures may be outdated, but the math and concepts remain the same.</b>
The table below is the Drop Rate table of Quest Drops.
The table below is the Drop Rate table of Quest Drops.
Every monster with a quest drop uses this Drop Rate table, however, depending on the monster's Loot Drop Table, most of the Luck Grades will be associated with dropping nothing.<br>
And in other instances, like [[Dire_Wolf#Loot_Tables|Dire Wolf]], a Luck Grade's rate may be split between two or more Loot Drops.<br>
This will not affect the calculations below, but they will determine an individual item's probability.


{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
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| style="background-color:#FFF4;" | <span class="colorrarity7">8</span> ||<span class="colorrarity7">0</span>
| style="background-color:#FFF4;" | <span class="colorrarity7">8</span> ||<span class="colorrarity7">0</span>
|}
|}
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.<br>
And in other instances, like [[Dire_Wolf#Loot_Tables|Dire Wolf]], a Luck Grade's rate may be split between two or more Loot drops.<br>
This will not affect the calculations below, but they will determine an individual item's probability.
<br>
<br>
<p style="font-size:18px; width:fit-content; border:1px solid #DD952A; border-radius:15px; padding:7px;">Click expand to see the calculations for 0 and 250 Luck.<p>
<p style="font-size:18px; width:fit-content; border:1px solid #DD952A; border-radius:15px; padding:7px;">Click expand to see the calculations for 0 and 250 Luck.<p>
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|-|Gold Coin Chest Example=
|-|Gold Coin Chest Example=
<b style="font-size:18px">Example last updated on [[Patch:6.5#Hotfix 53]].  Figures may be outdated, but the math and concepts remain the same.</b>


The table below is the Drop Rate table of the Gold Coin Chest.
The table below is the Drop Rate table of the Gold Coin Chest.
The Loot Drop table is rather simple. At Luck Grade 0, "0", you get nothing.  At Luck Grade 2, "2", you get 1x Gold Coin Chest.
Notice that despite the [[Gold Coin Chest]]'s item rarity being 7, its Luck Grade is actually 2.<br>
Item Rarity does not equal Luck Grade, despite the two being equal for most items.
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|- style="background-color:#FFF4;"
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| style="background-color:#FFF4;" | <span class="colorrarity7">8</span> ||<span class="colorrarity7">0</span>
| style="background-color:#FFF4;" | <span class="colorrarity7">8</span> ||<span class="colorrarity7">0</span>
|}
|}
The Loot Table for the Gold Coin Chest is rather simple. At Luck Grade 0 you get nothing.  At Luck Grade 2 you get 1 Gold Coin Chest.
Notice that despite the [[Gold Coin Chest]]'s item rarity being 7, its Luck Grade is actually 2.<br>
Despite the being equal for most items, Item Rarity does not equal Luck Grade.


<br>
<br>
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| style="background-color:#FFF4;" | <span class="colorrarity7">8</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
| style="background-color:#FFF4;" | <span class="colorrarity7">8</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|}
|}
</tabber>
</tabber>


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The wiki does not display the Drop Rate tables themselves, however it does show the alternative.
The wiki does not display the Drop Rate tables themselves, however it does show the alternative.
<div class="line" style="background-image:linear-gradient(to right,rgb(10,10,10),rgb(100,100,100),rgb(10,10,10))"></div>
==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.<br>
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.<br>
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: [[Luck#Probabilities from Luck|Probabilities from Luck]].
<div style="display:inline-block; vertical-align:top; min-width:550px; width:55%; margin-right:40px;">
{{#widget:DatasetsChart|uniqueId=Hoardtreasure_HR3|datasets={"labels":[0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500],"datasets":[{"label":"2","data":[1.0, 0.84902, 0.739258, 0.657067, 0.592511, 0.541233, 0.498804, 0.46412, 0.434549, 0.409781, 0.388129, 0.369863, 0.353686, 0.339913, 0.327543, 0.317101, 0.307695, 0.299859, 0.29273, 0.286992, 0.281855],"borderColor":"#DEDEDE","backgroundColor":"#DEDEDEAA"},{"label":"3","data":[1.0, 0.859332, 0.758213, 0.682312, 0.623696, 0.577007, 0.539248, 0.508346, 0.482832, 0.461465, 0.443576, 0.428578, 0.416101, 0.405624, 0.397022, 0.390038, 0.384619, 0.380532, 0.377716, 0.376136, 0.375806],"borderColor":"#62BE0B","backgroundColor":"#62BE0BAA"},{"label":"4","data":[1.0, 1.069009, 1.119123, 1.156519, 1.185646, 1.208831, 1.227867, 1.243414, 1.256328, 1.267184, 1.276612, 1.28445, 1.291163, 1.296779, 1.301836, 1.305849, 1.309243, 1.312074, 1.31445, 1.316101, 1.317201],"borderColor":"#4A9BD1","backgroundColor":"#4A9BD1AA"},{"label":"5","data":[1.0, 1.100804, 1.172956, 1.227479, 1.269845, 1.30346, 1.330864, 1.353216, 1.372208, 1.388088, 1.401257, 1.412595, 1.422235, 1.430634, 1.437221, 1.443142, 1.448091, 1.45173, 1.454583, 1.456776, 1.458504],"borderColor":"#AD5AFF","backgroundColor":"#AD5AFFAA"},{"label":"6","data":[1.0, 1.13174, 1.226789, 1.29844, 1.354044, 1.398666, 1.43386, 1.463527, 1.48857, 1.508992, 1.526345, 1.54074, 1.553723, 1.564084, 1.573002, 1.580436, 1.586554, 1.591385, 1.595093, 1.597827, 1.599808],"borderColor":"#F7A22D","backgroundColor":"#F7A22DAA"}]}|title=Treasure Hoard HR3 Luck's Effect on Each Luck Grade|yAxisLabel=Probability at  X  Luck  /  Probability at  0  Luck|xAxisLabel=Luck}}</div>
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===
<div style="display:flex">
<div style="flex:auto; min-width:430px">
'''Loot Summaries'''
Loot Summaries present basic sums of probabilities in loot table grouped by rarities and item types.<br>
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.<br>
Applying the ratio for luck 150 to the legend rarity we get: {{#tag:math|\color{White} 1.43386 \cdot 2.5\% = 3.58465\%}}, which matches the tables below.
<div style="display:inline-block; vertical-align:top; margin-right:40px;">
<table cellspacing="0" class="wikitable sortable jquery-tablesorter" style="border-collapse:collapse; text-shadow:0px 0px 4px #000; text-align:center; vertical-align:middle;">
<caption>Loot Summary at 0 Luck</caption>
<tr><th style="min-width:66px; background:linear-gradient(to top right,#EEE3 48%,#A2A9B1 50%,#EEE3 52%)"><div style="margin-left:2em;text-align:right">Type</div><div style="margin-right:2em;text-align:left">Rarity</div></th><th>Misc<br>100%</th></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity2">Common<br>15%</span></td><td><span class="colorrarity2">15.0%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity3">Uncommon<br>20.5%</span></td><td><span class="colorrarity3">20.5%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity4">Rare<br>45%</span></td><td><span class="colorrarity4">45.0%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity5">Epic<br>17%</span></td><td><span class="colorrarity5">17.0%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity6">Legend<br>2.5%</span></td><td><span class="colorrarity6">2.5%</span></td></tr></table></div>
<div style="display:inline-block; vertical-align:top; margin-right:40px;">
<table cellspacing="0" class="wikitable sortable jquery-tablesorter" style="border-collapse:collapse; text-shadow:0px 0px 4px #000; text-align:center; vertical-align:middle;">
<caption>Loot Summary at 150 Luck</caption>
<tr><th style="min-width:66px; background:linear-gradient(to top right,#EEE3 48%,#A2A9B1 50%,#EEE3 52%)"><div style="margin-left:2em;text-align:right">Type</div><div style="margin-right:2em;text-align:left">Rarity</div></th><th>Misc<br>100%</th></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity2">Common<br>7.48%</span></td><td><span class="colorrarity2">7.4821%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity3">Uncommon<br>11.05%</span></td><td><span class="colorrarity3">11.0546%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity4">Rare<br>55.25%</span></td><td><span class="colorrarity4">55.254%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity5">Epic<br>22.62%</span></td><td><span class="colorrarity5">22.6247%</span></td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;"><span class="colorrarity6">Legend<br>3.58%</span></td><td><span class="colorrarity6">3.5846%</span></td></tr></table></div>
</div>
<div style="flex:auto; margin-left:20px;">
'''Loot Table'''
Loot Tables are sorted alphanumerically by item name.<br>
These tables only display items that ''can'' drop, they won't display entries for dropping nothing.<br>
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.
<table cellspacing="0" class="wikitable stripedtable sortable jquery-tablesorter mw-collapsible" style="border-collapse:collapse; text-align:center; vertical-align:middle;">
<caption>Loot Table</caption>
<tr><th>Name</th><th>Type</th><th class="tooltip"><u>Luck Grade</u><span class="tooltiptext-left" style="left:50%; transform:translate(-50%); bottom:66%; width:100%">Luck Grades present on the graph but missing in the column below are associated with dropping nothing.</span></th><th>Rarity</th><th>Item Count</th><th>Probability</th></tr>
<tr style="border-top: 2.5px solid #b4bbc2;"><td rowspan="5">{{Iconbox|Ancient Scroll|image=Ancient Scroll.png|size=x60px|rarity=2}}</td><td>[[Misc]]</td><td><b><span class="colorrarity2">2</span></b></td><td><span class="colorrarity2">Common</span></td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity3">3</span></b></td><td><span class="colorrarity3">Uncommon</span></td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity4">4</span></b></td><td><span class="colorrarity4">Rare</span></td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity5">5</span></b></td><td><span class="colorrarity5">Epic</span></td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity6">6</span></b></td><td><span class="colorrarity6">Legendary</span></td><td>1</td><td>0.0833%</td></tr>
<tr style="border-top: 2.5px solid #b4bbc2;"><td rowspan="5">{{Iconbox|Blue Sapphire|image=Blue Sapphire.png|size=x60px|rarity=2}}</td><td>[[Misc]]</td><td><b><span class="colorrarity2">2</span></b></td><td><span class="colorrarity2">Common</span></td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity3">3</span></b></td><td><span class="colorrarity3">Uncommon</span></td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity4">4</span></b></td><td><span class="colorrarity4">Rare</span></td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity5">5</span></b></td><td><span class="colorrarity5">Epic</span></td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity6">6</span></b></td><td><span class="colorrarity6">Legendary</span></td><td>1</td><td>0.0833%</td></tr>
<tr style="border-top: 2.5px solid #b4bbc2;"><td rowspan="5">{{Iconbox|Ceremonial Dagger|image=Ceremonial Dagger.png|size=x60px|rarity=2}}</td><td>[[Misc]]</td><td><b><span class="colorrarity2">2</span></b></td><td><span class="colorrarity2">Common</span></td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity3">3</span></b></td><td><span class="colorrarity3">Uncommon</span></td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity4">4</span></b></td><td><span class="colorrarity4">Rare</span></td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity5">5</span></b></td><td><span class="colorrarity5">Epic</span></td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity6">6</span></b></td><td><span class="colorrarity6">Legendary</span></td><td>1</td><td>0.0833%</td></tr>
<tr style="border-top: 2.5px solid #b4bbc2;"><td rowspan="5">{{Iconbox|Diamond|image=Diamond.png|size=x60px|rarity=2}}</td><td>[[Misc]]</td><td><b><span class="colorrarity2">2</span></b></td><td><span class="colorrarity2">Common</span></td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity3">3</span></b></td><td><span class="colorrarity3">Uncommon</span></td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity4">4</span></b></td><td><span class="colorrarity4">Rare</span></td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity5">5</span></b></td><td><span class="colorrarity5">Epic</span></td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td><b><span class="colorrarity6">6</span></b></td><td><span class="colorrarity6">Legendary</span></td><td>1</td><td>0.0833%</td></tr>
<tr><td colspan="6">...</td></tr></table>
</div>
<div style="flex:auto; margin-left:20px;">
'''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.<br>
The table rows are sorted by total expected value per source, i.e. the sum of <code>count * probability * loot table rolls</code> for each source's subrow.
{{:DropTable:Viola_8}}</div></div>
====Example: Royal Diamond at 150 Luck====
Suppose we are interested in the Royal Diamond and we want to calculate the probability for 150 luck.<br>
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.<br>
Next, since the loot table presents probabilities at luck 0, we simply look up the probability for the Royal Diamond: 0.0833%.<br>
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 {{#tag:math|\color{White} 1.43386 \cdot 0.0833\% = 0.1194\%}}

Revision as of 03:02, 11 April 2025

Stats Damage Spell Restoration Luck
Enchantments Health Impact Power Footstep Sound
Movement Healing Action/Interaction/Cast Speed Silence
Shield Looted Handled Supplied Experience
Spells

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.

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! The domain has been adjusted from 0-500 to 0-5000 to better reflect user-collected findings.

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade00}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.


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.

Drop Rate tables generally sum to a power of ten. Since the Luck Scalars are simply 1 at 0 Luck, the probability calculation is trivial.

Using the Luck Scalars at 0 Luck, the dot product is

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


Using the Luck Scalars at 250 Luck, the dot product is

Luck Grade Drop Probability at 250 Luck
0
1
2
3
4
5
6
7
8


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 Table
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 luck
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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