Luck

2024-09-19T22:22:20Z

Jack: /* Loot Drop Tables and Drop Rate Tables */

{{MechanicsBar}}
__TOC__
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. 
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)

Any individual point of Luck contributes to a change in drop chances.

Luck is capped at 500. 
Sources of Luck:
*65 from max level blessing of Blythar.
*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]] (Better than max roll of 20 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)

==Loot Drop 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 Drop table and Luck Grade, will always have the same probability of dropping. 
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.

A Drop can be rolled more than once, but each roll is independent of the others. 
The Elite variant of [[Lich#Loot_Tables|Lich]] rolls their main gear Loot and Drop tables a total of {{Monster Data|Lich#Elite|Drops|Lich_Infernoboss_Elite}} times, theoretically making it possible (though ''extremely'' unlikely) to get {{Monster Data|Lich#Elite|Drops|Lich_Infernoboss_Elite}} identical Artifacts from a single [[Lich|Elite Lich]] kill.

==Luck Scalar==
[[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.'''

The true effect of Luck varies depending on Drop Rate tables.
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. While the table below has luck grade colored similar to item rarities, the two properties are not equivalent. 
Many loot tables will match Item Rarity one to one with item Luck Grade, but there are exceptions. Don't fall into the trap of thinking luck makes higher ''rarities'' more common; see the [[Cave_Troll#Loot_Tables|Cave Troll's quest drops]] for a counterexample.

<div style="display:inline-block; width:740px; vertical-align:top;">
'''Luck Scalar Table'''
{| cellspacing="0" style="text-align:center; text-shadow:0px 0px 4px #000; border:1px solid #FFF9; border-collapse:collapse;"
|- style="font-weight:bold; background-color:#FFF3;"
| rowspan="2" style="width:12%; border-bottom:1px solid #FFF0; border-right:1px solid #FFF9; margin-left:10px; margin-right:10px"| Luck Grade
| colspan="11"| Luck
|- style="font-weight:bold; background-color:#FFF3; border-bottom:1px solid #FFF9;"
| style="width:8%;"| 0
| style="width:8%;"| 50
| style="width:8%;"| 100
| style="width:8%;"| 150
| style="width:8%;"| 200
| style="width:8%;"| 250
| style="width:8%;"| 300
| style="width:8%;"| 350
| style="width:8%;"| 400
| style="width:8%;"| 450
| style="width:8%;"| 500
|- class="colorrarity0"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 0 || 1.000 || 0.950 || 0.900 || 0.850 || 0.800 || 0.750 || 0.700 || 0.650 || 0.600 || 0.550 || 0.500
|- class="colorrarity1"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 1 || 1.000 || 0.950 || 0.900 || 0.850 || 0.800 || 0.750 || 0.700 || 0.650 || 0.600 || 0.550 || 0.500
|- class="colorrarity2"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 2 || 1.000 || 0.975 || 0.950 || 0.925 || 0.900 || 0.875 || 0.850 || 0.825 || 0.800 || 0.775 || 0.750
|- class="colorrarity3"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 3 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000
|- class="colorrarity4"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 4 || 1.000 || 1.476 || 1.901 || 2.277 || 2.602 || 2.878 || 3.103 || 3.279 || 3.404 || 3.480 || 3.505
|- class="colorrarity5"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 5 || 1.000 || 1.547 || 2.036 || 2.468 || 2.842 || 3.159 || 3.418 || 3.620 || 3.765 || 3.851 || 3.881
|- class="colorrarity6"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 6 || 1.000 || 1.618 || 2.171 || 2.659 || 3.083 || 3.441 || 3.734 || 3.962 || 4.125 || 4.223 || 4.257
|- class="colorrarity7"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | 7 || 1.000 || 1.642 || 2.216 || 2.723 || 3.163 || 3.535 || 3.839 || 4.076 || 4.245 || 4.347 || 4.382
|- 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
|}

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].
The desmos graph displays the LaTeX equations. While the curves are continuous, 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}}
|-|1={{Stats_Data|luckgrade01}}
|-|2={{Stats_Data|luckgrade02}}
|-|3={{Stats_Data|luckgrade03}}
|-|4={{Stats_Data|luckgrade04}}
|-|5={{Stats_Data|luckgrade05}}
|-|6={{Stats_Data|luckgrade06}}
|-|7={{Stats_Data|luckgrade07}}
|-|8={{Stats_Data|luckgrade08}}
</tabber>
</div>

==Probabilities from Luck==
To calculate the drop rate at X Luck there are three steps. 
# For each Luck Grade's Drop Rate apply the corresponding Luck Scalar. 
# 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.) 
# 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.

<div class="line" style="margin-top:40px; margin-bottom:0px; background-image:linear-gradient(to right,rgb(10,10,10),rgb(100,100,100),rgb(10,10,10))"></div>

<tabber>
|-|Quest Drop Example=
The table below is the Drop Rate table of Quest Drops.

{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Rate
|-
| style="background-color:#FFF4;" | 0 ||220
|-
| style="background-color:#FFF4;" | 1 ||250
|-
| style="background-color:#FFF4;" | 2 ||200
|-
| style="background-color:#FFF4;" | 3 ||150
|-
| style="background-color:#FFF4;" | 4 ||100
|-
| style="background-color:#FFF4;" | 5 ||50
|-
| style="background-color:#FFF4;" | 6 ||20
|-
| style="background-color:#FFF4;" | 7 ||10
|-
| style="background-color:#FFF4;" | 8 ||0
|}

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. 
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. 
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.

<div class="mw-collapsible mw-collapsed" style="width: fit-content">
<div class="mw-collapsible-content">
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

{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}1.000 \cdot \textbf{220} } +
{\color[RGB]{100, 100, 100}1.000 \cdot \textbf{250} } +
{\color[RGB]{222, 222, 222}1.000 \cdot \textbf{200} } +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } +
{\color[RGB]{74, 155, 209}1.000 \cdot \textbf{100} } +
{\color[RGB]{173, 90, 255}1.000 \cdot \textbf{50} } +
{\color[RGB]{247, 162, 45}1.000 \cdot \textbf{20} } +
{\color[RGB]{227, 216, 140}1.000 \cdot \textbf{10} } +
{\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } = {\color{violet}1000} }}

{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 0 Luck
|-
| style="background-color:#FFF4;" | 0 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}1.000 \cdot \textbf{220} } }{ {\color{violet}1000} }=22\%}}
|-
| style="background-color:#FFF4;" | 1 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}1.000 \cdot \textbf{250} } }{ {\color{violet}1000} }=25\%}}
|-
| style="background-color:#FFF4;" | 2 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}1.000 \cdot \textbf{200} } }{ {\color{violet}1000} }=20\%}}
|-
| style="background-color:#FFF4;" | 3 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } }{ {\color{violet}1000} }=15\%}}
|-
| style="background-color:#FFF4;" | 4 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}1.000 \cdot \textbf{100} } }{ {\color{violet}1000} }=10\%}}
|-
| style="background-color:#FFF4;" | 5 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}1.000 \cdot \textbf{50} } }{ {\color{violet}1000} }=5\%}}
|-
| style="background-color:#FFF4;" | 6 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}1.000 \cdot \textbf{20} } }{ {\color{violet}1000} }=2\%}}
|-
| style="background-color:#FFF4;" | 7 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{10} } }{ {\color{violet}1000} }=1\%}}
|-
| style="background-color:#FFF4;" | 8 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } }{ {\color{violet}1000} }=0\%}}
|}

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

{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.750 \cdot \textbf{220} } +
{\color[RGB]{100, 100, 100}0.750 \cdot \textbf{250} } +
{\color[RGB]{222, 222, 222}0.875 \cdot \textbf{200} } +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } +
{\color[RGB]{74, 155, 209}2.878 \cdot \textbf{100} } +
{\color[RGB]{173, 90, 255}3.125 \cdot \textbf{50} } +
{\color[RGB]{247, 162, 45}3.441 \cdot \textbf{20} } +
{\color[RGB]{227, 216, 140}3.535 \cdot \textbf{10} }+
{\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } = {\color{violet}1227.42} }}

{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 250 Luck
|-
| style="background-color:#FFF4;" | 0 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.750 \cdot \textbf{220} } }{ {\color{violet}1227.42} }=13.443\%}}
|-
| style="background-color:#FFF4;" | 1 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.750 \cdot \textbf{250} } }{ {\color{violet}1227.42} }=15.276\%}}
|-
| style="background-color:#FFF4;" | 2 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.875 \cdot \textbf{200} } }{ {\color{violet}1227.42} }=14.258\%}}
|-
| style="background-color:#FFF4;" | 3 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } }{ {\color{violet}1227.42} }=12.221\%}}
|-
| style="background-color:#FFF4;" | 4 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}2.878 \cdot \textbf{100} } }{ {\color{violet}1227.42} }=23.448\%}}
|-
| style="background-color:#FFF4;" | 5 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.125 \cdot \textbf{50} } }{ {\color{violet}1227.42} }=12.868\%}}
|-
| style="background-color:#FFF4;" | 6 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}3.441 \cdot \textbf{20} } }{ {\color{violet}1227.42} }=5.607\%}}
|-
| style="background-color:#FFF4;" | 7 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{10} } }{ {\color{violet}1227.42} }=2.880\%}}
|-
| style="background-color:#FFF4;" | 8 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}1227.42} }=0\%}}
|}
</div></div>
 
Using the Luck Scalars at 500 Luck, the dot product is

{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.500 \cdot \textbf{220} } +
{\color[RGB]{100, 100, 100}0.500 \cdot \textbf{250} } +
{\color[RGB]{222, 222, 222}0.750 \cdot \textbf{200} } +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } +
{\color[RGB]{74, 155, 209}3.505 \cdot \textbf{100} } +
{\color[RGB]{173, 90, 255}3.881 \cdot \textbf{50} } +
{\color[RGB]{247, 162, 45}4.257 \cdot \textbf{20} } +
{\color[RGB]{227, 216, 140}4.382 \cdot \textbf{10} } +
{\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } = {\color{violet}1208.51} }}

{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 500 Luck
|-
| style="background-color:#FFF4;" | 0 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.500 \cdot \textbf{220} } }{ {\color{violet}1208.51} }=9.102\%}}
|-
| style="background-color:#FFF4;" | 1 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.500 \cdot \textbf{250} } }{ {\color{violet}1208.51} }=10.343\%}}
|-
| style="background-color:#FFF4;" | 2 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.750 \cdot \textbf{200} } }{ {\color{violet}1208.51} }=12.412\%}}
|-
| style="background-color:#FFF4;" | 3 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } }{ {\color{violet}1208.51} }=12.412\%}}
|-
| style="background-color:#FFF4;" | 4 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{100} } }{ {\color{violet}1208.51} }=29.003\%}}
|-
| style="background-color:#FFF4;" | 5 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.881 \cdot \textbf{50} } }{ {\color{violet}1208.51} }=16.057\%}}
|-
| style="background-color:#FFF4;" | 6 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}4.257 \cdot \textbf{20} } }{ {\color{violet}1208.51} }=7.045\%}}
|-
| style="background-color:#FFF4;" | 7 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{10} } }{ {\color{violet}1208.51} }=3.626\%}}
|-
| style="background-color:#FFF4;" | 8 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}1208.51} }=0\%}}
|}

|-|Gold Coin Chest Example=

The table below is the Drop Rate table of the Gold Coin Chest.
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Rate
|-
| style="background-color:#FFF4;" | 0 ||99900
|-
| style="background-color:#FFF4;" | 1 ||0
|-
| style="background-color:#FFF4;" | 2 ||100
|-
| style="background-color:#FFF4;" | 3 ||0
|-
| style="background-color:#FFF4;" | 4 ||0
|-
| style="background-color:#FFF4;" | 5 ||0
|-
| style="background-color:#FFF4;" | 6 ||0
|-
| style="background-color:#FFF4;" | 7 ||0
|-
| style="background-color:#FFF4;" | 8 ||0
|}

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. 
Despite the being equal for most items, Item Rarity does not equal Luck Grade.

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

<div class="mw-collapsible mw-collapsed" style="width: fit-content">
<div class="mw-collapsible-content">
Using the Luck Scalars at 0 Luck, the dot product is

{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}1.000 \cdot \textbf{99900} } +
{\color[RGB]{100, 100, 100}1.000 \cdot \textbf{0} } +
{\color[RGB]{222, 222, 222}1.000 \cdot \textbf{100} } +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } +
{\color[RGB]{74, 155, 209}1.000 \cdot \textbf{0} } +
{\color[RGB]{173, 90, 255}1.000 \cdot \textbf{0} } +
{\color[RGB]{247, 162, 45}1.000 \cdot \textbf{0} } +
{\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } +
{\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } = {\color{violet}100000} }}

{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 0 Luck
|-
| style="background-color:#FFF4;" | 0 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}1.000 \cdot \textbf{99900} } }{ {\color{violet}100000} }=99.9\%}}
|-
| style="background-color:#FFF4;" | 1 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | 2 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}1.000 \cdot \textbf{100} } }{ {\color{violet}100000} }=0.1\%}}
|-
| style="background-color:#FFF4;" | 3 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | 4 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | 5 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | 6 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | 7 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | 8 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|}

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

{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.750 \cdot \textbf{99900} } +
{\color[RGB]{100, 100, 100}0.750 \cdot \textbf{0} } +
{\color[RGB]{222, 222, 222}0.875 \cdot \textbf{100} } +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } +
{\color[RGB]{74, 155, 209}2.878 \cdot \textbf{0} } +
{\color[RGB]{173, 90, 255}3.159 \cdot \textbf{0} } +
{\color[RGB]{247, 162, 45}3.441 \cdot \textbf{0} } +
{\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } +
{\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } = {\color{violet}75012.5} }}

{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 250 Luck
|-
| style="background-color:#FFF4;" | 0 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.750 \cdot \textbf{99900} } }{ {\color{violet}75012.5} }=99.883\%}}
|-
| style="background-color:#FFF4;" | 1 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.750 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | 2 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.875 \cdot \textbf{100} } }{ {\color{violet}75012.5} }=0.117\%}}
|-
| style="background-color:#FFF4;" | 3 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | 4 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}2.878 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | 5 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.159 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | 6 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}3.441 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | 7 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | 8 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|}
</div></div>
 
Using the Luck Scalars at 500 Luck, the dot product is

{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.500 \cdot \textbf{99900} } +
{\color[RGB]{100, 100, 100}0.500 \cdot \textbf{0} } +
{\color[RGB]{222, 222, 222}0.750 \cdot \textbf{100} } +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } +
{\color[RGB]{74, 155, 209}3.505 \cdot \textbf{0} } +
{\color[RGB]{173, 90, 255}3.881 \cdot \textbf{0} } +
{\color[RGB]{247, 162, 45}4.257 \cdot \textbf{0} } +
{\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } +
{\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } = {\color{violet}50025} }}

{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 500 Luck
|-
| style="background-color:#FFF4;" | 0 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.500 \cdot \textbf{99900} } }{ {\color{violet}50025} }=99.850\%}}
|-
| style="background-color:#FFF4;" | 1 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.500 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | 2 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.750 \cdot \textbf{100} } }{ {\color{violet}50025} }=0.150\%}}
|-
| style="background-color:#FFF4;" | 3 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | 4 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | 5 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.881 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | 6 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}4.257 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | 7 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | 8 ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|}

</tabber>

<div class="line" style="background-image:linear-gradient(to right,rgb(10,10,10),rgb(100,100,100),rgb(10,10,10))"></div>

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.

<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. 
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.

===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: [[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.

===Table: 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: {{#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 100%</th></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Common 15%</td><td>15.0%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Uncommon 20.5%</td><td>20.5%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Rare 45%</td><td>45.0%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Epic 17%</td><td>17.0%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Legend 2.5%</td><td>2.5%</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 100%</th></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Common 7.48%</td><td>7.4821%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Uncommon 11.05%</td><td>11.0546%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Rare 55.25%</td><td>55.254%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Epic 22.62%</td><td>22.6247%</td></tr>
<tr><td style="background-color:#EEE3; font-weight:bold;">Legend 3.58%</td><td>3.5846%</td></tr></table></div>

===Table: 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.

<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">Luck GradeLuck Grades present on the graph but missing in the column below are associated with dropping nothing.</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>2</td><td>Common</td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td>3</td><td>Uncommon</td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td>4</td><td>Rare</td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td>5</td><td>Epic</td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td>6</td><td>Legendary</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>2</td><td>Common</td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td>3</td><td>Uncommon</td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td>4</td><td>Rare</td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td>5</td><td>Epic</td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td>6</td><td>Legendary</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>2</td><td>Common</td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td>3</td><td>Uncommon</td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td>4</td><td>Rare</td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td>5</td><td>Epic</td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td>6</td><td>Legendary</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>2</td><td>Common</td><td>1</td><td>0.5%</td></tr>
<tr><td>[[Misc]]</td><td>3</td><td>Uncommon</td><td>1</td><td>0.6833%</td></tr>
<tr><td>[[Misc]]</td><td>4</td><td>Rare</td><td>1</td><td>1.5%</td></tr>
<tr><td>[[Misc]]</td><td>5</td><td>Epic</td><td>1</td><td>0.5667%</td></tr>
<tr><td>[[Misc]]</td><td>6</td><td>Legendary</td><td>1</td><td>0.0833%</td></tr>
<tr><td colspan="6">...</td></tr></table>

===Example: Royal Diamond at 150 Luck===
Suppose we are interested in the Royal Diamond and we want to caculate what the probability is for 150 luck. 
We only need three pieces of information to calculate this: the luck grade, the probability at luck 0, and the 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 {{#tag:math|\color{White} 1.43386 \cdot 0.0833\% = 0.1194\%}}

===Table: Drop Source Table===
Drop Source Tables are displayed on item pages. For example, below is the drop source table for the Viola.

If an item has any drop source from loose loote, monsters, or props, the table will show all possible sources, 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 <code>count * probability</code> for each source's subrow.

<table cellspacing="0" class="wikitable stripedtable sortable jquery-tablesorter mw-collapsible" style="border-collapse:collapse; text-align:center">
<caption>Drop Source Table</caption>
<tr><th class="tooltip" style="width:40%">NameSorted by Total Expected Value in Descending Order Sum of all (Count * Probability)</th><th style="width:20%">Type</th><th style="width:20%">Count</th><th style="width:20%">Probability</th></tr>
<tr style="border-top: 2.5px solid #b4bbc2"><td rowspan="1">{{Iconbox|Weapon SkullRoom|image=Weapon SkullRoom.png|size=x60px|rarity=2}}</td><td rowspan="1">[[Loose Loot]]</td><td>1</td><td>0.2778%</td></tr>
<tr style="border-top: 2.5px solid #b4bbc2"><td rowspan="1">{{Iconbox|Frost Wyvern#Elite|image=Frost Wyvern.png|size=x100px|rarity=Elite}}</td><td rowspan="1">[[Monster]]</td><td>1</td><td>0.1667%</td></tr>
<tr style="border-top: 2.5px solid #b4bbc2"><td rowspan="1">{{Iconbox|Weapon GoldenRoom|image=Weapon GoldenRoom.png|size=x60px|rarity=2}}</td><td rowspan="1">[[Loose Loot]]</td><td>1</td><td>0.0444%</td></tr></table>

Dark and Darker Wiki - User contributions [en]

Luck