Luck

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.

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

Every monster with a quest drop uses the Drop Rate table.
However, depending on the monster's Loot Drop Table, many of the Luck Grade rates will be associated with dropping nothing.

And in other instances, like Demon Centaur, a Luck Grade's rate may be split between two Loot Drops.
This will not affect the calculations below, but they will determine an individual item's probability.

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

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

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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} }

Luck Grade	Drop Probability at 0 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {220}}}{\color {violet}1000}}=22\%$
1	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{100, 100, 100}1.000 \cdot \textbf{250} } }{ {\color{violet}1000} }=25\%}
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {200}}}{\color {violet}1000}}=20\%$
3	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1000}}=15\%$
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {100}}}{\color {violet}1000}}=10\%$
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {50}}}{\color {violet}1000}}=5\%$
6	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{247, 162, 45}1.000 \cdot \textbf{20} } }{ {\color{violet}1000} }=2\%}
7	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{10} } }{ {\color{violet}1000} }=1\%}
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}1000}}=0\%$

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

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {220}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {250}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {200}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {100}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.125\cdot {\textbf {50}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {20}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {10}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}={\color {violet}1227.42}$

Luck Grade	Drop Probability at 250 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {220}}}{\color {violet}1227.42}}=13.443\%$
1	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{100, 100, 100}0.750 \cdot \textbf{250} } }{ {\color{violet}1227.42} }=15.276\%}
2	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{222, 222, 222}0.875 \cdot \textbf{200} } }{ {\color{violet}1227.42} }=14.258\%}
3	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } }{ {\color{violet}1227.42} }=12.221\%}
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {100}}}{\color {violet}1227.42}}=23.448\%$
5	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{173, 90, 255}3.125 \cdot \textbf{50} } }{ {\color{violet}1227.42} }=12.868\%}
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {20}}}{\color {violet}1227.42}}=5.607\%$
7	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {10}}}{\color {violet}1227.42}}=2.880\%$
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}{\color {violet}1227.42}}=0\%$

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

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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} }

Luck Grade	Drop Probability at 500 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {220}}}{\color {violet}1208.51}}=9.102\%$
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {250}}}{\color {violet}1208.51}}=10.343\%$
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {200}}}{\color {violet}1208.51}}=12.412\%$
3	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1208.51}}=12.412\%$
4	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{100} } }{ {\color{violet}1208.51} }=29.003\%}
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {50}}}{\color {violet}1208.51}}=16.057\%$
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {20}}}{\color {violet}1208.51}}=7.045\%$
7	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {10}}}{\color {violet}1208.51}}=3.626\%$
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {0}}}{\color {violet}1208.51}}=0\%$

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

Luck Grade	Drop Rate
0	99900
1	0
2	100
3	0
4	0
5	0
6	0
7	0
8	0

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

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

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}={\color {violet}100000}$

Luck Grade	Drop Probability at 0 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {99900}}}{\color {violet}100000}}=99.9\%$
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
2	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{222, 222, 222}1.000 \cdot \textbf{100} } }{ {\color{violet}100000} }=0.1\%}
3	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
7	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$

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

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.159\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}={\color {violet}75012.5}$

Luck Grade	Drop Probability at 250 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {99900}}}{\color {violet}75012.5}}=99.883\%$
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {100}}}{\color {violet}75012.5}}=0.117\%$
3	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.159\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
7	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}
8	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}

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

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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} }

Luck Grade	Drop Probability at 500 Luck
0	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{50, 50, 50}0.500 \cdot \textbf{99900} } }{ {\color{violet}50025} }=99.850\%}
1	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{100, 100, 100}0.500 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
2	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{222, 222, 222}0.750 \cdot \textbf{100} } }{ {\color{violet}50025} }=0.150\%}
3	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
4	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
5	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{173, 90, 255}3.881 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
6	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{247, 162, 45}4.257 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
7	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
8	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}

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.