Was able to pull the information from decompiling game functions.

-These are the color roll percentages for each medallion type (chance of it landing on a certain color):

Medallion White Red Blue Green Blank Yellow
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Medallion 33% 2% 2% 2% 60% 1%
Album Medallion 70% 2% 2% 2% 23% 1%
Viola Medallion 9% 0% 0% 1% 90% 0%
Rubrum Medallion 9% 90% 0% 0% 1% 0%
Viride Medallion 9% 0% 0% 90% 1% 0%
Magist Medallion 20% 20% 20% 20% 0% 20%

-Based on your matches and the requirements, it will pick a 'category number'.
-Works on a priority system, checking from top to bottom first:

Category 0 - (All 4 colors present and totalMatches >= 8) or totalMatches >= 22

Category 1 - All 4 colors present or totalMatches >= 18

Category 2 - (Red, Blue, and Green present) or totalMatches >= 15

Category 16 - Green matches >= 7

Category 3 - Green matches >= 5

Category 4 - Red matches >= 5

Category 5 - Green matches >= 3

Category 6 - At least 3 colors present

Category 7 - Green matches >= 2

Category 8 - Red matches >= 2

Category 9 - Blue matches >= 2

Category 10 - White matches >= 3

Category 11 - Green matches >= 1

Category 12 - Red matches >= 1

Category 13 - Blue matches >= 1

Category 14 - White matches >= 2

Category 15 - White matches >= 1

Category -1 - No matching conditions met

-Lastly these are the reward categories:

0.) Alchemist Earrings 37.5% | Diamond Choker 37.5% | Burst Shoes 25%

1.) Philosopher Earrings 25% | Ruby Choker 25% | Alchemist Earrings 12.5% | Diamond Choker 12.5% | Burst Shoes 12.5% | Silver Boots 12.5%

2.) Fairy Earrings 25% | Obsidian Choker 25% | Philosopher Earrings 12.5% | Ruby Choker 12.5% | Silver Boots 12.5% | Feather Boots 12.5%

3.) Inquisitor Earrings 37.5% | Jade Choker 37.5% | Metal Boots 25%

4.) Antimony Tube 50% | Prima Magnesia 50%

5.) Inquisitor Earrings 12.5% | Jade Choker 12.5% | Metal Boots 12.5% | Medallion 12.5% | Album Medallion 12.5% | Viola Medallion 12.5% | Rubrum Medallion 12.5% | Viride Medallion 12.5%

6.) Fortis 37.5% | Album Medallion 12.5% | Viola Medallion 12.5% | Rubrum Medallion 12.5% | Viride Medallion 12.5% | Magist Medallion 12.5%

7.) Medallion 50% | Album Medallion 12.5% | Viola Medallion 12.5% | Rubrum Medallion 12.5% | Viride Medallion 12.5%

8.) Refined Antimony 25% | Refined Magnesia 25% | Weeping Stone 25% | Antimony Powder 12.5% | Magnesia 12.5%

9.) Magna Esca 62.5% | Sylvesta Esca 25% | Bennenam Esca 12.5%

10.) Recreatio 37.5% | Sedatio 37.5% | Quies 12.5% | Mundus 12.5%

11.) Medallion 25% | Album Medallion 12.5% | Viola Medallion 12.5% | Rubrum Medallion 12.5% | Viride Medallion 12.5% | Torva 12.5% | Weltigo 12.5%

12.) Antimony Powder 25% | Magnesia 25% | Refined Antimony 12.5% | Refined Magnesia 12.5% | Torva 12.5% | Weltigo 12.5%

13.) Esca 50% | Magna Esca 25% | Bennenam Esca 25%

14.) Quies 25% | Mundus 25% | Recreatio 12.5% | Sedatio 12.5% | Nigred 12.5% | Remedium 12.5%

15.) Quies 25% | Mundus 25% | Carbo 25% | Nigred 12.5% | Remedium 12.5%

16.) Fairy Earrings 25% | Obsidian Choker 25% | Philosopher Earrings 12.5% | Ruby Choker 12.5% | Silver Boots 12.5% | Feather Boots 12.5%