I just got a Librarian villager that has 0.0000000087509517% chance to appear, with proof (Java Edition 1.21.4)
I just rolled a villager with 4 enchanted books (that are all good).
https://reddit.com/link/1jca2ug/video/itpwabtwtxoe1/player
The chance (source Minecraft Wiki - Librarian Trading) to roll enchanted books at all are:
- First book 67%
- Second book 67%
- Third book 67%
- Fourth book 50%
To get all four trades as enchanted books, the chance is 67% * 67% * 67% * 50% ~= 15.04%
The librarian has equal chance to offer all different levels of enchanted books, excluding Soul Speed, Swift Sneak and Wind Burst (source Minecraft Wiki - Enchantments).
There are 9 Max Level 1 enchantments possible, 3 Level 2 (subtracted , 14 Level 3, 7 Level 4 and 7 Level 5.
That is 9*1+4*2+12*3+7*4+7*5 = 116 possible options of enchanted books to roll.
So, for the first book, there is one positive outcome of 116 options.
For the second book, there is one positive outcome of 115 options.
For the third book, there is one positive outcome of 114 options.
For the fourth book, there is one positive outcome of 113 options.
The calculation for total possibility is 0.67*(1/116) * 0.67*(1/115) * 0.67*(1/114) * 0.5*(1/113) = 8.7509517e-10.
Multiplying it by 100 (to get percentage), we get 8 decimal points. The chance to roll the villager that I just got is 0.0000000087509517%.
Holy crackers!
Posted Mar 16, 2025, 1:08 AM UTC