Calculate enchanted book probability

Calculates the probability that a fully unlocked librarian has at least one qualifying enchanted-book offer in Minecraft: Bedrock Edition 1.26.30.5.

Usage

enchanted_book_probability(
  enchantment = "minecraft:aqua_affinity=1",
  max_emeralds = 64,
  include_higher_level = FALSE
)

Arguments

enchantment

One identifier=level pair. The minecraft: namespace is optional. The default is the alphabetically first attainable enchantment.

max_emeralds

Inclusive original emerald-price cutoff from 0 through 64.

include_higher_level

FALSE requires the requested level. TRUE also counts higher valid levels of the same enchantment.

Value

One numeric probability from 0 through 1.

Details

A fully unlocked Bedrock librarian has four independent opportunities to offer an enchanted book. The book candidate is selected with probability 1/2 at novice, apprentice, and journeyman tiers and 1/3 at expert. Within each selected book trade, the model chooses one of 39 enchantments uniformly, then chooses uniformly among that enchantment's valid levels and generates its emerald price.

The function sums all qualifying level-and-price offers within each source trade, then calculates one minus the probability that none of the four book trades qualifies. A recognized enchantment that villagers cannot offer, such as Soul Speed, returns zero. Unknown identifiers and invalid levels produce errors; use enchantments() to inspect the registry.

max_emeralds applies to the original modeled price before demand, curing, or other adjustments. The default 64 includes every book price. A cutoff of 26 is useful when screening for the commonly targeted low-price librarian books, but the function does not simulate curing or promise a post-cure price.

Probabilities for book identity, level, and price follow the documented model described in villager_trades(). They are exact under that model, rather than a guarantee about undocumented Bedrock internals.

References

Microsoft, "Introduction to Enchantments"

Minecraft Wiki, "Trading"

Examples

# Calculate enchanted-book probabilities.
enchanted_book_probability()
#> [1] 0.04619302
enchanted_book_probability('mending=1', max_emeralds = 26)
#> [1] 0.02791063
enchanted_book_probability(
  'efficiency=2',
  include_higher_level = TRUE
)
#> [1] 0.0370841