Minecraft anvil mechanics for enchanted books

The supported book-application calculation

step levels = enchantment charges from the right-hand book
            + (2 ^ left work count - 1)
            + (2 ^ right work count - 1)
result work count = max(left count, right count) + 1

For each applicable enchantment on the book, multiply the resulting level by its book multiplier. The Java data’s anvil_cost is the item-sacrifice multiplier; an enchanted book uses half of that value, rounded down, with a minimum of 1. Confusing the two doubles many book costs. Unbreaking III therefore contributes 3 levels, Mending I contributes 2 and Thorns III contributes 12.

A worked history example

A compatible unenchanted target with work count 2 and an Unbreaking III book with count 1 cost 3 + 3 + 1 = 7 levels. The result has work count 3. It did not “use the anvil three times total”; the count represents inherited history depth. Its next penalty is 7.

Equal levels and unequal levels

Combining two books with the same enchantment at the same level raises it by one, up to the normal maximum. Sharpness III plus Sharpness III produces Sharpness IV. With unequal levels, the higher survives. A lower duplicate on the right can still incur an enchantment charge; it is not a free way to combine history.

The planner uses every supplied row and first seeks the highest duplicate levels obtainable from those rows. It then compares plans that fit the Survival cap before minimizing the selected objective. This avoids calling a cheap plan “optimal” when it silently discards a duplicate upgrade.

Compatibility and scope

The target must support every chosen enchantment, and all chosen enchantments must coexist. A book can store enchantments for different gear, but applying it to one item does not make every enchantment applicable. The public planner intentionally accepts one enchantment per row and an otherwise unenchanted target so this boundary remains visible.

For modeled book combinations, 40 levels or more in a single step triggers Too Expensive in Survival. Creative, renaming-only exceptions, material repairs, durability repair, multiple items in a stack, datapacks and server rules need their own calculations. No game-version toggle here pretends that every later release has been validated.