What's the most efficient way of combining books and tools to reduce experience cost? [duplicate]

Solution 1:

Gnembon covers the problem in his video:

Summarizing his findings, there are three main factors

• level of the enchantment (Fortune III will be three times as expensive as Fortune I); if a book or tool has multiple ones, that's just a sum.
• rarity of the enchantment - a multipler of the level; Efficiency counts as 1x, Fortune - 2x, so applying Efficiency IV will cost as much as Fortune II
• base cost - an extra cost added with every operation, doubles with every subsequent one.

That last part is the most prohibitive, meaning applying enchantments to a tool one after another will quickly drive the cost way up. The way to approach it is to combine enchantments in form of a binary tree - merge same cost books in pairs (then potentially merge these pairs), treating the original tool as one of the 'leaves' of the binary tree (same as one level 1 book).

When combining books swap their positions in the anvil and always choose the cheaper option, and prefer to merge items of similar cost.