Fortune

Fortune is an enchantment applied to mining and digging tools that increases the amount and/or chances of specific item drops. It does not increase experience drops.

Ore
For coal ore, diamond ore, emerald ore, lapis lazuli ore, redstone ore, iron ore, copper ore, gold ore]], nether gold ore, nether quartz ore, and amethyst cluster, Fortune I gives a 33% ($1/3$) chance to multiply drops by 2 (averaging 33% ($1/3$) increase), Fortune II gives a chance to multiply drops by 2 or 3 (25% ($1/4$) chance each, averaging 75% ($3/4$) increase), and Fortune III gives a chance to multiply drops by 2, 3, or 4 (20% ($1/5$) chance each, averaging 120% (1$1/5$) increase).

Generally speaking, Fortune gives a weight of 2 to a normal drop chance and adds a weight of 1 for each extra drop multiplier. In short, when an ore is mined, the chance for no bonus drops is $$\frac{2}{level+2}$$ and if a bonus is applied, there is an equal chance for any number of drops between 2 and $$level+1$$

The formula to calculate the average drops multiplier is $$\frac{1}{level+2}+\frac{level+1}{2}$$, which means Fortune IV gives 2.67x (2$2/3$) drops on average, Fortune V gives 3.14x (3$1/7$) drops on average, etc.

Discrete random
Glowstone, melons, nether wart, redstone ore, sea lanterns, and sweet berries use a, meaning each possible drop amount is equally likely to be dropped. Fortune increases the maximum number of drops by 1 per level. However, maximum drop limitations may apply: glowstone has a capacity of 4 glowstone dust, sea lanterns have a capacity of 5 prismarine crystals, and melons have a capacity of 9 melon slices. If a drop higher than these maximums is rolled, it is rounded down to the capacity.

Grass and ferns
Grass and ferns have a fixed chance, unaffected by Fortune, to drop wheat seeds. If the drop occurs, Fortune increases the maximum number of seeds that can be dropped by 2, by affecting a discrete uniform distribution.

Seeds
Beetroots (seeds only), carrots, potatoes, and wheat (seeds only) use a. Fortune increases the number of tests for the distribution, and thus the maximum number of drops, by 1 per level.

The binomial distribution in the default case is created by rolling three times (n=3) with a drop probability of 57% (p=.57), creating the typical drop of 0-3 seeds. Carrots and potatoes modify this value by adding a few fixed drops.

Tabulated probabilities
Fortune increases the probability of flint dropping from gravel; saplings and sticks dropping from leaves; apples dropping from oak and dark oak leaves and gold nuggets dropping from gilded blackstone, and twisting vines and weeping vines dropping from themselves.

Incompatibilities
Silk Touch and Fortune are mutually exclusive. If commands are used to apply both Silk Touch and Fortune to an item, the Silk Touch enchantment takes precedence over the Fortune enchantment for blocks affected by both enchantments. Use an avil to combine two enchanted items also stack to enchantments.

ID




Issues
Fortuna Enchantement 幸運 (エンチャント) Fortuna 时运