Probability of Catching a Bow with Mending and Infinity Enchantments in Minecraft

When engaging in Minecraft fishing, the likelihood of obtaining a bow with both the Mending and Infinity enchantments is a bit like finding a needle in a haystack. This guide explores the intricacies of enchantment mechanics and the chances of catching such a powerful bow. The analysis is based on the current Minecraft enchantment probabilities and the mechanics of fishing in the game.

Fishing for Bows

During the process of fishing, players have a slight chance of catching a bow. The base probability of catching a bow is approximately 0.8%, or 1 in 125. This means that each time a player casts their line, the chances of getting a bow are relatively low.

Enchantment Mechanics

When a bow is caught, it can come with any number of random enchantments. The specific enchantments on a bow are determined by a set of probabilities. Two important enchantments are:

Mending: This enchantment increases the durability of items and can appear when enchanting any item. The probability of Mending appearing on a bow is approximately 2.5%, or 1 in 40. Infinity: This enchantment allows bows to shoot arrows without needing to be refilled, making it highly sought after. Infinity can only appear on bows and has a much lower probability of around 1%, or 1 in 100.

Combined Probability of Both Enchantments

To find the chance of catching a bow with both Mending and Infinity, one must multiply the individual probabilities:

Probability of catching a bow is 0.8% (0.008). Probability of Mending on a bow is 2.5% (0.025). Probability of Infinity on a bow is 1% (0.01).

The combined probability is calculated as follows:

[P(text{Bow with Mending and Infinity}) P(text{Bow}) times P(text{Mending}) times P(text{Infinity})]

[P 0.008 times 0.025 times 0.01 0.000002]

This result means the chance of catching a bow with both Mending and Infinity is 0.0002%, or 1 in 500,000. Such a high level of rarity makes it virtually impossible to catch such a bow through regular fishing.

Summary and Recommendations

Here is a quick summary of the probabilities:

Base chance of catching a bow: 0.8% (0.008) Chance for a bow to have Mending: 2.5% (0.025) Chance for a bow to have Infinity: 1% (0.01) Combined chance for both: 0.0002% (1 in 500,000)

Given the extremely low probability, it is exceedingly rare to find a bow with both Mending and Infinity enchantments through regular fishing. However, developers at Mojang have deemed it too powerful for players to obtain naturally, making it even rarer. For those who desire such a bow, building an AFK (Away From Keyboard) fish farm and AFKing for at least 2 hours can improve the chances, although it is still a daunting task.