In Minecraft, the "Unbreaking" enchantment causes tools to last longer, but the exact durability of these tools is something that I have failed to find.
By using F3 + H I have found that the durability counter of the item does not change. The only thing I have noticed is that it will not decrease for a few broken blocks. Is there an actual value for how long each "Unbreaking" enchantment will last?
4 Answers
As correctly noted by Thorsal, the durability of an 'Unbreaking' item is not fixed, but depends on chance.
More specifically, the number of uses you will get out of a given tool will follow a binomial distribution. This is the same statistical law that predicts things like "how many heads will I get out of 100 coin tosses?"
Consider that a diamond pickaxe normally has durability of 1,536 uses. If you plot the binomial probability density function (PDF) for 1,536 'successes' with a 'success rate' of P = 1/2 = 0.5 (Unbreaking 1), P = 1/3 = 0.333 (Unbreaking II), and P = 1/4 = 0.25 (Unbreaking III) you get the following graph:
This shows that an Unbreaking III Diamond Pick will last, on average, about 6,144 uses (four times as long as a normal Diamond Pick.) However there is also a chance it will break after only 6,000 uses. Similarly, there is a chance it will last for 6,500 uses.
However there is basically no chance it will last longer than 7,000 uses, or less than 5,000 uses.
1According to the Wiki:
For most items,
(100/(Level+1))%chance a use reduces durability. On average, lifetime is (Level+1) times as long.
In other words, the actual durability on an item with the Unbreaking enchantment depends on chance and is no longer a fixed value.
This accounts for your observations that the durability didn't decrease and also the re-appearing of at tool you've just broken when you equip a similar tool in your hotbar.
6I've been reading a few books, and they told me a Diamond Sword has a durability of 1,562.
If you want to find the durability of a Diamond Sword with Unbreaking I, multiply the durability by 2.
If you want to find the durability of a Diamond Sword with Unbreaking II, multiply the durability by 3.
If you want to find the durability of a Diamond Sword with Unbreaking III, multiply the durability by 4.
If you do /give @p minecraft:diamond_sword 1 0 {ench: [{id:34,lvl:1000}]} and you want to find the durability, as you saw the command said {ench: [{id:34,lvl:1000}]}, {ench: meaning enchantment, [{id:34, meaning Unbreaking, and lvl:1000}]} meaning level M. That means you multiply 1,562 by 1,001, getting
a durability of 1,563,562.
Remember! To get the durability of an unbreaking weapon, the equation you have to do is:
2D (Durability of Weapon with no Unbreaking) * (U (Unbreaking Level) + 1) = DUW (Durability of Unbreaking Weapon)
I think that it is probably based on the amount of the unbreaking so unbreaking 1 would last 1.5 times longer unbreakin 2 would last 2 times longer and so on.
But that's just a theory a game theory!
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