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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?

26

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:

enter image description here

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.

  • If @Thorsal's quote is correct, then you want the negative binomial distribution, not the binomial distribution. I'm not sure whether you used the wrong distribution or just gave the wrong name... – Brilliand Apr 28 '14 at 18:25
5

According 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.

  • So in theory, a tool could last forever? Also, will being on a multiplayer server increase the amount of lag from a tool re-appearing for multiple blocks or a longer amount of time? – y0urs3lv Oct 28 '13 at 15:49
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    @y0urs3lv Hypothetically? A tool could last forever. Theoretically? No, because the chance of that happening is quite literally infinitely small. I'm not sure what you're getting at about lag, but no, a tool lasting longer can't affect lag. – SevenSidedDie Oct 28 '13 at 16:18
  • In theory, yes, but practically, no. In theory it is possible to roll 6 on a dice a thousand times in a row, but in practice.... I have no information on the lag it might produce, so I can't answer that for you. It should be little though. – Thorsal Oct 28 '13 at 16:20
  • I have brought the actual maths to the table. See my answer. – Li-aung Yip Oct 28 '13 at 16:50
  • @SevenSidedDie I meant that when you are on a server, will the "re-appearing of a tool" happen more often because the data is not local? Or, is that data stored locally instead? – y0urs3lv Oct 28 '13 at 22:58
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I'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:

D (Durability of Weapon with no Unbreaking) * (U (Unbreaking Level) + 1) = DUW (Durability of Unbreaking Weapon)

  • The books read are Hacks for Minecrafters: Combat Edition, Mojang Minecraft Combat Handbook, & Hacks for Minecrafters: Command Blocks. – user193792 Jul 26 '17 at 14:20
  • 1. Spaces in the command make it not work. 2. As the accepted answer says, it's a random chance. Your values are correct, but averages. – Fabian Röling Jul 26 '17 at 14:49
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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!

  • 4
    We have answers that cite sources and utilize math. At this point, unless the function of the unbreaking enchantment has drastically changed since Oct '13, unsubstantiated theories and guesses are not that useful. – Trent Hawkins Jul 26 '14 at 20:48

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