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Assuming use of the optimal mining pattern from this question at levels 11-15; will a diamond pickaxe on average find enough diamonds to make another before it runs out? Or, put another way, is mining for diamond with a diamond pickaxe sustainable?

Answers covering both single player and smp would be nice.

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There is no difference between single player and SMP. –  StrixVaria Aug 30 '11 at 20:23
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It's interesting that the answer to this question reveals a strategic choice: if you only want diamonds you should mine with iron because you'll get them slightly faster (taking into account the three spent on each diamond pick). However if you want other resources too it is a lot more efficient to mine with a diamond pick because in addition to slowly growing your diamond supply you will be bringing in a lot more iron, gold, redstone, coal, and lapis, plus not using up so much iron on pickaxes. And this effect is likely compounded further by the increased cave discovery. Cool! –  eMansipater Sep 2 '11 at 16:27
    
FYI, with a Unbreaking, or Fortune Enchant the duration of your pick or number of diamonds you get will be improved. If you are lucky enough to get a Unbreaking III + Fortune III, then you be pulling in those diamonds like crazy. –  Zoredache May 26 '12 at 9:43
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7 Answers

up vote 25 down vote accepted

Further analysis of Diamond probabilities:

Facts we need:

  1. Diamond occurs in 0.12% of rock (unverified).
  2. Using an efficient strategy we can expose 16* blocks for every 4 we dig (the ascii art doesn't account for two blocks you expose in front of you, so its actually 16, not 14). This breaks down to 4 blocks per dig. We're using Strix's method because diamond ore can appear in veins of 1, so you do not want to skip over any blocks. (if someone wants to do the math for the other methods, feel free to).
  3. Diamond pick lasts 1563 blocks.
  4. We're assuming worst case scenario of all rocks and no caves, as caves improves diamond probability due to increased surface area with no digging required.

Simple math after this point:

1563*4*0.12% = 7.5

So you can expect to find 7.5 diamonds per diamond pick in the worst case scenario with average luck so you will increase your pick count.

You want the floor of your dig to be at level 11 to avoid dropping into lava, which makes the ceiling at level 16, which is still inside the diamond zone.

Even if the ratio is 0.09%, you should expect 5.6 diamonds per pick, you'll still average more than you spend. The break even point is ~0.048%

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A typical tunnel actually exposes 8 blocks for every two you dig, so 16 for every 4 when they're arranged efficiently. There's two to the left, two to the right, one above, one below, and the two directly ahead that you couldn't see before. And does anyone know where the 0.12% figure comes from? It's unreferenced in the wiki, which is what the answer refers to, and said .09% only a couple days ago. –  eMansipater Sep 1 '11 at 17:38
    
I think this needs a bit more math: Diamond Ore blocks aren't the same as Diamond Gems, and it takes 3 Diamond Gems to make a Diamond Pick. Just because you found one pig doesn't mean you found one ham, etc. –  Darien Sep 3 '11 at 0:59
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@Darien can you clarify? Since when do diamond ore blocks not give a diamond gem? –  z - Sep 4 '11 at 3:02
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This may not have been the case when you asked, but now of course diamond ore blocks can give multiple gems through the use of the Fortune enchant on a pick. –  PeterL Dec 11 '12 at 16:26
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No, even if you mine efficiently. You should use stone or iron pickaxes for everything except what you need diamond pickaxes for, or if you're impatient and want to get through it quickly.

From the wiki:

Mining 771 blocks below elevation 18 has a 50% chance of finding at least one diamond ore.

This can be more accurately stated as "Revealing 771 blocks below elevation 18 has a 50% chance of finding at least one diamond ore." If you're mining efficiently, you can reveal, on average, 4 blocks per block mined. So in order to reveal 771 blocks, you have to mine around 193 blocks. Now, mining 193 blocks has a 50% chance to reveal at least one diamond ore.

A diamond pickaxe has a durability of 1563 blocks.

The probability of finding "at least one diamond ore" now becomes around 99.6%. However, remember that a pickaxe requires 3 diamond ore, not just 1. Your probability of getting 3 ore is much lower than your probability of getting 1 ore. You might find enough for another pickaxe almost every time, but eventually you will run out of diamonds.

So maybe you'll get lucky and sustain yourself. But that's pretty unlikely. You're better off just using stone or iron pickaxes.

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There's still a lot of uncertainty over 'at least one'. Since ore is generated in clumps, you'll uncover more than one (up to 9) most of the time. The distribution of sizes of seams seems to be unknown, but from my experience it seems to be 4 most of the time. –  fredley Aug 30 '11 at 20:23
    
@fredley But you can't count on that. I've found single diamond ore blocks and I've found multiple adjacent pockets for giant hauls of 15. We have to take the average case when figuring out sustainability, not the biased case from what you've experienced. –  StrixVaria Aug 30 '11 at 20:26
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This is definitely wrong, and a common mistake. Never use stone pickaxes when mining in an iron zone--an iron pickaxe is both faster and will find plenty of iron to make more with so do yourself a favour and lose the stone axes. Trust me on this one, I was all stone for the longest time. It's definitely a contest between iron and diamond--stone isn't even in the running because of all the time it makes you waste. –  eMansipater Aug 30 '11 at 20:27
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@eMansipater I never mathcrafted stone vs. iron, so that's good to know. I mathcrafted diamond a while ago and this is just a quick attempt to rehash my findings. –  StrixVaria Aug 30 '11 at 20:31
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I'm going to need to see better math than this. Crudely, if you reveal 4 blocks per block mined, you'll average 5.6 diamonds before your pick runs out just by the straight odds of .09% diamonds. This might be even further improved by the clumping of veins, causing you to find diamonds that otherwise wouldn't have been revealed by your tunnel. Subtract the 3 diamonds you spent to make the pick, and you're up 2.6 diamonds per 468.9 secs of mining. The same time with iron gets through 1172 blocks with 4.22 diamonds to show for it (but then you haven't gone as far, which means less caves too). –  eMansipater Aug 30 '11 at 21:10
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Diamonds occur approximately 4-5 times less often than iron in the same vein structure. Diamonds always occur in veins of at least 2 IF they are not cut off by another structure (cave, ore vein, mineshaft, non-ore vein (dirt, gravel, silverfish, etc)) the veins are essentially the same thing as iron veins. Diamond picks last 1563 hits, as opposed to 252 for iron, meaning they last ~6x longer. 4.5x rarer and 6x longer? Seems to me like hits of a diamond pick are actually CHEAPER than those of an iron one if you stick to mining at diamond-mining altitude 75% of the time.

so yes, basically, you get a whole lot of diamonds for each you spend.

Averaging one vein per chunk and 3.5 diamonds per vein (accurate values): and an average number number of blocks per chunk of around 16*16*14, it is almost perfectly 1/1000 that you will find diamonds as any given block.

this means that, assuming a (fairly realistic) 60% chance of seeing a vein spawned two blocks away horizontally, and maybe a (also fairly realistic) 45% chance of seeing one spawned immediately above the ceiling, or diagonal to any of the visible blocks or below the floor, and a (also fairly realistic) 80% chance of seeing one that spawns beside the ceiling or floor, you effectively uncover 0.6*4+0.45*6+0.8*4+1.0*8 = 16.3 blocks instead of just 8. so if you effectively notice an average of 16 blocks for every 2 that you mine excluding ore veins, and have a 1/3500 chance of finding a diamond vein in a given individual block, then you should find one vein for every 8/3500 blocks mined at level 16 (2 per meter) this works out to be every 473.5 blocks.

so basically, you get 3.5 diamonds per 473.5 blocks mined, or about 11.5 for every diamond pick.

so yes, there is a gigantic profit-margin on diamond-mining. now, the question is, assuming a realistic mining rate for untenanted picks, which gets more diamonds, iron or diamond picks? 11.5 per 6 iron picks, and it takes 0.4 seconds to mine a stone block, meaning a diamond-gathering rate of roughly 54 seconds per diamond, at the cost of 18 iron per 11.5 diamonds. or 12.0 seconds per iron, -18 for every 46, meaning a net gain of 11.5 diamonds, about 13 gold, and 28 iron.

so for iron-pick-mining 1 diamond, 2.7 iron, ~1.2 gold and 8 redstone ore per 54 seconds.

diamond picks mine effectively only 8.5 diamonds, as they cost 3 to make. But they cost no iron, and mine at 0.3 seconds/block, this means that they get about a net of one diamond per 55 seconds of ideal shaft-mining. while this is almost 2% slower, it is compensated for by the fact that it mines

~.98 diamonds, 6 iron, 1.6 gold, and 10.66 redstone ore per 54 seconds.

think stone might be more efficient? I have heard this so many times, stone is cheap, why waist diamonds/iron?

stone gets about 0.5 diamonds, 3 iron, 0.8 gold, and 5.33 redstone ore per 54 seconds, but a better pick is required to actually mine most of it.

so, stone is slightly better than iron for mining iron, iron is insignificantly better at mining diamonds than diamond, and everything is MUCH better at mining other stuff than the previous tool.

as for wood, it takes 1.15 seconds to mine stone, NEVER USE IT, it is nearly twice as slow as stone, totally non-sustainable by mining. even for getting stone, only a moron uses wood. GET RID of wooden picks THE INSTANT you have 3 stone. stone picks get about net=97 cobble a minute, wood only get about 52.

so, diamond mining and literally don't care at all in any way whatsoever about another ore? use iron, maybe. Otherwise, diamonds really are the best picks.

but is gold sustainable: 31 hits, ~1/50 that of diamond. mining a rare ore, gold. gross rate is gonna be 50% faster than diamond, or 2.4 gold per 54 seconds. gross losses are gonna be 75* those of diamond, or 26.25 gold per 54 seconds. net is -23.85 gold per 54 seconds, gold is very, very, very unsustainable. on the other hand, it gets 2 diamonds, 9 iron and 16 redstone in that period, all of which of course, cannot be mined with a gold pick. so shaft-mining with gold is a trade of 2 diamonds, 9 iron, 16 redstone, some coal, some lapis, some emerald, etc for 23.85 gold, probably not worth it.

IN SHORT: every pick can provide a full set of it's own kind of tool over it's lifetime at the altitude it is intended to mine at, let alone itself. the one exception is gold.

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nice first post! –  z - Dec 11 '12 at 13:24
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The math from yx.'s answer sounds right on the money, but one thing I'm surprised no one mentioned in the other answers is how your mining strategy could be greatly improved by enchanting your pickaxe. Two enchantments (assuming you are lucky enough to get them) could help immensely:

  • Unbreaking: Increases the effective durability of the tool. At the maximum level of III, your pickaxe will last an average of 4 times longer (i.e. around 6252 uses).

  • Fortune: Multiplies the drop rate of items from blocks. At the maximum level of III, your pickaxe will net you on average 2.2 diamonds per block.

With those two maximum enchantments on one pickaxe, the mining strategy cited by yx., and a diamond ore occurrence rate of 0.0846% within levels 2-17, we get the following average estimate of the number of diamonds mined per enchanted diamond pickaxe:

1563 * 4 * 4 * 0.000846 * 2.2 = 46.5 diamonds per pickaxe!!!

Yep, enchanting is definitely the way to go.

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+1, enchanting is huge. I recently acquired an Unbreaking III/Fortune III diamond pickaxe, and my diamond acquisition rate has skyrocketed. (I only use it to mine diamonds! I use iron for everyday mining.) –  senderle Sep 27 '12 at 21:13
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Yes, if you mine efficiently. If you use the most efficient mining strategy at level 18 or below you will easily find enough diamond to replenish your supply of pickaxes, and more.

From the wiki:

Mining 771 blocks below elevation 18 has a 50% chance of finding at least one diamond ore.

(Note that using an efficient mining strategy will vastly improve this figure!)

A diamond pickaxe has a durability of 1563 blocks.

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Actually, that quote just uses the straight odds of .09% and going by that you will find an average of only 1.4 diamonds before your pickaxe runs out, less than half of what you need to make another one. I'm assuming an efficient mining strategy improves on this because you see more blocks than you mine. But I'd need to see the math to believe that this makes using a diamond pick worthwhile. –  eMansipater Aug 30 '11 at 20:08
    
@Mansipater If you want the full mathematical analysis of mining strategy it's in this huge forum post. Not for the faint hearted. –  fredley Aug 30 '11 at 20:16
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@fredley Your link is broken. –  StrixVaria Aug 30 '11 at 20:18
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Possibly because you're logged in, fredley? It doesn't work for me either. –  eMansipater Aug 30 '11 at 20:23
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When Minecraftforum was bought a while back, they changed the forum - and broke the old links, including that one :( –  Cyclops Aug 30 '11 at 22:28
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I would like to note that while diamond ore CAN occur singularly, if we are mining for it this is less likely. In caves, where ore gets over-written by air, this is more common. I dont have hard numbers from code but in my experiance, when mining you get about 2.4 diamonds per vein on average.

A lot of this is luck. I performed a small branch mining operation in two different areas. One gave me 3 diamonds and the other gave me 19.

I would advice, if one really wants to mine with diamonds, to search caves until they find a deep one and collect the few exposed diamonds, then begin the branch mine.

I will note however that, for passing through stone, diamonds are not much faster than iron. I find iron to be the more valuable material however (mine carts, railroads, buckets, "good enough" weapons and armor).

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They are absolutely sustainable. With two diamond picks, one with eff 5, silk touch, and unbreaking 3; and the other with fortune 3, I am able to mine roughly 40 diamonds from the ore per pair of these full condition picks on levels 9-14, given you use the most efficient mining technique, which is tunnel, block, block, block, tunnel. This is so because diamond ore commonly occures in veins that are wide enough to be spotted in one of the tunnels. This method is also best for searching for all other Overworld ores. On bad days, one can expect to get less than 20 but more than 10. This amount is easily able to repair and make more diamond tools and armor. All other answers aside, I gurantee the sustainability and efficiency of diamond picks through personal experience.

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This requires XP for enchanting though: do you get enough before the picks break that it's truly sustainable, or is XP a bottleneck? –  SevenSidedDie Jun 5 '13 at 19:26
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