Are Diamond Pickaxes sustainable for diamond mining in Minecraft?
Solution 1:
Further analysis of Diamond probabilities:
Facts we need:
- Diamond occurs in 0.12% of rock (unverified).
- 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).
- Diamond pick lasts 1563 blocks.
- 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%
Solution 2:
Diamonds occur approximately 4-5 times less often than iron, in the same vein structure. Diamonds always occur in veins of at least 3 if they are not cut off by another structure (cave, ore vein, mineshaft, dirt, gravel, silverfish, etc). The diamond 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 last 6x longer? Seems to me like diamond pics are actually CHEAPER than iron pics if you stick to diamond-mining altitude 75% of the time.
So yes, basically, you get a whole lot of diamonds for each 3 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 enchanted picks, which gets more diamonds, iron or diamond pics?
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 waste 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, so 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 going to be 50% faster than diamond, or 2.4 gold per 54 seconds.
- Gross losses are going to be 75* those of diamond, or 26.25 gold per 54 seconds.
- Net is -23.85 gold per 54 seconds, so 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, so probably not worth it.
TL;DR: Every tier of pick can provide a full set of it's own kind of tool over it's lifetime if mined at the correct y-level. The one exception to this is gold.
Solution 3:
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.
Solution 4:
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.