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.