On the mesa we can find a big lot of gold, but only gold, not diamond :/
I haven't specifically mined for diamond in a mesa, but I'm fairly certain that isn't true. My understanding is that below a certain point stone and ores generate as normal like in any other biome. That is why when you go below a certain Y value you no longer see any of the mesa blocks while caving.
The reason I was asking, as I have still yet to find diamonds there, is because I think emeralds are only found in one biome. I was curious and thought maybe this was a trade-off for the massive gold deposits.
IMO, everybody overstates the rarity of diamonds; I never have any issues finding them.
For some idea, the Wiki has this chart:
The results indicate what is expected — that when tunnels are close together they are not efficient because the miner will encounter diamonds which were already removed by the adjacent tunnel(s). A maximum efficiency is reached at a spacing of around 6 blocks (that is, 6 solid blocks left in-between the tunnels). At this spacing, efficiency is about 0.017, corresponding to 1.7% of blocks removed being a diamond. At this spacing, the tunnels effectively become independent of each other and so, statistically speaking, the chance of encountering an ore are maximized because there is no chance the ore has been removed by an adjacent tunnel.
1.7% of blocks mined being diamond ore is quite a lot - that's one in 59 blocks, or about one diamond ore per minute if you mine 1 block per second (easy to do even without enchanted tools); for comparison, if you mined out everything below layer 16 you'd mine around 3328 blocks (11 whole layers plus 4 layers which average 50% bedrock) for only about 3 diamonds, or around 1000 blocks per diamond. Over a whole chunk below sea level it is around 5000 blocks per diamond, so good mining practices can increase the yield nearly 100-fold (and even more if you avoid chunks that had diamond found before).
In fact, while I normally use a spacing of 3 blocks (tunnels every 4th block) I think I'll do 7 blocks the next time I make a mine (7 would be 2 tunnels per chunk-width, half as many as what I currently make), which will halve the amount of mining that I need to do, which is not a really lot even as-is (in my current world I found 91 diamonds and only mined that many because I was looking for a rarer mod ore. I also did not use Fortune so that could have been around 200 diamonds. If in 1.9+ just put Mending on your gear and you (hopefully) never have to use diamonds again).
Also, none of the "normal " ores are affected by the biome; the extra gold in Mesa biomes is just that - 20 additional veins between layers 32-79, with the normal 2 veins between layers 0-31 below that, much as Extreme Hills has the same percentages of normal ores (there is a very slight chance that emerald can displace diamond but since emerald generates afterwards the only way this can happen is if a vein of diamond sticks out of the chunk it is placed in and into a previously generated chunk; in any case with an average of 5.5 emerald ore attempts per chunk over 28 layers (4-31) there is only a 0.0767% (1/1303) chance of a given block being emerald within that range).
Over a whole chunk below sea level it is around 5000 blocks per diamond, so good mining practices can increase the yield nearly 100-fold (and even more if you avoid chunks that had diamond found before).
This was obviously a momentary oversight, TheMasterCaver is the go to expert on world generation, amongst other things, and has explained this many times including to me when I was wondering about it years ago.
Because of the way the edges of the generated part of the world are filled with ores etc the contents of a chunk are shifted by half a chunk (to the south east I think) and a chunk can contain up to 4 diamond veins. It's the shifted "chunks" that can only contain a single diamond vein (not counting diamonds crossing the border from veins in neighbouring shifted "chunks")
It is with a great deal of trepidation I prepare to press "Post", it seems that I must have misunderstood something, or maybe world generation was changed recently.
Also I agree that diamonds are abundantly available, though I enjoy mining, I can see how they would seem rare to someone who was only mining/caving to scrape together a few diamonds so they could get back to whatever it is that they enjoy.
I always branch mine at level 12 because that's the same level as lava. That way i can toss water and keep going. I never dug in the mesa though. I usually dig in extreme hills. Extreme hills seems to have more diamonds and ores than most places. But I play console edition so that might be the case on console.