Well, in my first couple days of Minecraft (a couple years ago) I didn't really mine for diamodns. I stuck to stone tools and building a house. Yet nowadays, I don't really play Survival but a couple weeks ago I made a Singleplayer world and in three days, I got 6 blocks of diamonds, 60 blocks of iron, 60 blocks of lapiz, and 20 blocks of gold. People don't realize if you know what your doing, how much more efficient it can be. My suggestions for getting diamonds is digging down to around 7 elevation, then starting a strip mine. The most efficient strip mine is to mine a 3 by 3 tunnel for about 10 blocks. After that, just mine passages out of it for about 50 blocks. Let's make something to make you understand. Let's say your in your 3 by 3 tunnel looking at the long wall. In the diagram, "|" means no block. "[]" means block.
| [] [] | [] [] | [] [] |
| [] [] | [] [] | [] [] |
As you can see, you get as many blocks as possible. One 2 by 1 passage can see six blocks. This compact mining will let you do this in as little time as possible. Also in a compact area. Here is another diagram to see whatblocks you see while mining a 2 by 1. Please use the key in the above diagram for this one too.
- [] -
[] | []
[] | []
- [] -
Okay that should help you get more diamonds

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PS. I know this is hard to understand so feel free to ask questions and I will happily answer them.