I'm curious what the chances are of finding something of value without using x-ray; i.e. digging down randomly.
Since I do not know, and I believe that chances are slim that someone has a definitive answer, let's do some science!
Since the wild was recently reset, I took the opportunity to collect Mining Data in the wild.
This has some value as to provide some insight as to X-Ray prevention.
Setup: Dig straight down in random locations. Inventory was documented.
Mining Data:
Site 1:

Taken 1/3/2016 @ -2889, 5018
Blocks Dug: 64
Stopped At (Y): 3
Reason: Hit Bedrock
Ores Dug: 0
Ores Found: Coal, Iron
Notes: Found nothing of interest.

Site 2:

Taken 1/3/2016 @ 5713, 3141
Blocks Dug: 63
Stopped At (Y): 5
Reason: Hit Bedrock
Ores Dug: 0
Ores Found: Gold
Notes: The gold was dug up and replaced with stone. It was 4 blocks. Other than that, nothing unusual.

Site 3:

Taken 1/3/2016 @ -6377, 2150
Blocks Dug: 11
Stopped At (Y): 51
Reason: Cavern
Ores Dug: 0
Ores Found: None
Notes: That was fast.

Site 4:

Taken 1/3/2016 @ -2057, 8946
Blocks Dug: 64
Stopped At (Y): 2
Reason: Hit Bedrock
Ores Dug: 22
Ores Found: Diamond, Iron
Notes: I did not expect this. The minerals were dug up and replaced with stone, except for the giant shaft.

Site 5:

Taken 1/3/2016 @ 3895, -3427
Blocks Dug: 53
Stopped At (Y): 11
Reason: Hit Cavern
Ores Dug: 2
Ores Found: Coal
Notes: Unlike Site 3, this cavern should not be explored. It's a lava lake, and I was luck enough not to dig into it.

Site 6:

Taken 1/3/2016 @ 3347, -6955
Blocks Dug: 36
Stopped At (Y): 31
Reason: Hit Mineshaft
Ores Dug: 0
Ores Found: None
Notes: Dug straight into a mineshaft support by chance. This is why exactly I'm doing this.

Site 7:

Taken 1/3/2016 @ -102, 3682
Blocks Dug: 45
Stopped At (Y): 27
Reason: Hit Cavern
Ores Dug: 0
Ores Found: Classified
Notes: I suspect that cave generation is increased at the moment I excavated the cavern. Also, I forgot to label the sign on the surface (whoops).

Site 8:

Taken 1/3/2016 @ -1155, 5222
Blocks Dug: 36
Stopped At (Y): 31
Reason: Hit Mineshaft
Ores Dug: 2
Ores Found: Iron
Notes: What is with these mineshafts!? Was the generation chance of hitting a form of cavity increased!?

Site 9:

Taken 1/3/2016 @ 2358, 6637
Blocks Dug: 13
Stopped At (Y): 53
Reason: Hit Cavern
Ores Dug: 0
Ores Found: Classified
Notes: That was really fast.

Summary:

Probability of hitting a cavity when digging straight down: 66%

I'm curious if you guys agree to this mining data.
Also, I will admit that I was never using X-Ray during the entire study.