Alright, here's my take on all the fancy mining methods (Assuming you want diamonds):
1. Digging large rooms is obviously inefficient. I don't think I need to explain why.
Given that, some people then say to dig in a web like patterns, with two blocks betweeen shafts.
This is great and all... but wouldn't mining in a 1x2 straight line and never stopping simply be better?
1. It removes the need to take time to turn around and whatnot, a small amount per iteration but it adds up.
2. It still maintains maximum possible efficiency per block revealed other than digging a 1x1, which could simply be added to the sides of your 1x2 tunnel.
3. Sure, web mining would reveal every ore block in the chunk, but there's no difference between the diamonds in this chunk and the diamonds in the next chunk. Nobody cares. Who cares if you miss diamonds in this chunk if you get the ones in the next chunk faster? Diamonds are diamonds.
Keep in mind this is a conversation about efficiency not thoroughness because thoroughness is a confusing term that isnt useful whatsoever.
Only interested in the ratio of time in to diamonds out. That's it.
So to finalize my question
Is it not simply most effective to dig in a straight line only big enough for your player model to fit through?
The only issue with digging in a straight line is the distance covered, which will ultimately reduce throughput since you'll have to spend more and more time simply getting to and from where you are mining. Aside from that, according to the Wiki spacing your tunnels at least 6 blocks apart (a tunnel every 7th block) achieves maximum efficiency, with about 1.7% of blocks mined being diamond ore (for comparison, this is about 15 times higher than their per-block abundance between layers 5-12 so your mining efficiency is 15 times higher than if you simply mined every block):
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. Above a spacing of 6, efficiency does not increase greatly because ore collection rate is simply a function of the distribution of ores within the level. Note: in the above graph, efficiency appears to drop-off at a spacing of 10. This is simply a limitation of the size of the level used to model the process, resulting in a large error at high spacings. If a larger level were used, the line would smoothly come to a maximum efficiency and stay there.
I have not verified this but my own experiences suggest that it is accurate; I've averaged about one diamond ore per 120 blocks (only counting tunnels, not ores taken from the sides) with a spacing of 3 (one tunnel every 4 blocks), an efficiency of about 0.0083, very close to what the chart shows.
Interestingly, despite a doubling in the spacing (from 3 to 6) you get about the same amount of diamond ore per chunk (many people try to maximize the yield per area as well as time, which is why a 2-3 block spacing is common; the data above suggests that the chances of missing veins is still relatively low, more so when you mine all ores as veins can be indirectly exposed when you mine another ore).
Also, when considering all ores, of which there are about 27 times more than diamond ore alone (there are around 10 coal, 8 redstone, 6 iron, 1.2 gold, and 0.8 lapis per diamond ore on layers 11-12) this suggests that nearly half of all mined blocks can be ore (1.7% * 27 = 45.9%). A higher spacing is likely necessary to maximize the amount of coal found due to its larger veins (unless they did account for diamond found by mining other ores, as a 6 block spacing is consistent with the length of coal veins).
In addition, if you mine an average of one block per second this results in the following mining rates for each ore per hour:
Total: 1650 (3600 resources per hour; 5500 with Fortune III)
To put this into perspective, I average around 800 ore mined per hour when caving, which is generally seen as a quite high number (I have never kept track of how long branch-mining takes, which is also affected by the fact that I start out using stone tools and do not use an Eff V diamond pickaxe until I start caving, and it is much easier to keep track of the time spent caving since it is basically all I do later on).
A mine in a 3*3 pattern on z = 9. I find that diamonds are usually between layers z = 7 - 12. As a result, I'm covering layers 9, 10 and 11, whilst also able to see diamonds at levels 12 and 8, with a horizontal spread of 3 (x, x = x - 1, x = x + 1). So basically, I'm covering a full spread of 12 blocks on the outer rim not counting the 9 blocks between them, per each y + 1 (in this scenario). So assuming y = 10, the net coverage is 10 * 21, or y * n where n is the coverage of each y, = 210 or 21y.
Though I do believe that all methods will likely have the same output, this is the one that works best for me especially since you're more likely to break into a cave.
Apologies for the mathematics, and note that I'm using z as vertical, x and y as horizontal. I can't actually remember which is which.
So you cover 21 blocks with 9 mined or 2.333 blocks per mined block, 1X2 tunnels are almost twice as efficient with 8 blocks covered per 2 mined or 4 blocks per mined block. (1X3 would show you 8 blocks per 3 mined or 3.666 blocks per mined block.)
And a 1X2 tunnel covers 4.5 times the distance/area increasing the number of caves you find.
A 1X2 tunnel with 1X1 poke holes to the sides and upwards is probably even more efficient but I can't be bothered, prefering to just mine straight ahead until I find ores.
I prefer mining at Y (height) = 11 since that is just above lava lake level, when I run into a lava lake I just dump water on it and continue at the same level. When I don't mine at Y=5 that is, obstinately mining my way through the lava lakes which I enjoy but would never suggest is an efficient mining method.
Alright, here's my take on all the fancy mining methods (Assuming you want diamonds):
1. Digging large rooms is obviously inefficient. I don't think I need to explain why.
Given that, some people then say to dig in a web like patterns, with two blocks betweeen shafts.
This is great and all... but wouldn't mining in a 1x2 straight line and never stopping simply be better?
1. It removes the need to take time to turn around and whatnot, a small amount per iteration but it adds up.
2. It still maintains maximum possible efficiency per block revealed other than digging a 1x1, which could simply be added to the sides of your 1x2 tunnel.
3. Sure, web mining would reveal every ore block in the chunk, but there's no difference between the diamonds in this chunk and the diamonds in the next chunk. Nobody cares. Who cares if you miss diamonds in this chunk if you get the ones in the next chunk faster? Diamonds are diamonds.
Keep in mind this is a conversation about efficiency not thoroughness because thoroughness is a confusing term that isnt useful whatsoever.
Only interested in the ratio of time in to diamonds out. That's it.
So to finalize my question
Is it not simply most effective to dig in a straight line only big enough for your player model to fit through?
The only issue with digging in a straight line is the distance covered, which will ultimately reduce throughput since you'll have to spend more and more time simply getting to and from where you are mining. Aside from that, according to the Wiki spacing your tunnels at least 6 blocks apart (a tunnel every 7th block) achieves maximum efficiency, with about 1.7% of blocks mined being diamond ore (for comparison, this is about 15 times higher than their per-block abundance between layers 5-12 so your mining efficiency is 15 times higher than if you simply mined every block):
I have not verified this but my own experiences suggest that it is accurate; I've averaged about one diamond ore per 120 blocks (only counting tunnels, not ores taken from the sides) with a spacing of 3 (one tunnel every 4 blocks), an efficiency of about 0.0083, very close to what the chart shows.
Interestingly, despite a doubling in the spacing (from 3 to 6) you get about the same amount of diamond ore per chunk (many people try to maximize the yield per area as well as time, which is why a 2-3 block spacing is common; the data above suggests that the chances of missing veins is still relatively low, more so when you mine all ores as veins can be indirectly exposed when you mine another ore).
Also, when considering all ores, of which there are about 27 times more than diamond ore alone (there are around 10 coal, 8 redstone, 6 iron, 1.2 gold, and 0.8 lapis per diamond ore on layers 11-12) this suggests that nearly half of all mined blocks can be ore (1.7% * 27 = 45.9%). A higher spacing is likely necessary to maximize the amount of coal found due to its larger veins (unless they did account for diamond found by mining other ores, as a 6 block spacing is consistent with the length of coal veins).
In addition, if you mine an average of one block per second this results in the following mining rates for each ore per hour:
Coal: 612
Redstone: 490
Iron: 367
Gold: 73.4
Diamond: 61.2
Lapis: 49
Total: 1650 (3600 resources per hour; 5500 with Fortune III)
To put this into perspective, I average around 800 ore mined per hour when caving, which is generally seen as a quite high number (I have never kept track of how long branch-mining takes, which is also affected by the fact that I start out using stone tools and do not use an Eff V diamond pickaxe until I start caving, and it is much easier to keep track of the time spent caving since it is basically all I do later on).
TheMasterCaver's First World - possibly the most caved-out world in Minecraft history - includes world download.
TheMasterCaver's World - my own version of Minecraft largely based on my views of how the game should have evolved since 1.6.4.
Why do I still play in 1.6.4?
So you cover 21 blocks with 9 mined or 2.333 blocks per mined block, 1X2 tunnels are almost twice as efficient with 8 blocks covered per 2 mined or 4 blocks per mined block. (1X3 would show you 8 blocks per 3 mined or 3.666 blocks per mined block.)
And a 1X2 tunnel covers 4.5 times the distance/area increasing the number of caves you find.
A 1X2 tunnel with 1X1 poke holes to the sides and upwards is probably even more efficient but I can't be bothered, prefering to just mine straight ahead until I find ores.
I prefer mining at Y (height) = 11 since that is just above lava lake level, when I run into a lava lake I just dump water on it and continue at the same level. When I don't mine at Y=5 that is, obstinately mining my way through the lava lakes which I enjoy but would never suggest is an efficient mining method.
Just testing.