Tunnels: Multilevel Mining

continued from Tunnels: Basic Math of Efficient Mining

Update: A kind commenter recently pointed out to me that my "most time efficient" mining pattern is actually not the most time efficient! I've updated my post with a more efficient pattern that takes more advantage of the tendency of ore to appear in clusters. See my conclusions section for the updated pattern.

Maximizing visibility ratios and block ratios for multilevel mines is really a fun exercise, but it’s little more than a guess-and-check procedure. Before we start with the guessing-and-checking, though, I want to introduce a “rule” that helps narrow down candidates.

Golden Rule: Each level of tunnels should be shifted to the left or right from the one below it (“staggered”).

To consider why this is, look at the following two diagrams. One illustrates tunnels directly on top of each other, while the other illustrates a “staggered” system. The grey squares are unexposed spaces, the green squares are exposed ones, and the white are empty (that is, part of the tunnel).

The non-staggered system only exposes 11 blocks, to the staggered system’s 12. This is because the upper tunnel in the non-staggered system shares its floor with the ceiling of the lower tunnel, while the staggered system exposes another block instead.

Before we get into the results, I want to quickly make a quick note about my calculations. Feel free to skip it if you just want to see the most efficient mining patterns.

Calculation Note

In calculating the ratios of these mines, I’m assuming that the mine is basically being tessellated beyond the diagram. In other words, the ratios represent the mining pattern repeated ad ifinitum, and may differ slightly depending on where in the pattern your mine starts and ends. Counting the green squares and white squares on the pattern grids does not always produce accurate results.

Results: The Two (Now Three) Optimal Patterns

I’ve narrowed it down to two patterns which (I believe) are the most ideal. In other words, any alteration to these patterns tends to degrade their effectiveness. Pattern one maximizes block ratio – that is, it’s more efficient in terms of finding minerals quickly. Pattern two maximizes visibility ratio: it allows you to find all ore in an area, guaranteed. Pattern three takes advantage of the tendency of ore to appear in clusters by reducing the visibility ratio in order to reduce the amount of digging required to collect all the ore from an area.

Pattern Number	Block Ratio	Visibility Ratio
One	4	8/9 = 88.8%
Two Three (submitted)	3 4	1 = 100% about 50%

Pattern One

 

Pattern Two

Pattern Three

Summary Recommendation

It’s important to remember that ore tends to occur in veins, not just one-block pieces here and there. As such, the 89% visibility ratio of Pattern One will likely not result in any ore being missed – even if there is ore in the narrow areas of the ground that are unseen, it is likely that the ore would be in a vein that extends at least one block up, down, left or right, which would make the vein visible in a tunnel.

In other words, Pattern One is much more unlikely to actually miss ore than it’s visibility ratio suggests. Because of this and its block ratio advantage, Pattern One is commonly thought to be the most effective mining pattern, while Pattern Two is usually relegated to multiplayer server mines which are used by multiple people, when efficiency is less important and a perfect visibility ratio is desired.

Update: In terms of time efficiency, Pattern Three is actually the most effective. Since it is highly likely that ore appears in clumps, trying to expose all the ore in an area is actually unnecessary. In other words, tunnels have two ways of exposing ore: one is direct exposure, in that you can see the blocks directly, and the other is indirect exposure, where you can't see the block but blocks around it have been directly exposed so you can just assume that it isn't ore. Pattern Three takes advantage of indirect exposure to let the miner use fewer tunnels to excavate the same area.

Final Note: One must consider how to get to those upper mines from the shaft. A lot of miners angle their shaft upwards in the direction of the tunnels, producing a form of stairs and making their access shaft take the form of an italic v, or rather by a plane intersecting the vertical plane at a 45 degree angle. Alternatively, some miners might use ladders and many build staircases between floors in their access shaft.