Every ore block in several generated worlds, the density readings a player would get over them, and tens of thousands of simulated vertical shafts per strategy. The simulated player only knows what the game tells them: node-search counts and ore they can see on a wall. The question: given the reading where you stand, how should you dig, and how much ore should you expect per point of tool durability?
The blue field is the density reading a player gets anywhere on the map. Rings are real ore bodies of 5 or more blocks, sized by block count. Axes are in blocks from the survey's north-west corner; faint lines mark the game's 512-block map regions. The reading comes from a smooth noise map, not from the blocks, so it shows where deposits are likely, not where each one is.
Your current method at every shaft location: dig to bedrock, node search every 6 blocks at radius 6, and chase every hit with the direction-finding routine below. Grouped by the density reading at the top of the shaft; grey dots are the individual worlds.
A density reading costs 3 durability (three samples a few blocks apart). The simulated prospector walks in a straight line from a random spot, taking a reading every so many blocks, until one reaches the target word. Then they climb: take four compass readings a set distance out and step to the best, while it keeps improving.
Each bar is one strategy run over every shaft location in every world, digging to bedrock. "R6 every 6" is your current method: node search radius 6, one probe every 6 blocks down. Strategies at your world's radius are drawn in colour; small ticks show each world separately.
A node search tells you how many ore blocks are nearby, not where they are. But the count is a hard-edged box: a probe sees ore only if it is within R blocks up or down. So the highest probe that still counts ore sits exactly R blocks above the deposit's top, and the shaft above you is already dug, so finding that height costs only probes. The simulated player uses this routine, and nothing else, every time a probe finds the target ore:
Same shafts, stopped at a fixed depth below the surface block you started from. That depth is also the number of rope ladders you need, so you can hold it without seeing your Y coordinate.
Side arms: after the first probe that leads to a deposit, dig four tunnels of the given length from the shaft at that level, probing every 2R+1 blocks. “Each hit” repeats that after every such probe.
Grids of 4×4 shafts dug one after another at a fixed spacing, each ore with its recommended method (R6 every 13, stopping at its best depth). Anything an earlier shaft mined is gone for the later ones. The chart shows how much ore a later shaft still gets, as a share of what the same shaft finds on untouched ground.
Average cumulative ore against durability spent, following the shaft down. Dots mark every 24 blocks of depth. A line that flattens means the rest of the shaft mostly costs durability.
Left: once a shaft has found its first deposit, compare the ore you get by digging on down with what a brand-new shaft at the same reading would give on average. Right: how often another deposit of the same ore sits within a given distance, measured from a deposit and from a random spot.