Ore

Ore is a block type in Minecraft. Ores are primarily collected for crafting purposes, such as pickaxes, shovels, and more. Redstone ore is used as a type of "wiring", which can be used to create redstone circuits, compasses and clocks. Ore can also be combined to create a block of the material's type for iron, gold, diamond, and lapis lazuli. Blocks are expensive, requiring nine of each ore to create, and are mainly recommended for storage purposes or building.

Availability
In Minecraft Beta, the following is the distribution of ores according to the altitude. (Layers are number of blocks above the lowest layer of bedrock.) * These points are above the maximum map height, and were extrapolated based on the pattern of (2^n, [2^n]+1 to [2^n]+3, [2^n]+4).

Redstone has the same layer and line-size statistics as Diamond, but is generated 8 times per chunk as opposed to 1.

Ore is created by picking two points a certain distance apart, drawing a line between the points, and filling in any Stone blocks within a certain distance of the line with the ore being done in that round. Source (Section 3.11)

Ore also varies depending on the section of the map it is generated in, due to a bug in the spawning algorithm. In the quadrant south-west of the point (0,0), ore spawns approximately 50% more than in the quadrant north-east of the point (0,0). The quadrants north-west and sout-east of the point (0,0) split the difference between the extremes. (See image below)

Minecraft Classic
In MineCraft Classic, you can find exposed Coal, Gold and Iron in large amounts, from roughly 10 to 30 in a vein. Lapis Lazuli, Diamond & Redstone are not found because they were added in a later update.

Erze Rudy