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I was thinking... Diamonds spawn in veins, but if two or more veins spawn next to each other, it looks like one larger vein, even though technically it is multiple veins.

The largest possible size for a single diamond vein is 10. Also, only one vein spawns per chunk. If there is a corner between 4 chunks, then theoretically it is possible for 4 veins of size 10 to converge on that one spot. They would all have to touch each other but not overlap. This would create a "vein" of 40 diamond ores.

Any diamond vein has approximately a 1 in 200 chance to be a 10-vein. (I think).

Given any chunk, the probability that the diamond vein spawns in a specific corner is about 1 in 100 (which is mostly a guess)

Given any four diamond veins, the probablility that they are roughly the same height above bedrock is about 1 in 500 (which is another guess)

So we have 200^4 * 100^4 * 500 = 1 in 80,000,000,000,000,000,000 chance

But the chance that a cave system or something else will break the diamond vein is about 1 in 4 (which is another guess), which will decrease the chance to about 1 in 100,000,000,000,000,000,000. (1 in 100 quintillion).

There are 18,446,744,073,709,551,615 possible seeds in Minecraft (18 quintillion).

So if we checked every possible seed, and looked at the 4 chunks around spawn, we would be lucky to find even 1 vein of 40 diamond.

However, if we checked the chunks within 100 blocks or so of spawn for each seed (or about 156 chunks per seed), we would be checking 18,446,744,073,709,551,615 x 156 = 2,877,692,075,498,690,051,940 (2.8 sextillion) chunks.

In those chunks, we expect to find 2,877,692,075,498,690,051,940 divided by 100,000,000,000,000,000,000, or about 29 veins of 40 diamond.

To look at it another way, a Minecraft world has (60,000,000/16) ^ 2 = 14,062,500,000,000 (14 trillion) chunks.

So if we took a million worlds, they would have 14,062,500,000,000,000,000 (14 quintillion) chunks in them, which is slightly more than the chance of a 40-diamond vein spawning. So that means, we might get 1 vein of 40 diamond if we searched through a million worlds completely, all the way to the world border.

Leave a comment if I did some of the math wrong! (Or if my guesses at the start are wrong.)

It is likely that no such vein exists because Java's Random only has 2^48 = 281 trillion unique states (it only uses 48 out of 64 bits) - this means that with about 14 trillion chunks in a world you only need about 20 worlds to exhaust every possible seed (assuming no overlap; even if two seeds have matching chunks they will be in different patterns so can appear very different). In fact, for any given seed there are 65535 other seeds that will have the exact same ore generation, aside from biome-exclusive ore (emeralds in Extreme Hills, additional gold in Mesa) and where biome-dependent structures generate (the same RNG is used for all chunk population and ores generate after structures so they will change the sequence when ores generate), since the upper 16 bits have no effect on most world generation (only the biome generator uses all 64 bits as it uses its own special RNG):

In a similar manner the chance of the largest possible single cave system (not considering the width and length of individual caves) in 1.6.4 is one in 8.8 x 10^52 chunks but such a thing likely does not exist because there are only 281 trillion unique seeds (if every chunk in every world were unique there would be 2.6 x 10^32 unique chunks, which would require a RNG with at least 108 bits).

I was thinking... Diamonds spawn in veins, but if two or more veins spawn next to each other, it looks like one larger vein, even though technically it is multiple veins.

The largest possible size for a single diamond vein is 10. Also, only one vein spawns per chunk. If there is a corner between 4 chunks, then theoretically it is possible for 4 veins of size 10 to converge on that one spot. They would all have to touch each other but not overlap. This would create a "vein" of 40 diamond ores.

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Any diamond vein has approximately a 1 in 200 chance to be a 10-vein. (I think).

Given any chunk, the probability that the diamond vein spawns in a specific corner is about 1 in 100 (which is mostly a guess)

Given any four diamond veins, the probablility that they are roughly the same height above bedrock is about 1 in 500 (which is another guess)

So we have 200^4 * 100^4 * 500 = 1 in 80,000,000,000,000,000,000 chance

But the chance that a cave system or something else will break the diamond vein is about 1 in 4 (which is another guess), which will decrease the chance to about 1 in 100,000,000,000,000,000,000. (1 in 100 quintillion).

There are 18,446,744,073,709,551,615 possible seeds in Minecraft (18 quintillion).

So if we checked every possible seed, and looked at the 4 chunks around spawn, we would be lucky to find even 1 vein of 40 diamond.

However, if we checked the chunks within 100 blocks or so of spawn for each seed (or about 156 chunks per seed), we would be checking 18,446,744,073,709,551,615 x 156 = 2,877,692,075,498,690,051,940 (2.8 sextillion) chunks.

In those chunks, we expect to find 2,877,692,075,498,690,051,940 divided by 100,000,000,000,000,000,000, or about 29 veins of 40 diamond.

--------------------------------------------------------------------------------------------------------------------------------------------------

To look at it another way, a Minecraft world has (60,000,000/16) ^ 2 = 14,062,500,000,000 (14 trillion) chunks.

So if we took a million worlds, they would have 14,062,500,000,000,000,000 (14 quintillion) chunks in them, which is slightly more than the chance of a 40-diamond vein spawning. So that means, we might get 1 vein of 40 diamond if we searched through a million worlds completely, all the way to the world border.

Leave a comment if I did some of the math wrong! (Or if my guesses at the start are wrong.)

It is likely that no such vein exists because Java's Random only has 2^48 = 281 trillion unique states (it only uses 48 out of 64 bits) - this means that with about 14 trillion chunks in a world you only need about 20 worlds to exhaust every possible seed (assuming no overlap; even if two seeds have matching chunks they will be in different patterns so can appear very different). In fact, for any given seed there are 65535 other seeds that will have the exact same ore generation, aside from biome-exclusive ore (emeralds in Extreme Hills, additional gold in Mesa) and where biome-dependent structures generate (the same RNG is used for all chunk population and ores generate after structures so they will change the sequence when ores generate), since the upper 16 bits have no effect on most world generation (only the biome generator uses all 64 bits as it uses its own special RNG):

http://www.minecraftforum.net/forums/minecraft-java-edition/seeds/2229720-can-two-different-seeds-produce-identical-worlds

In a similar manner the chance of the largest possible single cave system (not considering the width and length of individual caves) in 1.6.4 is one in 8.8 x 10^52 chunks but such a thing likely does not exist because there are only 281 trillion unique seeds (if every chunk in every world were unique there would be 2.6 x 10^32 unique chunks, which would require a RNG with at least 108 bits).

TheMasterCaver's First World - possibly the most caved-out world in Minecraft history - includes world download.

TheMasterCaver's World - my flagship mod which combines my own ideas with 1.7+ features, with emphasis on underground content.

Why do I still play in 1.6.4?