Marble

① First, let's clear up the meaning of “marble.” It can mean “marble” as in “a marble floor” or “a marble pillar.” It can also mean “marble” as in a small glass ball. Let's leave it at this for now.
② Next, let's clear up the meaning of “clustering illusion.” When you search for this term along with the word “probability” you can find an example about a jar which is filled with marbles of two colors, white and black. After you fill the jar and mix up the marbles inside, instead of the marbles appearing like a chess board, with the colors equally and evenly mixed together in a checker pattern, you will notice clumps of white marbles and clumps of black marbles here and there in the jar. These clumps, which seem non-random, despite actually being randomly distributed, are the clustering illusion.
③ From the above explanation you can see that the term marble comes from marble in the glass ball sense, not the marble floor sense of the word.
④ Even in a situation where you have half black marbles and half white ones and you mix them up, “logically” you assume that the white and black should be evenly mixed since there are equal amounts, but when you check the result you don't see an even mix, you see clumps and groups in the pattern. This is precisely where clustering illusion comes in, and the result of a series of random coincidences may seem as though it was purposefully realized by someone, despite it actually being a natural phenomenon1. So when probability itself is being interfered with, one might understand that materializing Brunstud Castle might not be so implausible (through a perfect series of “natural” and “random” coincidences brought about by the reality marble or marble phantasm).
Accordingly, when the world is connected with a marble phantasm or reality marble, probability is interfered with, and a series of phenomena, which could only ever be considered to be random coincidences, is deliberately generated.

Colorful MOON Tsukihime: Tsukihime Glossary
Translator's Notes
  1. ^ Like a rock that looks as though it were shaped by a human into a cat shape, but it was actually just from natural erosion over time.