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As the Japanese name implies (空想具現化 Kuusou Gugenka), Marble Phantasm is the ability to materialize a phantasm, a vision.
It is the ability of an elemental or True Ancestor to connect their will to nature, to interfere on probabilities, and to transfigure the surrounding world at will according to their vision of the world. As the user is part of nature, he can change the world as he wishes, but in the end, what an elemental can act on is only something within the scope of nature. A transformation independent from nature (such as transforming a human) cannot be realized, unless done indirectly (animals can be managed).

In the settings of Tsukihime, the spiritual realm isn't a world separated from the real world, but localized regions thought of by the elemental that creates them; hence it is possible for a human to stray into it.

In the story, when Arcueid uses Marble Phantasm on Roa, she turns layers of the atmosphere in the corridor into a vacuum that cut him like a knife would a radish. Although Roa himself was not affected, there was no way to avoid being chopped in pieces by the atmosphere, and Roa only narrowly managed to remain as just his ankles - Arcueid's imagination didn't go as far as having the floor dislocate.
When not restricted, Arcueid can create a village in the mountains. But where humans have made changements, it will take more time to first break it down.

The Millenium Castle Brunestud in the mountain area that Arcueid lives in is a product of her Marble Phantasm.

Source: based on the Tsukihime Dokuhon PlusPeriod dictionary entry (p.178) and the dictionary resource at Jonnobi

The English name comes from a metaphor. When drawing a marble in a bag of black marbles with a 1% chance of drawing the one white marble, Marble Phantasm is the ability to raise that chance to 100% and definitely pick the white one amongst all the black ones; this remains within the laws of the world.

For comparison purpose, following a similar metaphor, a Reality Marble would be, on the other hand, the ability to turn all the marbles into white ones; this is something the world wouldn't naturally allow. While this can be considered to be more efficient, this is, however, the only one effect such a Reality Marble could specialize in.