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Slider comments on The ganch gamble - Less Wrong Discussion
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The mirrored side breaks the rooms usage as a tiled room. If you walk in you will see your reflection and see less of the pattern than if the details were actually copied. Design that doesn't survive use. The "wit" is more smartass than wise.
One could also argue that by the same logic having both halfs as mirrors would have been a superior room as it would have been way more repetetive. That highlights that it is more concept art than esthetics.
It's worse than that; it doesn't work at all. To give the impression of an exact copy of the other side's ornamentation you'd need a mirror across the middle of the room. But I take it the literal meaning of the story is not really the point and it's not very important that it wouldn't work in real life.