Cut a Rock companion
Cut a Rock Nova Prism Odds
Nova Prism sits at 0.1% on both readable room boards. That is one in a thousand rocks, so half of the players who break 693 rocks will still have none.
9.5%
693
2,302
Breaking 100 rocks at a 0.1% Nova Prism rate gives a 9.5% chance of at least one Nova Prism. Each rock is rolled separately, so the arithmetic assumes the rolls are independent and that the board's 0.1% applies to every rock in the room.
Room 2 and Room 3 print the same 0.1% figure, so the room choice changes what you mine alongside the Nova Prism, not the Nova Prism odds.
What the number means
The calculation is 1 minus 0.999 to the power of the rocks you break. It assumes every rock is an independent 0.1% roll, which is the reading the floor board supports, not a mechanic the developer has documented.
Room 3 adds a 15% Rare slot that Room 2 does not have, so the two rooms differ in what you get alongside a Nova Prism, not in the 0.1% itself. If you are mining for the Prism alone, pick the room where the other slots sell or cut better for you.