Square-1: Probability of Occurrence?

[Abel]

Hi. I just wonder if anybody knows, or has calculated the square-1's probability of occurence for the cube shapes? I mean which shape has the highest probability to occur and which has the lowest?

 

[TMOY]

Well, for a given shape you always have 8! ways to permute corners, 8! ways to permute edges and 4 configurations of the middle layer. It has to be divided by the order of symmetry of the shape, that is the number of such configurations which are identical up to moves of the U and D layers and/or cube flipping. Then the most likely are the shapes with no symmetry at all, and the less likely is the cubeshape which has order 32 (4 on each layer + cube flipping).

 

[Lucas Garron]

I have. Thread. Distribution CSV.

 

[Abel]

Well, for a given shape you always have 8! ways to permute corners, 8! ways to permute edges and 4 configurations of the middle layer. It has to be divided by the order of symmetry of the shape, that is the number of such configurations which are identical up to moves of the U and D layers and/or cube flipping. Then the most likely are the shapes with no symmetry at all, and the less likely is the cubeshape which has order 32 (4 on each layer + cube flipping).

Thanks for the reply.

I have. Thread. Distribution CSV.

Thank you very much this is what I was searching for!