So, I have recently gotten into speed-cubing, and I ran into a very interesting problem.
According to the World Cube Association, a cube is legal if it takes at least two moves to solve. So, I want to find the probability that any given Rubik's Cube is solvable in two moves.
So, I wanted to find out the probability that you get a cube that is solvable in exactly two moves, as a figure like that could put in perspective how much luck is involved in speed-cubing. I have no idea where to start because I have no idea how probability works except for the stuff you learn in high-school and early college.
Any ideas where to start?
According to https://www.cube20.org/, there are 243 positions (in half turn metric) exactly two moves away from solved. And there are 43,252,003,274,489,856,000 possible positions, so there is a 1 in 177,991,783,022,592,000 chance of randomly getting a cube that can be solved in exactly 2 moves, or about .0000000000000000056%