The most improbable thing you've ever seen?

[Borodog]

[ QUOTE ]
It should be noted that you didn't actually randomly "solve" the cube, but rather your pattern-seeking brain noticed it was one permutation away from being solved. Therefore, to calculate the probability of the event, you need to consider the set of all configurations no more than one permutation away from every "solved" state, which includes the number of solved states as a subset.

I haven't done the calculation, but maybe this expands the set of all relevant configurations enough to make the event not as improbable as you first thought.

[/ QUOTE ]

It expands it by a factor of 27, since there are only 27 possible rotations from any state.