I find that there is almost no way to scramble and find a pair matched with at least one color.

They don't necessarily have to be already matched to be an easy case. If when you solve your cross the way you normally would you have a set of 2 pieces belonging to a pair that can be matched/inserted in a few moves, that's also an easy case. Similarly, if you can modify your cross by a few moves to end up with an already solved pair in place (x-cross) that's also an easy case.

The point was mainly that there are a finite number of scrambles that can be put on the puzzle. X% of them have an fast/easy cross/X-cross or easy first pair for white, X% have afast/easy cross/X-cross or easy first pair for blue etc. So for every color you

*can *start on, you are adding a percentage chance of getting a case that is faster than if you couldn't start on that color. If we assume it's equally likely to find a good cross/x-cross case per color, you're essentially giving yourself 6*that percentage to find a good case if you can start from any side.

It would be hard to find what this percentage actually is, because the definition of 'easy cross' 'easy x-cross' and 'easy first pair' are all very liquid, but it stands to reason that having 6 possible starting sides is 6x more likely to find a good start.

Chris