There's more to Gambit than you realize, and that was what I was asking. I'm actually getting at the actual patterns.
xox
oxx
as opposed to
oxx
oxx
In both instances, the rate of any given box is 1/3, but if you had them as back-to-back patterns, you would find that the rates for my completely made up example are
Upper left 1/2
Upper middle 1/2
Upper Right 0/2
Lower Left 2/2
Lower Middle 0/2
Lower Right 0/2
In actuality, I felt like the lower middle or upper right were 'correct' more often than other boxes. So I'm wondering if anyone else noticed a similar trend.
I assume that each possible pattern has exactly one permutation in the rotation, and the patterns are picked randomly. But I never kept data. It would be interesting to actually record where they ended up just to see if one box had a statistical advantage over the others.