Nope, I still do not follow your explanation Ginger. Thanks for your effort though.
Your table of what can happen with any one turn is helpful and easy to understand.
After that I am lost.
I did go off on a tangent and found that in any 2 consecutive goes:
the prob of throwing 6 heads and NOT 2 sixes is (50+5)/(48*48) = 55/2304
And the prob of throwing 2 sixes and NOT 6 heads is (56+7)/(48*48) = 63/2304
I do not know what to do with that ...
I am just trying to show you my train of thought.
I do not care if you give up but if you want to explain what you are saying clearly I will try and understand.
Perhaps Pangolin14 has a class solution that can be shared with us both?