1st solution (intuitive one):

AA, ABA, ABBA, BAA, BABA, BBAA -> A wins

BBB, BBAB, BABB, ABBB -> B wins

calculate probabilities to each sequence and add up per player

2nd solution (counterintuitive):

Game will end in at most 4 games:

AAAA -> A wins

AAAB AABA ABAA BAAA -> A wins

AABB ABAB ABBA BAAB BABA BBAA -> A wins

ABBB BABB BBAB BBBA -> B wins

BBBB -> B wins

#combos a player wins/total number of 4 game combos (16) yields the same solution.

Solution 2 gives me troubles. Can you give me an intuition why it is valid and why it is equivalent to solution one?

Thanks