Edward A. answered • 04/05/18

Math Tutor, Retired Computer Scientist and Technical Communicator

Anna, here are two generalizations that may help:

* each branch has the probability 1/2

* each complete path to a win has the probability of (1/2) to the power of the length of the path. That is, if there are only two more games, the probability of the path is (1/2) to the power 2, or 1/4

now here are the remaining paths

BBB

BBPB

BBPP

BPBB

BPBP

BPP

PBBB

PBBP

PBP

PP

BBPB

BBPP

BPBB

BPBP

BPP

PBBB

PBBP

PBP

PP

Now write down the path probability next to the path, add up the ones that end in P.