Dependence of forward Zeckendorf game strategies on reverse game winners

Let the forward and reverse Zeckendorf games be played from corresponding starting positions, with each game having a winning player under optimal play. Forward–reverse Zeckendorf conjecture. The winning strategy for the forward Zeckendorf games is dependent upon who wins the reverse Zeckendorf game. This conjecture proposes a relationship between the winning structures of the forward and reversed games; the source does not provide a resolution.