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Symmetry of information states that $C(x) + C(y|x) = C(x,y) + O(\log C(x))$.We show that a similar relation for online Kolmogorov complexity does not hold.Let the even (online Kolmogorov) complexity of an n-bitstring $x_1x_2... x_n$be the length of a shortest program that computes $x_2$ on input $x_1$,computes $x_4$ on input $x_1x_2x_3$, etc; and similar for odd complexity. Weshow that for all n there exist an n-bit x such that both odd and evencomplexity are almost as large as the Kolmogorov complexity of the wholestring. Moreover, flipping odd and even bits to obtain a sequence$x_2x_1x_4x_3\ldots$, decreases the sum of odd and even complexity to $C(x)$.

Asymmetry of the Kolmogorov complexity of online predicting odd and even bits