  We introduce the sequence-set betting game, a generalization of An. A.
Muchnik's non-monotonic betting game. Instead of successively partitioning the
infinite binary strings by their value of a bit at a chosen position, as in the
non-monotonic game, the player is allowed to partition the strings into any two
clopen sets with equal measure. We show that, while there is no single
computable sequence-set betting strategy that predicts all non-Martin-L\"of
random strings, we can construct two strategies such that every
non-Martin-L\"of random string is predicted by at least one of them.
