Kolmogorov-Loveland randomness vs Martin-Löf randomness

A sequence $X \in 2^\mathbb{N}$ is Kolmogorov-Loveland random (KL-random for short) if no computable non-monotonic betting strategy can win infinitely much money playing against it. A sequence $X \in 2^\mathbb{N}$ is Martin-Löf random (ML-random for short) if no c.e. monotonic betting strategy can win infinitely much money playing against it.

• Muchnik, Semenov and Uspensky proved that Martin-Löf randomness implies Kolmogorov-Loveland randomness.
• Merkle, Miller, Nies, Reimann and Stephan proved that if $X$ is KL-random then $X$ has arbitrarily dense subsequences which are ML-random.

This is often considered one of the most significant open problems in algorithmic randomness and has been open for close to 30 years.