How far is Kolmogorov-Loveland randomness from Martin-Löf randomness?

We’ll call a map from basic to clopen sets of binary sequences an $\mathit{\text{encoding}}$ if it preserves uniform Lebesgue measure and the disjointedness relation. For some notion of randomness $R$ we can ask if there is a computable encoding $E$ such that for every non-Martin-Löf-random (non-MLR) sequence $\alpha$, the sequences in $E(\alpha )$ are non-$R$. Thus we can use $E$ and randomness test for $R$ to construct a randomness test for MLR. We show that there is no such $E$ for partial computable randomness (PCR), but there is one for Kolmogorov-Loveland randomness. Indeed, there is a total computable $E$ and a pair of total computable non-monotonic betting strategies such that on every sequence in $E(\alpha )$ at least one of the strategies wins whenever $\alpha$ is non-MLR.