  We show that a pair of Kolmogorov-Loveland betting strategies cannot win on
every non-Martin-L\"of random sequence if either of the two following
conditions is true:
  (I) There is an unbounded computable function $g$ such that both betting
strategies, when betting on an infinite binary sequence, almost surely, for
almost all $\ell$, bet on at most $\ell-g(\ell)$ positions among the first
$\ell$ positions of the sequence.
  (II) There is a sublinear function $g$ such that both betting strategies,
when betting on an infinite binary sequence, almost surely, for almost all
$\ell$, bet on at least $\ell-g(\ell)$ positions among the first $\ell$
positions of the sequence.
