  We study the biased $(2:b)$ Walker--Breaker games, played on the edge set of
the complete graph on $n$ vertices, $K_n$. These games are a variant of the
Maker--Breaker games with the restriction that Walker (playing the role of
Maker) has to choose her edges according to a walk. We look at the two standard
graph games -- the Connectivity game and the Hamilton Cycle game and show that
Walker can win both games even when playing against Breaker whose bias is of
the order of magnitude $n/ \ln n$.
