  We consider a simple random walk W_i in 1 or 2 dimensions, in which the
walker may choose to stand still for a limited time. The time horizon is n, the
maximum consecutive time steps which can be spent standing still is m_n and the
goal is to maximize P(W_n=0). We show that for dimension 1, if m_n grows faster
than (\log n)^{2+\gamma} for some \gamma>0, there is a strategy for each n such
that P(W_n = 0) approaches 1. For dimension 2, if m_n grows faster than a
positive power of n then there are strategies keeping P(W_n=0) bounded away
from 0.
