  We study a one-dimensional random walk with memory. The behavior of the
walker is modified with respect to the simple symmetric random walk (SSRW) only
when he is at the maximum distance ever reached from his starting point (home).
In this case, having the choice to move farther or to move closer, he decides
with different probabilities. If the probability of a forward step is higher
then the probability of a backward step, the walker is bold, otherwise he is
timorous. We investigate the asymptotic properties of this bold/timorous random
walk (BTRW) showing that the scaling behavior vary continuously from
subdiffusive (timorous) to superdiffusive (bold). The scaling exponents are
fully determined with a new mathematical approach.
