allows a progressive narrowing of the jump length distribution around $N_{\mbox{\tiny{y}}}$ as the extensive phase evolves and the searcher gathers and accumulates information from the landscape. Since the player has perfect memory about his trajectory (visited cells remain open), trajectories that start with large displacements tend to create landscapes that are fragmented in patches of length $N_{\mbox{\tiny{y}}}$ in which long movements are inefficient. To show the existence of this feedback we split the data of the extensive phase in four subdivisions: (i) from jump 1 to 5, (ii) 6 to 10, (iii) 11 to 15, and (iv) 16 to the end. The distributions for each of these pieces are shown in Fig. \[nonst\]a, \[nonst\]b, \[nonst\]c and \[nonst\]d respectively, and they can be fitted by a family of gamma distributions (dashed lines in each panel) of decreasing mean, mode and variance (See Table \[tabla-partidas\] for numerical values of these parameters and details of the distributions). Then the total distribution of Fig. \[fig3\]a can be approximated by a gamma function defined in terms of the parameters of the distributions of the pieces (dashed line in Fig. \[fig3\]a). This approach shows an excellent agreement with a direct fitting of the whole extensive phase 