(full line in Fig. \[fig3\]a).

At this point, we have shown the existence of an optimal size for the neighborhood of the target, as well as an improvement in the search efficiency when the value of $N_{\mbox{\tiny{y}}}$ is revealed at the beginning of the round. In addition, these informed strategies evolve through information gathering during the extensive phase towards a dominant jumping distance equal to the lateral length of the neighborhood of the target, $N_{\mbox{\tiny{y}}}$. In the following sections we develop a theoretical framework and a family of models based on random walks to study the basic principles behind these results and how they can be transfered to more general scenarios, with irregular shapes for the information region.

Model for blind searchers: numerical simulations and analytical approximation {#model-for-blind-searchers-numerical-simulations-and-analytical-approximation .unnumbered}
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We develop a minimalistic searching model based on random walks to explain previous experimental results on the basis of simple dynamical rules. The model has the three main ingredients obtained from the data analysis: (i) two modes of movement defined by the mean length of the displacements: $1/\lambda_{\mbox{\tiny{int}}}$ and $1/\lambda_{\mbox{\tiny{ext}}}$; (ii) in the absence of any information (no yellow cell clicked) the direction is completely random (uniform distribution in the 