player can limit the search area. The position of this area, as well as the location of the target inside it, is random, changes from round to round and is unknown to the player.

Data from $230$ rounds were collected. As a general result, *a priori* information accelerates the search and reduces its stochasticity. Blind searchers need on average $31.30$ clicks to find the target when $N_{\mbox{\tiny{y}}}=5$ (subset of $65$ rounds from the $500$ trajectories analyzed for blind experiments, see Supplementary Table I ), while informed players use $25.5$ clicks. The two-tailed P value on the difference of these mean values obtained using an unpaired t-test, $3\times10^{-4}$, is highly statistically significant. The standard deviation also decreases, indicating a narrowing in the distribution of the number of displacements and therefore in the randomness of the process: $\sigma_{\mbox{\tiny{b}}}=14.10$ for blind searchers and $\sigma_{\mbox{\tiny{i}}}=10.50$ for the informed ones. To find out what stage of the search is more strongly affected by the initial information, we analyze the number of clicks done in each phase of the search. We repeat this factorization for the blind and the informed cases and compare both of them (Fig. \[split\]). From Fig. \[split\]b and \[split\]c, we observe that 