The Lévy-flight model extends the diffusion model by introducing the α-parameter, which shapes the noise distribution in evidence accumulation during binary decision-making. Lower α-values correspond to heavier-tailed noise distributions, allowing for sudden, large changes or “jumps” at any stage of the accumulation process. Although it has been shown that α can enable more accurate data fits, its psychological interpretation remains underexplored. This study investigates whether α captures guessing behavior, particularly sophisticated guessing. Sophisticated guessing is based on partial information and thus involves some accumulation of evidence. We hypothesize that lower α-values, and therefore more frequent jumps, are associated with increased guessing. Across multiple studies, we encouraged or discouraged guessing through instructions. Study 1 employed a brightness discrimination task in which α-values did not significantly differ between conditions. This unexpected result might be due to high stimulus ambiguity driving consistent guessing across both conditions. To address this, Study 2 employed a numerical mean-value computation task that allowed participants to achieve varying levels of confidence by considering either full or partial information. Here, participants exhibited lower α-values when instructed to make educated guesses, supporting the interpretation of α as an indicator of sophisticated guessing. These findings provide preliminary evidence that α may serve as a tool for detecting guessing behavior, with practical applications, such as the exclusion of inattentive participants.