There is a complex interaction between short- and long-term statistics of earlier percepts in modulating perceptual decisions, yet this interaction is not well understood. We conducted experiments, in which we independently manipulated the appearance probabilities (APs) of abstract shapes over short and long time ranges, and also tested the effect of dynamically changing these probabilities. We found that, instead of simply being primed by earlier APs, subject made decisions so that they reduced the discrepancy between recent and earlier APs. Paradoxically, this leads to favor the less frequent recent event if it was more frequent in the long past. Moreover, this compensatory mechanism did not take effect when the difference in APs between long past and recent times was introduced gradually rather than abruptly. This leads to a paradox false and lasting negative compensation with uniform APs after a momentary abrupt shift followed by a gradual return. We replicated our key human finding with behaving rats, de onstrating that these effects do not rely on explicit reasoning. Thus instead simply following the rule of gradually collected event statistics, perceptual decision making is influenced by a complex process in which statistics are weighted by significance due to detected changes in the environment.