Murakami (2009) demonstrated the tendency toward underestimating the possible success of uncertain events after "lucky" events in terms of "Luck Resource Belief." However, this notion does not necessarily entail a consequent decision to avoid a high-risk option due to low expectations. A "relativity hypothesis of luck" has been proposed to explain this tendency from the perspective of the relative value of several relevant events. This hypothesis suggests that a lucky result by itself does not carry a negative value. Indeed, when considerations include future outcomes, the value of the lucky outcome shifts, which demonstrates relative cognitive change. To examine this change and the tendency to assign value to lucky results, we distributed questionnaires (Study 1) and conducted an experiment involving predictions about the actual outcomes of World Cup soccer matches (Study 2). The results indicated that the occurrence of a lucky event before subsequent important events was associated with avoidance of a high-risk option only for respondents with a "Luck Resource Belief," because this belief involves devaluing the lucky outcome before subsequent important events. These results support the "relativity hypothesis of luck" and are discussed in terms of their implication for anticipated regret.