Previous research has shown that gamblers prefer numbers they choose themselves because this choice allows them to feel more in control of the (random) outcome. We identify other conditions under which people find numbers "special" (i.e., worthy of betting more on than other numbers). By manipulating gambling task type and assigning participants a number by an endogenous system outside their own control (as is done in numerology, astrology, and other paranormal systems), we find that indeed people prefer to bet on numbers derived from particular special systems. The mechanism underlying this preference is enjoyment with the task—not control. Further, the enjoyment associated with this "specialness" is related to the prevalence of certain types of numbers (i.e., numbers based on dates and names) in the fortune-telling world and not to other factors such as individuality or even belief in the associated system. We replicate these findings using actual money and show that this prevalence-to-enjoyment link already exists in memory for dates and names and is activated and strengthened by priming the fortune-telling systems relevant to those special random numbers. Finally, we present a model of special random numbers that integrates our findings with other determinants of valuation such as regret and subjective probability. Our results expand the realm of special random numbers beyond control. Our enjoyment model has implications not only for understanding gambling, but also for understanding how reasoning under uncertainty is influenced by little-understood phenomena (such as fortune-telling systems) without affecting subjective probability or actual beliefs.