We study the preference for strategic uncertainty when subjects play matching pennies and coordination games. The scanned subject has the option to ‘play’, in which case both receive outcomes according to their moves, or ‘opt-out’ and receive the same sure amount along with the ‘opponent’ outside the scanner for whom half the trials are relegated to a die. Having an ‘opt-out’ option enables us to estimate subjects’ certainty equivalent under four types of uncertainties—game (matching pennies versus coordination) × play (strategic versus random). Our observation of subjects valuing playing coordination more than matching pennies supports a preference for shared plight in the income inequality literature. This preference is modulated by whether subjects face conscious or random play. Specifically, in matching pennies, subjects require a premium to play when the opponent makes a conscious move compared with a random move. Yet, they are willing to accept a discount to play coordination strategically rather than randomly. In accounting for the observed differential risk preferences, our brain imaging results distinguish an explanation drawn from source preference, which is self-regarding, from one based on social preference under uncertainty, which is other-regarding. We observe that activations in the amygdala and the orbital prefrontal cortex are modulated by the game × play interaction, extending previous finding of their association with decision making under ambiguity. Finally we employ a source-dependent expected utility model to analyze the behavioral and imaging data and find that the value of playing the various games is encoded in the striatum.