In video recommendation, a critical component that determines the system's recommendation accuracy is the watch-time prediction module, since how long a user watches a video directly reflects personalized preferences. One of the key challenges of this problem is the user's stochastic watch-time behavior. To improve the prediction accuracy for such an uncertain behavior, existing approaches show that one can either reduce the noise through duration bias modeling or formulate a distribution modeling task to capture the uncertainty. However, the uncontrolled uncertainty is not always equally distributed across users and videos, inducing a balancing paradox between the model accuracy and the ability to capture out-of-distribution samples. In practice, we find that the uncertainty of the watch-time prediction model also provides key information about user behavior, which, in turn, could benefit the prediction task itself. Following this notion, we derive an explicit uncertainty modeling strategy for the prediction model and propose an adversarial optimization framework that can better exploit the user watch-time behavior. This framework has been deployed online on an industrial video sharing platform that serves hundreds of millions of daily active users, which obtains a significant increase in users' video watch time by 0.31% through the online A/B test. Furthermore, extended offline experiments on two public datasets verify the effectiveness of the proposed framework across various watch-time prediction backbones.