To guarantee safe and robust deployment of large language models (LLMs) at scale, it is critical to accurately assess their adversarial robustness. Existing adversarial attacks typically target harmful responses in single-point, greedy generations, overlooking the inherently stochastic nature of LLMs. In this paper, we propose a novel framework for adversarial robustness evaluation that explicitly models the entire output distribution, including tail-risks, providing better estimates for model robustness at scale. By casting the attack process as a resource allocation problem between optimization and sampling, we determine compute-optimal tradeoffs and show that integrating sampling into existing attacks boosts ASR by up to 48% and improves efficiency by up to two orders of magnitude. Our framework also enables us to analyze how different attack algorithms affect output harm distributions. Surprisingly, we find that most optimization strategies have little effect on output harmfulness. Finally, we introduce a data-free proof-of-concept objective based on entropy-maximization to demonstrate how our tail-aware perspective enables new optimization targets. Overall, our findings highlight the importance of tail-aware attacks and evaluation protocols to accurately assess and strengthen LLM safety.