Turbulent wind and stochastic waves—the main sources of environmental loading on floating wind turbine (FWT) structural components, significantly contribute to uncertainty in the characterisation of design load values. Given there is an infinite number of possible realizations of these environmental states, a minimal number of wind and wave seeds that ensures an acceptable convergence of ultimate loads and fatigue damage is sought. Especially as this uncertainty undermines the robustness of reliability calculations. This paper addresses this issue by carrying out in-depth statistical bootstrap analysis. Recommendations on the minimum number of wind and wave seeds are subsequently made at 95% confidence level.