Laser-induced damage threshold determination as a function of the number of incident pulses on a specific optic is a classic problem in laser damage studies. There are several models of the fundamental mechanisms explaining the fatigue laser damage behavior including temperature accumulation and changes of electronic or chemical material structure. Herewith we discuss the effects of unstable laser radiation on S-on-1 laser-induced damage probability. Numerical simulations of S-on-1 measurements for specific cases of defect densities, spot sizes and beam jitters are performed. It is demonstrated that the statistical effects of {\textquotedbl}pseudo-accumulation"reasoned by unstable laser radiation in transparent dielectrics containing nanometer sized defects leads to accumulation-like behavior. The magnitudes of the random beam walking and the energy fluctuations are directly related to the damage probability. Experimental results are also introduced to illustrate the theoretical results.