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Cycle-to-cycle variation in combustion phasing and combustion rate cause knock to occur differently in every cycle. This is found to be true even if the end gas thermo-chemical time history is the same. Three cycles are shown that have matched combustion phasing, combustion rate, and time of knock onset, but have knock intensity that differs by a factor of six. Thus, the prediction of knock intensity must include a stochastic component. It is shown that there is a relationship between the maximum possible knock intensity and the unburned fuel energy at the time of knock onset. Further, for a small window of unburned energy at knock onset, the probability density function of knock intensity is self similar when scaled by the 95th percentile of the cumulative distribution, and log-normal in shape.