I'm not a virologist, so don't take my thoughts on this as gospel, but no, I dont think you're technically correct. The cyclical nature of viruses is not the result of purely random, independent events (e.g., rolling a 27-sided die). Instead, viruses exist either in the human population as Influenza A/B/C, or in natural "reservoirs" in harmless form to their host animal (swine, monkey, bird, etc.) Over time, various genetic mutations occur randomly resulting in antigen drift, which in turn result in differences in lethality, transmissibility, inter-species transmissibility, etc. Antigen drift is not a random, independent event; it is a cumulative progression, and thus a dependent process. So the "cycle" of pandemic depends not on "pure luck" but rather a predictible sort of progression. This is why the 1957 Asian flu was followed by the 1968 Hong Kong flu. Efforts to predict flu pandemic is tricky. In 1972, there was a scare over swine flu that turned out to be the pandemic that never happened. More recently, virologists have gotten better at predicting drift, and in recent years, they have been able to look at all of the emerging flu strains worldwide, and predict with great accuracy which antigen combination should be used for vaccination. Recent evidence from the field suggests that avian flu (which as you know is the same sort of flu that caused the 1918 pandemic) has jumped from chickens to humans. Interspecies jump is a big step. The next big mutation that people are concerned about is human-to-human transmissibility via aerosol. When this happens, you get a pandemic. When the strain also has high lethality like the H5N1 variant appears to have, you get a superflu.