  Context: We investigate the distribution of optically high and low states of
the system AM Herculis (AM Her).
  Aims: We determine the state duty cycles, and their relationships with the
mass transfer process and binary orbital evolution of the system.
  Methods: We make use of the photographic plate archive of the Harvard College
Observatory between 1890 and 1953 and visual observations collected by the
American Association of Variable Star Observers between 1978 and 2005. We
determine the statistical probability of the two states, their distribution and
recurrence behaviors.
  Results: We find that the fractional high state duty cycle of the system AM
Her is 63%. The data show no preference of timescales on which high or low
states occur. However, there appears to be a pattern of long and short duty
cycle alternation, suggesting that the state transitions retain memories. We
assess models for the high/low states for polars (AM Her type systems). We
propose that the white-dwarf magnetic field plays a key role in regulating the
mass transfer rate and hence the high/low brightness states, due to variations
in the magnetic-field configuration in the system.
