  We report large systematic errors in Monte Carlo simulations of the
tricritical Blume-Capel model using single spin Metropolis updating. The error,
manifest as a $20\%$ asymmetry in the magnetisation distribution, is traced to
the interplay between strong triplet correlations in the shift register random
number generator and the large tricritical clusters. The effect of these
correlations is visible only when the system volume is a multiple of the random
number generator lag parameter. No such effects are observed in related models.
