  We predict that the four-loop contribution \beta_3 to the QCD \beta function
in the MS-bar prescription is given by
  \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where
N_f is the number of flavours and the coefficient of N_f^3 is an exact result
from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we
estimate \beta_3 = (7.6 \pm 0.1) x 10^3. We discuss our estimates of the errors
in these QCD predictions, basing them on the demonstrated accuracy of our
method in test applications to the O(N) \Phi^4 theory, and on variations in the
details of our estimation method, which goes beyond conventional Pade
approximants by estimating and correcting for subasymptotic deviations from
exact results.
