Take a look at the autocorrelation of the parameter that you want to calculate. Say the value of parameter x at the Monte Carlo step n is x(n). Form the autocorrelation:

a(m) = for n in range(n_steps - m)

If a(m) shows an exponential decay with the form a(m) ~ exp (-m/M) then you should be able to get reliable average values of x with some M number of steps. If the autocorrelation is oscillatory, then it seems that increasing sampling steps wouldn't help and you need to accept an error margin.