When Do Antithetic Variates Help?

You estimate $\mathbb{E}[f(Z)]$ for $Z \sim N(0,1)$ by averaging $\tfrac12\big(f(Z_i) + f(-Z_i)\big)$ over $N/2$ independent draws (antithetic variates), using the same total number $N$ of function evaluations as plain Monte Carlo.

In which case is the antithetic estimator guaranteed to have lower or equal variance than plain Monte Carlo?