Average value of Phi at a standard normal draw

Let $X$ be standard normal and let $M$ denote the standard normal cumulative distribution function. Compute $\mathbb{E}[M(X)]$.

$1/2$. Applying a continuous variable's own CDF to it gives a uniform on $[0,1]$ (probability integral transform), whose mean is $\tfrac12$. Equivalently, $M(X)=\mathbb{P}(Y\le X\mid X)$ for an independent copy $Y$, and $\mathbb{P}(Y\le X)=\tfrac12$ by symmetry.