Optimal shrinkage straight from the signal-to-noise ratio

You shrink a noisy estimate $x$ toward an anchor $b$ using $\hat\mu = w\,x + (1-w)\,b$. Instead of the raw numbers, you are told the signal-to-noise ratio, defined as the squared distance from the anchor over the noise variance: $\text{SNR} = d^2/\sigma^2 = 3$.

What weight $w$ minimizes the mean squared error?