The Copier and the Blind Guesser

A denoising autoencoder is being trained on a tiny dataset of four strips. Each strip is 4 pixels long, with brightness from $0$ to $1$:

Before a strip reaches the network, each of its pixels is knocked out (set to $0$) independently, with probability $p$. The target is always the clean strip.

A network's score is its reconstruction loss (subtract, square, average over the 4 pixels), averaged over the four strips and over the random knock-outs. In other words, it is the loss the network gets on average.

Two lazy networks have learned nothing about strips:

• the copier outputs exactly the corrupted strip it was given;
• the blind network ignores its input entirely and always outputs the same strip, namely the single strip that gives it the lowest possible score on this dataset.

When the damage is light, the copier scores better.

At what knock-out probability $p$ do the two networks score exactly the same?

Round to 2 decimal places.