I expected this too, so I asked an LLM to write a quick Go program that would tell me how many bytes repeated. I created a 1.44MB file from /dev/random and then ran it through the program. Here are the bytes that repeat the most.

  Top 10 repeated byte patterns and their counts:
  Bytes: 7eda16, Count: 3
  Bytes: 65b1a4, Count: 3
  Bytes: 71d745, Count: 3
  Bytes: b72808, Count: 2
  Bytes: 60e3ee, Count: 2
  Bytes: 6e9152, Count: 2
  Bytes: 26446b, Count: 2
  Bytes: e4a05a, Count: 2
  Bytes: 67f86a, Count: 2
  Bytes: 92c487, Count: 2

Since the most common three byte sequence only appears 3 times, it seems like a non-starter. No longer byte sequences appeared more than twice either.

I generated the random digits with this:

  dd if=/dev/random of=random.bin bs=1024 count=1440