How do I get a random entry's URL from a Entries field? I have a Entries field and I'd like to return a URL for one randomly picked entry.

I could loop through all the entries, but I'd like to do something more efficient. Can I return an array of URLs? Or better yet, is it possible to randomly get one URL all at once?
It is possible to have the query pick a random entry.
From the Craft Entries Fields docs we see that entry.entriesFieldHandle is a shortcut for

craft.entries({
  relatedTo: { sourceElement: entry, field: "entriesFieldHandle" },
  order: "sortOrder",
  limit: null
})


And what we want is to order the entries randomly, and then limit the number we retrieve to only one:

craft.entries({
  relatedTo: { sourceElement: entry, field: "entriesFieldHandle" },
  order: "RAND()",
  limit: 1
})


So to retrieve one random entry and get its url:

{% set randomEntry = craft.entries({
      relatedTo: { sourceElement: entry, field: "entriesFieldHandle" },
      order: "RAND()",
      limit: 1
    }).first()
%}
{% if randomEntry %}
  {% set randomUrl = randomEntry.url %}
{% endif %}