Discard old builds was activated on my installation a few moments ago with this configuration:
Days to keep builds: 60
Max # of builds to keep: 40

Strangely, it kept builds 1, 325, 326, 327, ..., 359 (total of 35 builds).

The bug is that Build 1 (built on Mar 28, so more than 60 days old by May 28) was removed from the file system but it is still showing up in the build history and it links to a 404 error page.

It is very unfortunate that I did not keep a picture of the build history before I enabled "discard old builds", because I think there is a second bug lurking in there: it should have kept 5 more builds between builds 2 and build 324 (if they were within the 60 days). Does Jenkins keep a list of what it deleted and why in its logs somewhere?

I hope the "discard old build" feature never assumes to find a successful build because some jobs take several hundred builds before hitting a successful one, and some jobs never succeed because in large installations. Large installation with thousands of tests, there is always something going wrong somewhere to make the build fail (example: 1999 tests pass, and one test fails due to a glitch somewhere, and consequently the build fails).