Puzzling $| behavior

saintmike has asked for the wisdom of the Perl Monks concerning the following question:

Can anyone explain why

   $| = 0;
   print "first=", $|, " second=", $|--, "\n";
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prints "first=1 second=0" and

   $| = 1;
   print "first=", $|, " second=", $|--, "\n";
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prints "first=0 second=1"?