You can NOT map drives unless the users have passwords. No blank passwords will work.

So – all users will have the passwords identical to their usernames for these accounts.

WS1/ws1, WS2/ws2, etc.

One account had the drives mapped with no passwords, then the next day – no maps; but:
START > PROGRAMS > ADMINISTRATIVE TOOLS > LOCAL SECURITY POLICY > LOCAL POLICIES > SECURITY OPTIONS > ACCOUNTS: Limit local account use of blank passwords to console logon only – disabled

appears to be a possible workaround.