I did once have a "Feud," with one of my own Socks, but I soon found it stupid and useless and tried hard to get the Admin to ban that Sock.
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In hindsight, I realized I could have either A. STOPPED logging in under that Account like you said, or B, just asked the Admin outright for a ban. Another Poster had said something like,"Can I please get a permanent ban? I don't want to be an Active Member on this Website anymore," and the Admin granted him his wish.