I had an opportunity to go head to head with someone
once. I was in the established pattern, there were about
3 or 4 of us. I called my turn to base. Shortly after,
this guy announces base.

I'm looking around like my head was detached from my body.
I called and asked if he really had announced base because
I can't find anyone. He never answers.

I'm still looking and turn final. I announce my position
and he announces final.

Lo and behold, there he is, about a mile away from me coming
from the opposite direction. I move over to the right a bit
and stop my descent. Someone told him that he was opposite
the calm wind runway. He announces he's leaving the area and
splits.

I go around and do it all again.

(Note to self: Remember that yours isn't the only pattern,
there's another on the other runway)