Editing Angel problem (section)

=== Máthé's 2-angel proof ===

Máthé<ref name="M"/> introduces the ''nice devil,'' which never destroys a square that
the angel could have chosen to occupy on an earlier turn.  When the angel plays against the nice devil it concedes defeat if the devil manages to confine it to a finite bounded region of the board (otherwise the angel could just hop back and forth between two squares and never lose).
Máthé's proof breaks into two parts:

#he shows that if the angel wins against the nice devil, then the angel wins against the real devil;
#he gives an explicit winning strategy for the angel against the nice devil.

Roughly speaking, in the second part, the angel wins against the nice devil by
pretending that the entire left half-plane is destroyed
(in addition to any squares actually destroyed by the nice devil),
and treating destroyed squares as the walls of a maze,
which it then skirts by means of a "hand-on-the-wall" technique.
That is, the angel keeps its left hand on the wall of the maze
and runs alongside the wall.
One then proves that a nice devil cannot trap an angel that adopts this strategy.

The proof of the first part is by contradiction, and hence Máthé's proof does not immediately
yield an explicit winning strategy against the real devil.
However, Máthé remarks that his proof could in principle be adapted to give such an explicit strategy.