[computer-go] Re: Probable-eye heuristics

[Richard Brown]

The eye-detecting heuristics caught my attention.  I haven't
investigated them rigorously, but at first blush:

It seems that, as stated, they would label Black's central
eye below as "false".

  + O O O O + +
  O @ @ @ O + +
  O @ + @ O + O
  O O @ + @ O +
  + + O @ + @ O
  + + O @ @ @ O
  + + O O O O +

It seems that they might also label White's upper-left and
lower-right eyes as false, unless I have misunderstood.

But what is nagging me even more is that they neglect
the notion of eyes comprising more than one point.

  + O O O O + +
  O @ @ @ O + +
  O @ + + @ O O
  O O @ @ + @ O
  + + O @ a @ O
  + + O O @ O +
  + + O O O O +

Black's upper-left eye is "real" in the sense that, if White
plays on one of the two points in it, Black's subsequent
capture of the white stone reduces the eye to the heuristics'
definition.  But is there a convenient way to observe this fact
without lookahead?  (Granted, the lookahead is trivial, but
the question is whether a shortcut, if one exists, is worthwhile.)

In the case of the lower-right, clearly Black can make one "real"
eye by playing at 'a', and equally clearly White can destroy it,
so this too depends on subsequent play.  But in the former
case (upper-left Black eye) Black needn't play:  The "eye"
is already "real".  In the latter, a move by either side is
urgent.

Then there is the type of two-space "eye" which permits a
throw-in and/or snapback.  Are there convenient heuristic
shortcuts for detecting these?

  + O + + + + O
  O O O O O O O
  @ @ @ O @ @ @
  @ + a @ b + @
  O @ @ O @ @ +
  O O O O O @ @
  + + + + O O +

Which of Black's two space eyes in the diagram are "real"?

If Black 'a', they both are.  If Black 'b' instead, White
can still "falsify" the other one by playing at 'a'.  And,
if it is White to play in the above diagram, White 'b' kills
the entire group!  In that case, neither eye is "real".

So it is clear that whether these two-space eyes are "real"
or not depends on subsequent play.  What that suggests to me
is that "true-eye vs. false-eye" heuristics are in fact of
limited value, even for the single-eye case, and that looking
ahead and playing it out is of greater value.

A better question, I think, than whether an "eye" is "real",
is rather, "how many suicide-points exist for the other guy"
on the _whole_collection_ of stones.  In each of the three
diagrams above, finding the answer to that question -- even
if a little lookahead is required -- seems to make the question
of whether any individual vacant point is a "real eye" or a
"false eye" somewhat moot.

Ko, being a _temporary_ suicide point for the other guy, is of
course a tricky beast, but it too, is not difficult to detect.

It may be that I have not read carefully enough, and so I may
have missed the point of these real-eye/false-eye heuristics,
but they seem to me to be of less value than just asking "how
many suicide-points exist (or can be made to exist) for the
other guy?" and just "playing it out" until the question is
answered.

In fact I will be bold enough to assert that, since the heuristics
in fact miscategorize some real eyes as false (e.g., the central
eye in the first diagram), that they are of negative value, and
represent a failed approach.

I am certain that, if I have indeed missed something, or if I have
misunderstood something, or if I have made a mistake above, some
reader will be kind enough to point out to me the error of my ways.

-- 
Richard L. Brown             Office of Information Services
Senior Unix Sysadmin         University of Wisconsin System
                              780 Regent St., Rm. 246
rbrown at uwsa.edu              Madison, WI  53715