Let me address some of your points directly: > ... > > In Go, the forbidden ko point is another piece of information you could > add, being similar to en-passent capture possibilities in that it is only > about what happened in the last move. > > You may well say "2 identical configuration - one with a forbidden ko > point and one without, are simply NOT the same position." > > But the approach of including bits of information about the past > is inherently flawed since it cannot be taken to its extreme. We cannot > say "it is illegal to repeat an entire history of positions". > > That's why the simplest approach to superko is to include no information > whatsoever, not even turn.
But I feel this is taken to the extreme. You can expect the same results from MOST positions that are situationally equivalent - but side to move differences are enormous. Consider for example the opening position. With black to move we expect black to win very handily (without komi.) But if black makes a pass move, the positions are in no sense equivalent. In fact, you don't have to work hard to construct anomalous examples, just about every position in the game, short of the extreme endgame, has a different game theoretic evaluation depending on which side gets to move first. PSK takes this concept of "not bothering to capture a position perfectly" to absurd extremes. It considers positions that are consistently many stones apart in game theoretic value as being the same. The only reason to have a KO rule is to prevent by force, long cycles. So I don't see a point in imposing more restrictive conditions than necessary. Having said that, I see your point about situational super ko. Even in SSK we compare positions that have some details of history NOT in common. So they are indeed different positions in a pure sense. By that definition no positions can ever repeat because they always have a different "modern" history. So even if we wanted to, we can't have an effective game shortening rule that says "identical" positions cannot repeat. SSK is the best we can do in a practical sense. > I don't understand how you can argue that this is more complicated > than considering configuration+turn. > If you consider superko to be the rule that you cannot repeat a STATE of > the game, then what's the simplest possible choice of state? The simplest choice is to consider all positions equivalent - since we have decided that we can be arbitrary about how we define state. But then every move is illegal. But you have chosen a rule which makes more move illegal than necessary because it's "simple", so if you need to play that game, then it's simpler to say all positions are equivalent. You might also consider a rule that says never move to a point that was once inhabited. I think that might be an interesting variant of the game but it's not GO. But since we have decided that a position doesn't have to have all details in common, why not? > I'd argue it's whatever entails the minimum amount of information. > You can't include less information than the board configuration, obviously. But it seems rather arbitrary to make that statement. I guess my answer it that you obviously must include side to move information as a minimum to even consider positions at least "similar", even if you give up on the idea of perfectly identical. > And that by itself is good enough for all practical purposes, as you admit. Not for ALL practical purposes. I think PSK is a poor choice for a solver engine combined with database-like tables. It produces more positions that cannot be resolved cleanly. It produces exceptions that are normally not logical/predictable and it even invalidates Benson life. > And that is why I consider PSK the most logical choice. Yes, you are using the argument that a shorter description makes it superior. You wonder why I consider PSK more complicated. It's more a semantics issue. From my point of view I see a meaningful concept having to be altered - making it more complicated. Perhaps from my many years of chess programming I have never considered a white to move position to be equivalent in any way to a black to move position. To describe this concept in chess terms we have to introduce terms like "triangulation", which is the process of wasting a move in a meaningful way to achieve the same position but with the colors reversed. But PSK is less complicated, as you say, if you consider it from the information complexity point of view. It's just that everything else gets more complicated. Certain moves that wouldn't get dropped now get dropped from the list of legal choices. My last post was almost (but not quite) tongue in cheek about throwing out KO rules completely. It's simpler and more logical that PSK or any of the KO variants, it's just not PRACTICAL unfortunately. It occurred to me that on CGOS, I could eliminate the KO rule entirely and you simply play the game until you win it outright, or you lose on time! I'm not that crazy, but I hate all of the KO rules. I just think SSK is better behaved. - Don > In my paper on the combinatorics of Go, I discovered that PSK also > leads to the simplest mathematical characterization of a game of go. > The game graph consist of all legal positions (configurations) with edges > between them corresponding to non-pass-moves. A game of Go is precisely > a simple path through this graph, starting at the empty node. > > Using SSK would lead to a far less elegant characterization. > > > Your example may illustrate a problem with superko. It's my belief > > that superko can create bizarre and anomalous situations like this > > The occurance of bizarre situations appears to be a very common > phenomenon in Go, whether you have PSK or not. Go is such a rich > and subtle game that you cannot expect too many rules to hold without > their share of exceptions. For instance, a group with 2 "false" eyes can > be unconditionally alive in some cases. We may admire this richness rather > than view it as something anomalous that needs fixing. > > Who is to say that SSK doesn't lead to similarly bizarre situations? > My guess is that they exist there as well, just harder to find... > > regards, > -John _______________________________________________ computer-go mailing list [email protected] http://www.computer-go.org/mailman/listinfo/computer-go/
