One solution to all of this is to HAVE NO KO RULE!
Then all the nonsense goes away. It then comes down to each player
having his fate in his own hands. If you want to win, you will avoid
cycles, but you are not arbitrarily told what a cycle is or what version
of some cycle rule is considered illegal. Indeed, there are no illegal
moves in the KO sense.
This also greatly simplifies the rules. The KO rule is often the most
confusing to beginners with all it's variations and is difficult to
state concisely. Imagine being able to do away with it entirely!
This gives 3 possible results for all possible games:
1. Black wins
2. White wins
3. Game never completes.
I would argue that after an infinite number of moves, a game be
considered a draw. Neither side wanted to fight for it or neither side
could attain a win - so a draw is the logical conclusion to such a game.
This all has great beauty. A game is never decided by a KO side-effect.
The responsibility of winning - or even of making progress is put upon
the players themselves. From a programmers prospective there are no
GHI issues (unless the programmer creates it for practical reasons.)
But now we have one itty bitty practical inconvenience. How to you
conduct tournaments and matches where games can last forever?
Since GO currently has arbitrary KO rules for practical convenience, why
not introduce another arbitrary but practical rule to handle this
situation? After all, we just got rid of the nuisance KO rule?
The rule we could introduce (which can be concisely stated) is to set a
move number limit on the game. If a game goes to move N, it is over
and a draw is declared. (Or we could award the game to WHITE if we want
to make draws impossible.)
My guess is that in practical play human players will notice the cycles,
and either come to a draw agreement or break the cycle.
When programs play, this may not always happen. I argue that the
arbitrary game limit is no more arbitrary than rules of KO which we
impose for practical reasons only.
We could make N be 2 * boardsize. On 9x9 a game is over after 162
plays. It would be 722 for 19x19.
Ok, let me change CGOS to do it this way now .... just kidding.
- Don
On Mon, 2006-10-23 at 16:44 +0200, John Tromp wrote:
> On 10/23/06, Don Dailey <[EMAIL PROTECTED]> wrote:
>
> > I don't believe in positional superko. I know that 99.9% of the time it
> > makes little or no difference, but I don't see how it can be correct.
> > 2 identical configuration - each with different color to move are simply
> > NOT the same position.
>
> They are by definition. The other superko rule is called Situational
> SuperKo for a reason. It uses the word situation to denote the combination
> of position and turn.
>
> As a chess player, you must be used to the phrase
> "in this position, with white to move..."
> There also, turn is considered a piece of additional information.
>
> Turn is just one piece of information about the past that you can add
> to position to make you feel it better describes the possible futures.
> In chess there are many other such pieces of information, such as
> castling rights and possibility of en-passent captures. You may feel
> that these are also an inherent part of the position, because they
> affect the future. But why stop there? The future also depends on
> when 3-fold repetition occurs, so maybe past occurances should
> also be included in the notion of position? Clearly, this leads us astray.
>
> 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.
> 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?
> I'd argue it's whatever entails the minimum amount of information.
> You can't include less information than the board configuration, obviously.
> And that by itself is good enough for all practical purposes, as you admit.
>
> And that is why I consider PSK the most logical choice.
>
> 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
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