I think there is a terminology problem. And yes, I did understand the original purpose.

Let me try to make it a bit clearer?

Of course for just determining if a particular arrangement of stones on the board is possible (legal) one can speak of "the state of the board". But what I am saying is that a particular arrangement of stones on the board might be more than one statefor the purposes of the game of go.

Let me try to put it another way. Doduhdah, are you not intending to be able to determine if given a state (the way you want to define it) can be transitioned into some other state? << by adding a stone; aka, making a move >> In other words, after you have determined "this is a legal state" being unable to determine what states would be possible subsequent states?

Sorry for the confusion. In the context of this discussion regarding the visualization of valid and
invalid states, I'm only interested in individual states and not in sequences of states (like a move,
which is a sequence of two states).

The number of valid states for a 3x3 goban is 12675 and that's exactly the number of positions KGS will
let you set up when you edit a custom game, as opposed to the 7008 states KGS will not let
you set up on a 3x3 goban, because they involve at least one stone or chain that lacks liberties.

So for this notion of validity that is only concerned with individual states, the only aspect that is relevant
is whether or not all chains/stones on the goban have at least one liberty.

Stop using the word "state"! Both of you! You're killing me.

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instead, they could use: condition, shape, situation, circumstances, position, predicament, plight

Somehow I feel that 'valid state' seems more appropriate than 'legal position'.


I thought state space was a fairly universally accepted concept.

http://en.wikipedia.org/wiki/State_space

"In games, the state space is the set of all possible configurations within the game."

And this would be neither a valid state nor a legal position nor possible configuration.

Click Here To Show Diagram Code

[go]$$
$$+---+
$$|.XO|
$$|..X|
$$|...|
$$+---+[/go]

Yes, one of the 7008 possible invalid states on a 3x3 goban.

Wbt the word “constellation”, as this is not only about position but about position of stones in relation to other stones’ positions.

Grtz, Tom

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I actually tend to use state the way Mike does, and I think that's more common in abstract discussions of the game, rules, etc.

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Question:

Assuming the original definition of legal state (all groups have at least one liberty) there is a question of "reachable" states. Take this example:

Click Here To Show Diagram Code

[go]$$
$$+---+
$$|X.O|
$$|XX.|
$$|.X.|
$$+---+[/go]

[/quote]

In go, black and white stones are placed alternately and once placed, not moved unless removed by capture. Only one white stone could have been captured (the number of black stones placed on the board can never be less than the number of white stones placed) so there are too few white stones present in the diagram.

So that would be a legal state but not a reachable legal state?

What about passing?

Click Here To Show Diagram Code

[go]$$
$$+---+
$$|...|
$$|...|
$$|.1.|
$$+---+[/go]

White passes

Click Here To Show Diagram Code

[go]$$
$$+---+
$$|3..|
$$|...|
$$|.X.|
$$+---+[/go]

White passes

Click Here To Show Diagram Code

[go]$$
$$+---+
$$|X.6|
$$|75.|
$$|.X.|
$$+---+[/go]

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passing -- good point.

Click Here To Show Diagram Code

[go]$$B at , at
$$+---+
$$|921|
$$|734|
$$|.56|
$$+---+[/go]

(but of course there exist actual unreachable positions)

Such as? This doesn't seem obvious to me at all. I think we can construct arbitrarily long sequences of capturing and under-the-stones tesujis to create any (valid) board state we want. Even a single white stone, assuming black started and never passed, is possible.

Click Here To Show Diagram Code

[go]$$
$$+---+
$$|..X|
$$|...|
$$|X..|
$$+---+[/go]

Oh, that's a handicap game.

Great. The negative has 2 eyes.

I don't see how there are states that are unreachable, except under certain assumptions
(like players not doing weird things like filling up their own eyes, which would usually
be unreasonable given the goal of the game).

For the concept of theoretical games, where the only assumption is that both sides play
in accordance with the rules, any valid state can obviously be reached.

There are no unreachable legal states, unless you're willing to impose certain assumptions on the
behavior of the players, like acting in accordance with the goal of the game and not just playing
moves that are allowed according to the rules.
For instance, it would be allowed for one player to keep passing from the start as the other player
keeps playing moves until they feel they have enough stones on the goban that the opponent will no
longer be able to create any living groups.
It would be a nonsensical game, but it's still a valid game, as both players play valid moves.

I think one takeaway from this is that it exposes how much and aggressively we as humans prune the game tree when evaluating moves and positions. Presumably, as we get stronger, we do it even more. This is demonstrated both by beginning players who worry that their position might collapse if their opponent plays at A, B, and C, as well as by professionals who overlook a sequence that completely destroys their opponent in a game because it requires an unforced empty triangle, or similar "bad" moves.