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Re: Rule variant between "Old hnefatafl" and Copenhagen

Posted: Fri Aug 30, 2019 3:29 am
by Ytreza
sqAree wrote:
Thu Aug 29, 2019 10:44 pm
as in, it's possible to construct a game tree from that position onwards leading to a black win, with both parties cooperating), otherwise it's a draw."
I assume that your point is that the player playing black moves all pieces, also playing white's turn. I also assume that white did not build an edge fort (otherwise it is an identified win for white, or maybe a draw but still well identified). Then either the king is in a draw fort, or the king can be captured by 4 attackers. If the king is in a draw fort, the player playing black can destroy the fort on white's turn and then the king can be captured by 4 attackers. In all cases, it seems to me that a sufficient (and obviously necessary) condition for black to win is to have 4 or more pawns, and your rule reduces to "black will then win, except if he has less than 4 pawns, in which case it is a draw". This looks more like an exception than a rule ^^ It does not help to solve the repetition issues.

Actually with the edge fort set as winning condition, what's the problem with stating that any repetition is forbidden for white? The only case I can think of were I would like to justify a draw for white is when white has a central fort and black too few pieces to enclose it. It looks like the king is quite safe in this case (not "starving"). This may even enrich white's possibilities with a reborn of the central fort! White's strategy would more or less looks like:
1/ Try to reach a corner!
2/ If all corners are closed, try to build an edge fort!
3/ If it seems not possible, use all your tactical machinery to decrease the number of attackers and build a big central fort in the same time.

But again it would be very difficult for white and probably impossible at high level... The minimal number of pawns required to build a central fort is 8, so white can only afford to lose 4 pawns. And to enclose it black needs only 12 pawns. So white has to exchange 4 defenders against 12 attackers. Seems tough!

To summarize:

1. White wins by reaching a safe position where it is not possible to capture the king nor to enclose all defenders with only black moves (this last precision in order to get rid of diagram 8b : if black contests white's claim for the win, he can move his pieces as he wants and try to capture or enclose)
2. Black wins by preventing white from winning.
3. Stalemate = loss.
4. White must break any repetition cycle, except if he reached a winning position before the repetition.

1. White wins if:
- king in a corner
- edge fort

Black wins if:
- he captures the king or encloses all defenders
- he forces white into a repetition cycle.
- the board position is repeated several times.
- all defenders have been captured and the king cannot escape
- the corners are closed and only 3 defenders remain
- the corners and edges are closed and white has too few pieces to shieldwall capture

About the closure of corners and edges, I think it is an important point. When playing black, it is quite boring when the corners are closed and the edges sealed such that the only thing to do is to push everything towards the center. The win is obvious in these cases but still under the current rules black has to play it. In pratice black could claim his victory, and again the board is frozen and white can try to show how to build an edge fort or escape, moving only the defenders.

In any case, I think that this formulation is elegant and functional, very close to Copenhagen while solving its issues about repetition. However I still have the intuition that if the attacker force is "very destroyed", it should be a draw even if the remaining attackers can prevent white from winning. For instance if there are only 3 defenders remaining, each blocking a corner, against the king alone, and everybody is desperatly running from one edge to the other... But I don't manage to find a proper definition of "very destroyed".

EDIT : I got an idea. Actually my concern is that this rule of white losing if he doesn't win encourages black to play very safe, and almost not play at all when in a good position (not risking to lose on a mistake)! What is white can "call for a draw" at any time? In this case, either black accepts the draw, recognizing he cannot prove that white cannot win, or he continues playing without the threat of losing in order to either capture, enclose, or put white into a repetition cycle. If then white manages to win, it is a draw. If black captures or encloses or white repeats, black wins.
I'm thinking for instance of a situation where black can close some corners and seal edges easily, but has too few pieces to do both at the same time. He needs to open the corners to bring pieces in the center, giving a possibility for white to escape. If a non win if a loss for white, black has no interest in risking this.

EDIT 2 : On a terminology note, I would put the stalemate, move repetition and board repetition in the same loss condition for white :
3. Starving : if white cannot make progress towards the win, white loses.

EDIT 3 : Other idea: in case of repetition, all pieces in the repetition cycle are removed (because starved to death), and then the attackers play. The king can be removed this way if he is in the repetition cycle, in what case the attackers win.
As they often involve the king, repetitions would then often mean the threat of a loss for white, which reduces to our previous idea. However when they do not involve the king, they could become a nice tactical tool to exchange pieces (e.g. to simplify the position before endgame).

Re: Rule variant between "Old hnefatafl" and Copenhagen

Posted: Sun Sep 01, 2019 1:53 am
by Ytreza
So after thinking again about all this, I would suggest the following reformulation (trying to be the most concise and complete as possible):
1. Initial setup
Board = 11x11 squares, pieces = 12 defenders + king + 24 attackers.
Initial position as Copenhagen.

2. Movement
2.1. Attackers play first, then the game proceeds by alternate moves.
2.2. Unlimited orthogonal displacements on free rows or columns.
2.3. Only the king can stop on center and corners but the other pieces can jump over the center.

3. Capture
3.1. A pawn is captured if it's sandwiched between two enemy pieces (pawns or king) on the enemy move.
3.2. A line of pieces blocked against the board edge by a line of enemy pieces is captured by completing the encirclement with a flanking move. However if the king is in the line, only the pawns are captured.
3.3. The king is captured by 4 attackers.
3.4. Pieces can be captured against the innocupied center and the corners.

4. Victory for the defenders
The defenders win if the king reaches a corner or if it is alive and, whatever the number of free moves given to the attackers, they can neither occupy a square adjacent to the king nor surround all defenders.

5. Victory for the attackers
The attackers win if, whatever the number of free moves given to the defenders, they can never win, or if the defenders are unable to make the position evolve (and did not already win).

6. Draw
If no capture occurs in 100 moves, the outcome is a draw.
Relation to Copenhagen rules (here => Copenhagen):
1,2 => 1,2,3,4
3.1, 3.4 => 5.a
3.2 => 5.b
4 => 6.a
4 => 6.b (the king on an edge fort cannot be approached, however here it does not need to have contact with the edge).
3.3, 5 => 7.a (if the king is captured white cannot reach a position where the king is alive).
3.3, 5 => 7.b
5 => repetition = loss for white (the position does not evolve) => 8b (the diagram is not a winning position as black can approach the king in one free move).
5 => stalemate for white = loss for white (the position cannot evolve).
4 => stalemate for black = loss for black (the king cannot be approached).
6 => 10

Remark: 5. implies that if black isolate the king such that an edge fort cannot be built, and surround all other defenders in another part of the board, then black wins, which seems very reasonable to me and would cut some very long and annoying endgames where black has to capture all defenders in order to put white in stalemate.

Apart from the repetitions leading to a loss for white, this formulation is actually essentially a rephrasing of the Copenhagen rules. Nevertheless I think that concision and reduction to the essential is very important. When I explain the rules to other people as currently formulated, I can see how I lose their attention when I come to what looks like a lot of exceptions (shieldwall, no capture of the king on the edge, edge forts...) It is much better when I let them somehow discover the consequences of the essential rules (i.e. presenting the few simples points I listed above and then the current rules as natural consequences). The game is essentially the same but looks much more attractive, which encourages them to give it a try.

Re: Rule variant between "Old hnefatafl" and Copenhagen

Posted: Sun Sep 01, 2019 4:47 pm
by Hagbard
Ytreza wrote:
Tue Aug 27, 2019 7:30 pm
but I still don't understand why the capture of the king on the edge has been removed in the Copenhagen rules.
Invention of The Fetlar Hnefatafl Panel, first introduced in the Fetlar Hnefatafl 11x11. This prevents that the king can be captured by just two black pieces next to a corner.
Ytreza wrote:
Tue Aug 27, 2019 7:30 pm
3) Captures
-> Line of any number of pieces (including the king or even reduced to the king alone): shieldwall capture. The corner may participate in capture.
Clever idea. This would do away with "the dead squares", where the king cannot be captured.

It would also solve this embarrassing case:
where the king obviously is in big trouble and yet is not captured, because he is on a "dead square".

Shieldwall capture of the king on the edge would probably affect the game balance very little, only shorten a game which black would win anyway.

Already now an efficient tactic against a king on the edge is to quickly entrap him there, immobilize him by surrounding him with black pieces, then comfortably kill off all other white pieces, and finally force the lone king to leave the edge and be caught.

Ytreza wrote:
Tue Aug 27, 2019 7:30 pm
5) Stalemate and repetitions
The suggestion about fusing the concepts of repetitions and edge win fort could be changed into this form:
Repetition is forbidden. Except for the king when the king uses it to mark a king's edge escape.

King's edge escape.
The king wins by edge escape, if he three times repeatedly moves from an edge square to a neighbouring square, all repetitions using the same two squares, meanwhile without moving any other pieces, and meanwhile no pieces are captured.

Re: Rule variant between "Old hnefatafl" and Copenhagen

Posted: Sun Sep 01, 2019 7:57 pm
by Ytreza
Note that my last suggestions for the winning conditions solve the cases you mention without requiring the capture of the king on the edge. Indeed, if the king is isolated in an indestructible structure, it is not possible for white to win, whatever number of free moves are given to him. In such case, black would claim victory, and if white contests, he would have to show how he can reach a win without black playing. If white manages to do so, he wins. If not, black wins.

About the repetition, when you write "forbidden", do you mean "forbidden for white"?

Your definition of edge escape does not require the king to be in a fort. It may open too easy wins for white. There is also the issue about black not caring, i.e. not playing the repetition, and the game can continue forever.

Sidenote on capture of the king on the edge: I realised that the capture of the king by flanking move against a corner will actually never occur. Also, the shieldwall capture of pawns seems to be already rare (a good threat to force moves but scarcely realised in practice), not to mention shieldwall capture surrounding also the king... So the only relevant case seems to be the capture of the isolated king. But if the king is surrounded by 3 attackers against the edge, the attackers only need 3 moves to seal the position (one on the left, one on the right, one on the top) and only 2 more to build an indestructible structure over the king (meanwhile white may try to threaten a shieldwall capture but it seems complicated... Therefore a strategy based on the isolation of the king does not seem to be a good line for white (if someone has a counterexample, I will be happy to be found wrong!) Letting the king being surrounded can only be a tactical move with a short-term (less than 3-4 moves) objective. So I don't think there is much to lose by allowing this capture. Maybe the variant is not as important as it looks at first.

The nice thing about allowing the capture of the king on the edge is that it removes what looks like a somehow artifical exception in the rules.

Re: Rule variant between "Old hnefatafl" and Copenhagen

Posted: Sun Sep 01, 2019 9:42 pm
by Hagbard
Ytreza wrote:
Sun Sep 01, 2019 7:57 pm
About the repetition, when you write "forbidden", do you mean "forbidden for white"?
The case of repetition is general, the same for all variants.

Keeping rules simple, it is also the same for both colors. (Right now the enclosed-repetition is only mentioned for white, but it does not change anything to use it for black, too.)

- It's true, you suggested to forbid only the white repetition. I appreciate that that would pull the Copenhagen game balance in the right direction.
Ytreza wrote:
Sun Sep 01, 2019 7:57 pm
Your definition of edge escape does not require the king to be in a fort. It may open too easy wins for white.
I had a second look at it, and I believe you're right, it would be too easy.

Ytreza wrote:
Tue Aug 27, 2019 7:30 pm
3) Captures
-> Line of any number of pieces (including the king or even reduced to the king alone): shieldwall capture. The corner may participate in capture.
I imagine a version "Copenhagen2" for test, where this small change of shieldwall is in effect.
At the same time, detection for repetitions will look for black confinement-repetition, for symmetry in the black/white handling, though it's not expected ever to happen to black.
Anything more to change?

Re: Rule variant between "Old hnefatafl" and Copenhagen

Posted: Thu Sep 05, 2019 4:58 am
by jrton80
While I tried to read all this, I keep getting hung up on the concept of black repetition. I just cannot see it. Things like sqAree's imgur example ( would be just so improbable it boggles the mind. I supposed maybe when I first started playing but in any game I have played in the last year White would have resigned long before that formation could ever have happened. Playing Black there are just too many things to cover to be pissing around move one piece repeatedly unless forced to do so by the White. White repetition happens when locked up by Black or due to the complete lack of imagination of the player.

That being said, I like the shieldwall rule appling if even if the King is on the edge. The final piece being on one end of the line would be a different twist on things. The corner capture would be different than the current Old Hnefatafl so the guillotine would not be gutted.

Why is it called a Guillotine? The City French came up with that one and a bloody machine it was - it was the country French which were Normans. I always thought of it as the King's anvil - completely different mental images.


Re: Rule variant between "Old hnefatafl" and Copenhagen

Posted: Thu Sep 05, 2019 9:00 am
by Ytreza
I tend to agree with you on repetitions. But if you are right there is all reasons to set repetitions as a loss for white (or white needs to change his move). As you say, it would not change most of the games (maybe even not a single one (?)) while being clearer, more elegant and easier to put into computers/AI.
One of my concern is still that for an AI capable of computing long variations, there may be only one possible move for black at some point in endgame, but it would not be obvious to see it is the only one.

I like the guillotine better than the anvil because the guillotine gives you a sense of how deadly it is, and also this idea of an automatic machine. This tactic is really "the machine of death!"