Copenhagen Hnefatafl

Tafl rules
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Hagbard
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Re: Copenhagen Hnefatafl

Post by Hagbard » Thu Mar 08, 2012 6:20 pm

Image
Here white attacks on a full line, and black must use not one but several pieces to block.
Last edited by Hagbard on Fri Mar 17, 2017 12:47 pm, edited 1 time in total.

crust
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Re: Copenhagen Hnefatafl

Post by crust » Thu Mar 08, 2012 8:32 pm

Good example Hagbard - this is a repetitive situation which nevertheless features not very much repetition in the actual moves. Classic situation where an umpire could judge straight away that it was a draw situation, but a computer couldn't. But is it repetitive check?

I'm beginning to realise (I'm a bit slower than you guys) that "check" is actually hard to define in hnefatafl. I would have said it was check if the king can move to the square next to the corner on the following move - but of course in a way that's not check because it's the corner square that wins, not the one next to it (even though in hnefatafl it amounts to the same thing). Likewise I would have said it was check if the king could move to an open edge file on the following move, being then unstoppable. But that implies that "check" means ANY position where the king is about to move to an unstoppable winning position. It could be quite hard to identify, especially if the "checking" move is two or three moves before the win, for instance there could be a chain of 4 moves resulting in an inevitable win for white, where all of black's responses are forced moves, (see hnefatafl puzzle) now would that be check [i:1zvwh7k9]right at the beginning of the sequence[/i:1zvwh7k9], or only at the end?

If check can't be defined, then neither can perpetual check. That destroys my argument, that repetitive draw should be a defeat for the player who started it, but only if check is involved. This issue is difficult! Like the offside rule in football? My brain is melting, I'll have to re-read all of the posts on this subject. And meditate.

Evans, your posts are highly illuminating! Your knowledge of eastern games as well as old Norse is very welcome here. Are you a Jedi, too? :D

Adam
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Re: Copenhagen Hnefatafl

Post by Adam » Sat Mar 10, 2012 11:08 pm

Hello forum. Mind taxing time again.

Following the fun science references, Crust and I have been referring to the rules now being tested on Aage's site as the 'weak' copenhagen interpretation, and a version forbidding perpetual check as the 'strong' copenhagen interpretation. Otherwise the rules are the same.
crust wrote:But is it repetitive check?
Crust and I have a had a discussion about all these latest perpetual check considerations and I think we have made some headway, pretty much where Evans was heading in that last paragraph. Here is a summary:


Tafl check can be defined if, as Evans was hinting at, we consider 'preventable mate in 'n' positions': 'Check' is any move that threatens mate in 'n' moves, preventable by a blocking manoeuvre by the opponent.

The multiple moves perpetual check situation may be hard to resolve for a computer, but for humans its easy:

So, looking at hagbards last set up, with six black pieces on row 3, the king on row 4, and nothing on rows 1 and 2:

Any "preventable mate in 'n'" threat that involves indefinitely threatening mate in 'n' where the 'victim' is forced to respond but where the aggressor cannot achieve checkmate is to be abandoned by the aggressor if each preventable mate in 'n' position has been shown to fail a maximum of 3 times.

So Hagbard's last example has, as far as i can see at least 8 mate in 'n' positions (assuming black moves as economically as possible to prevent opening more of the 9 possible mate in '2 or 3' options on B to J, and the 2 mate in '1' options on A and K. Meaning white is free to explore all those possibilities, but as long as the two players are aware that black will always block, they both know its a waste of everyone's time and energy to pursue the attack.

If white has other pieces, white must be allowed to use the check leverage to position blacks pieces as they choose, before bringing in reinforcements, but three repeats of each attack position is ample to allow for this. However, if this is not whites plan the rule is simple enough, white is making essentially the same threat, so at some point they have to move another piece or play a non checking move with the king. How you program that I leave to Aage!


As for Crusts 'windmill' puzzle, I don't see any problem here either. Each corner attack position is a self contained "preventable mate in 'n'" situation. One simply applies the 'no more than three repeats' rule to each situation. If someone is cunning enough to come up with a "preventable mate in 'n'" chain that carries us around the board and back to the original board set up, the rule can still be applied as you are then repeating a series of identical board set ups. You cant go around the board more than 3 times.

As for the 'who started it?' problem, this is an illusion. Any situation that presents a repeating board pattern, can always be easily traced back to who started it, even a complex series of moves that lead us back to the original board position. It will always be self-evident which player made the first move in the repeating pattern.

It may well be that the player who made the move immediately BEFORE the repeat pattern MEANT for this to happen, thereby by using the forbidden perpetual check to set a trap for the opponent, ultimately forcing them to play a non threatening move! Cunning indeed. But that's fine, no different to using check to force the opponents hand.

And perhaps its actually easy to program this, as the computer can likely see repeat coordinates much easier in complex situations than we can.

Adam
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Re: Copenhagen Hnefatafl

Post by Adam » Sun Mar 11, 2012 12:01 am

Hagbard wrote: Image
In the end game, this situation could happen: both white and black lost 12 men, and left is the lone king and just enough blacks to block the corners. If the game ends as shown in the diagram, shouldn't this be a white win? The king did escape to the edge, can move and is not captured. Maybe he can be captured, but we'll never know, because black doesn't try, so the king is as safe as in a fort. If black should try to go after the king, the king would probably escape to a corner.
This poses an interesting problem. I think in practice black would have long since trapped the lone king. But of course in this position black can easily refuse to try to capture the king thereby forcing a stalemate. But trying to capture the king would quickly degenerate into perpetual check forced by white, so with Strong Copenhagen rules, it would be in blacks interest to go after the king anyway and certainly win.

The extremely unlikely situations where black is able to force a perpetual "preventable mate in 'n'" are also solved by the no more than 3 repetitions of a preventable mate in 'n' pattern. In practice such situations would be very easy to develop in to black wins anyway.

As to whether white 'should' win in this situation, I would say no. Black has slaughtered all the other men, the king is a dead man. With the Copenhagen edge fort, we are saying that the king can't get out of the board unless he reaches a corner exit, or has enough men to help him escape under/over the board edge.

Hagbard
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Re: Copenhagen Hnefatafl

Post by Hagbard » Sun Mar 11, 2012 9:30 am

Image
It was easy for white to lure the computer into this perpetual check. It's hard to tell, but if it's also possible against a human opponent to from the start quickly go for perpetual moves, and easier than to win, it can be abused.

Hagbard
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Re: Copenhagen Hnefatafl

Post by Hagbard » Sun Mar 11, 2012 11:53 am

Adam wrote:Following the fun science references, Crust and I have been referring to the rules now being tested on Aage's site as the 'weak' copenhagen interpretation, and a version forbidding perpetual check as the 'strong' copenhagen interpretation. Otherwise the rules are the same.
Strong and weak copenhagen interpretation... :D
Adam wrote: Any "preventable mate in 'n'" threat that involves indefinitely threatening mate in 'n' where the 'victim' is forced to respond but where the aggressor cannot achieve checkmate is to be abandoned by the aggressor if each preventable mate in 'n' position has been shown to fail a maximum of 3 times.

So Hagbard's last example has, as far as i can see at least 8 mate in 'n' positions (assuming black moves as economically as possible to prevent opening more of the 9 possible mate in '2 or 3' options on B to J, and the 2 mate in '1' options on A and K. Meaning white is free to explore all those possibilities, but as long as the two players are aware that black will always block, they both know its a waste of everyone's time and energy to pursue the attack.

If white has other pieces, white must be allowed to use the check leverage to position blacks pieces as they choose, before bringing in reinforcements, but three repeats of each attack position is ample to allow for this. However, if this is not whites plan the rule is simple enough, white is making essentially the same threat, so at some point they have to move another piece or play a non checking move with the king. How you program that I leave to Aage!

As for Crusts 'windmill' puzzle, I don't see any problem here either. Each corner attack position is a self contained "preventable mate in 'n'" situation. One simply applies the 'no more than three repeats' rule to each situation. If someone is cunning enough to come up with a "preventable mate in 'n'" chain that carries us around the board and back to the original board set up, the rule can still be applied as you are then repeating a series of identical board set ups. You cant go around the board more than 3 times.

As for the 'who started it?' problem, this is an illusion. Any situation that presents a repeating board pattern, can always be easily traced back to who started it, even a complex series of moves that lead us back to the original board position. It will always be self-evident which player made the first move in the repeating pattern.
The examples involving several pieces and movements on full rows, or even complex repetitive movement patterns several times around the whole board as indicated by crust's puzzle, show that a perpetual moves situation cannot be detected simply by counting the number of side steps done by some piece.

The method which covers it all, is to detect when the exact same board position is obtained for the third time. The computer can do that. The player who does the definitive move, has done an illegal move.

I wonder if it is possible for the real attacker to lure or force the opponent to be the one who does that illegal move?

Image
- Actually, in this example the real attacker (white) is the one who does the move immediately before the definitive move. Could be that when the same board position is obtained for the third time, the last two moves are illegal, making white the perpetrator here. (Then again - if the black k10 piece would accidentally start out on the j10 square, this rule too would fail, judging the wrong perpetrator...).
Update: Solved.

Hagbard
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Re: Copenhagen Hnefatafl

Post by Hagbard » Mon Mar 12, 2012 1:45 pm

Image
Edge draw fort based on one edge square only!

Hagbard
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Re: About the draw concept

Post by Hagbard » Mon Mar 12, 2012 3:58 pm

conanlibrarian wrote:Also, I think you are to "infected" by the modern chess rules, look at the rules for Xiangqi and Shogi (Chinese and Japanese chess). They both have rules for breaking perpetual threat situations quite similar to the proposed rules above.
Evans wrote:If we do find a rule though that is able to be clean and best for both corner Tafl and edge Tafl as well, then I would not complain! But my suggestion was more for corner Tafl.
What about adding a "strong version" of a perpetual moves rule to the current tournament:
Rule+3) If the exact same board position is obtained for the third time, the player responsible for the perpetual moves must do an alternative move, or lose.

The computer does the counting and already writes a message at the second occurrence of the same board position, and also indicates who is the perpetual "attacker". It's implemented already and the computer does this since today.

The rule appears to cover all the cases mentioned in this discussion and would work for corner tafl as well as for edge tafl.

The introduction of a rule+3 does not affect the tournament games already completed, since they didn't have perpetual moves.

crust
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Re: Copenhagen Hnefatafl

Post by crust » Tue Mar 13, 2012 12:09 am

That seems like a good idea - we will see how it plays! I'll update my copenhagen introduction to include the new rule.

By the way, I think I got the first copenhagen win (win only possible under copenhagen rules) in game where I played white against Chuck Ward -thanks Chuck for a great game, now you have to watch the edges as well as the corners! Unless someone else beat me to it. Haven't managed a total enclosure yet though.

My first impressions are that copenhagen rules are a brilliant addition, as they make the game more unstable and more likely to "tip" decisively one way or the other, thus resulting in a win/defeat rather than a draw.

Kratzer
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Re: Copenhagen Hnefatafl

Post by Kratzer » Tue Mar 13, 2012 8:00 pm

The new edge dynamic is indeed very refreshing. I am beginning to like this variant, too. Great work, everybody!

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