Rule variant between "Old hnefatafl" and Copenhagen
Posted: Tue Aug 27, 2019 7:30 pm
Hello!
I discovered the Hnefatafl game during a recent trip in Norway (wonderful country btw! ^^) and got more and more interested in it. I kind of fell in love with its asymmetry, not only in the sense that black and white have two different winning conditions, but most of all because their reasoning should be very different: black has to make long-term plans involving strategical thinking in order to patiently surround (reminds me of the game of Go) while white has to set up a good position where its pieces are mobile and control a lot of squares, and then look for tactical opportunities (reminds me of Chess). As I enjoy both Go and Chess, it is not a surprise after all that I quickly got to enjoy Hnefatafl.
Anyway, as it is asymmetric, I did some research about the odds and I was surprised to learn that in Copenhagen Hnefatafl the odds are highly in favour of white (1.4 ratio seems high to me!), while the "old Hnefatafl" rules are much more balanced (1.1 is good, close to chess or go I suppose). I also found a computer science paper by P. Hingston, "Evolving Players for an Ancient Game: Hnefatafl", which concludes that white has more winning chances in some simplified set of rules (btw, it would be very interesting to follow this line of research! unfortunately I'm a physicist, not a computer scientist ). Now I assume that the "old" rules were discarded because they lack some fun concepts of the Copenhagen rules, as the edge forts, but I still don't understand why the capture of the king on the edge has been removed in the Copenhagen rules.
After some games played with family and friends, I come to write my personal set of rules, following two goals: simplicity and elegance (with Go for model!), and similar odds. It is some variants of the Copenhagen rules that I wanted to share with you in order to ask what you, experts of this game, think about them. Of course I'm a newbie to Hnefatafl and I guess there are very good reasons why my variants are not as good as I think they are. I just wanted to know these reasons
So here are the rules I would use:
1) Initial position
Same as Copenhagen.
2) Movement
Same as Copenhagen.
3) Captures
3.1) Capture in the center : same as Copenhagen.
3.2) Capture on the edge
-> Isolated pawn: same as Copenhagen.
-> Line of any number of pieces (including the king or even reduced to the king alone): shieldwall capture. The corner may participate in capture.
Difference with Copenhagen: a non-isolated king can be captured on the edge by shieldwall capture, and an isolated king can be captured on the edge if it is completely surrounded and the opponent flanks.
Reason: Gives more winning chances to black in order to equilibrate the odds (1.1 ratio in “old” rule when the king can be captured on the edge VS 1.4 in Copenhagen).
Remark: importantly, in contrary to the “old” rule, the king cannot be captured by a third attacker if already sandwiched on the edge. In particular it cannot be captured by an attacker on a second line when he is sandwiched between the corner and another attacker. This is important in order to not have a king weaker on the edges than the other pieces. This also implies that the guillotine tactic works as in Copenhagen rules.
4) Victory conditions
For black : capture the king or surround all white pieces (as in Copenhagen)
For white : place the king on a corner square.
Difference with Copenhagen: the edge fort is not a winning condition for white.
Reason: decrease white’s potential to equilibrate the odds, and the rules are more elegant as the concept of edge fort is not explicitly introduced (but it is not discarded, see "repetitions" below).
5) Stalemate and repetitions
5.1) Stalemate
If one side has no more legal move available, he loses (as in Copenhagen).
5.2) Repetitions
After 3 repetition cycles, white must change his move, except if the repetition concerns only the king and the king has no other possible move than the one leading to the repetition. If black does not break the repetition cycle, it is an agreed draw.
Reasons:
In Copenhagen, the identification of the “aggressive player” may not be straightforward in some situations. As far as I understand, the “aggressive player” is the one who wins if the other player does not respond. It is often easy to see who wins in an endgame repetition, but this is not the case in middle game. A very skilled AI may know for instance that some response is forced because she would compute a lot of variations and seeing only one reliable, but then she would need to explain why the move is forced to the opponent in order for him to agree upon the repetition situation… My point is that this rule seems to require the knowledge of who’s winning in any given repetition position, which I guess is not even computable in general. So in my opinion this rule lacks of elegance, although I agree that it works in practice.
The obvious rule regarding repetitions would be that white cannot repeat or he loses (I have seen Hagbard proposing this in some thread). While this is simple and seems to equilibrate the game, there are two major inconvenients:
i/ The edge fort is lost.
ii/ White may be put in a situation where the repetition is forced or the king is captured (in particular when the king is surrounded on the edge).
This is why I introduced the exception that the repetition may concern the king only. This reintroduces edge forts (upon the assumption that any edge fort may be reduced to an edge fort where only one move is possible), and prevents the aforementioned cases where the king is captured by breaking the repetition cycle.
Note that the central forts are not reintroduced as I keep the winning condition of complete surround for black.
Finally, I personally find this rule about repetitions more elegant than the explicit mention of the edge fort in the Copenhagen rules, as the edge fort is implied here by a generic and easily explainable rule. It reminds me a lot about the game of Go, where the rule is : “any completely surrounded group is captured”, and the consequence is “make two eyes to live”. The concept of eye (= fort) is not invented in itself but contained in the more fundamental rule. It’s like in physics: you don’t say “fluids exist in nature”, but rather “particles exist in nature and move like that”, and then you discover that the particles may assemble into molecules and then the molecules may have a specific emergent behaviour that you call “fluid”.
Hope you'll find this interesting and not straightforwardly stupid!
Best regards
Ytreza
I discovered the Hnefatafl game during a recent trip in Norway (wonderful country btw! ^^) and got more and more interested in it. I kind of fell in love with its asymmetry, not only in the sense that black and white have two different winning conditions, but most of all because their reasoning should be very different: black has to make long-term plans involving strategical thinking in order to patiently surround (reminds me of the game of Go) while white has to set up a good position where its pieces are mobile and control a lot of squares, and then look for tactical opportunities (reminds me of Chess). As I enjoy both Go and Chess, it is not a surprise after all that I quickly got to enjoy Hnefatafl.
Anyway, as it is asymmetric, I did some research about the odds and I was surprised to learn that in Copenhagen Hnefatafl the odds are highly in favour of white (1.4 ratio seems high to me!), while the "old Hnefatafl" rules are much more balanced (1.1 is good, close to chess or go I suppose). I also found a computer science paper by P. Hingston, "Evolving Players for an Ancient Game: Hnefatafl", which concludes that white has more winning chances in some simplified set of rules (btw, it would be very interesting to follow this line of research! unfortunately I'm a physicist, not a computer scientist ). Now I assume that the "old" rules were discarded because they lack some fun concepts of the Copenhagen rules, as the edge forts, but I still don't understand why the capture of the king on the edge has been removed in the Copenhagen rules.
After some games played with family and friends, I come to write my personal set of rules, following two goals: simplicity and elegance (with Go for model!), and similar odds. It is some variants of the Copenhagen rules that I wanted to share with you in order to ask what you, experts of this game, think about them. Of course I'm a newbie to Hnefatafl and I guess there are very good reasons why my variants are not as good as I think they are. I just wanted to know these reasons
So here are the rules I would use:
1) Initial position
Same as Copenhagen.
2) Movement
Same as Copenhagen.
3) Captures
3.1) Capture in the center : same as Copenhagen.
3.2) Capture on the edge
-> Isolated pawn: same as Copenhagen.
-> Line of any number of pieces (including the king or even reduced to the king alone): shieldwall capture. The corner may participate in capture.
Difference with Copenhagen: a non-isolated king can be captured on the edge by shieldwall capture, and an isolated king can be captured on the edge if it is completely surrounded and the opponent flanks.
Reason: Gives more winning chances to black in order to equilibrate the odds (1.1 ratio in “old” rule when the king can be captured on the edge VS 1.4 in Copenhagen).
Remark: importantly, in contrary to the “old” rule, the king cannot be captured by a third attacker if already sandwiched on the edge. In particular it cannot be captured by an attacker on a second line when he is sandwiched between the corner and another attacker. This is important in order to not have a king weaker on the edges than the other pieces. This also implies that the guillotine tactic works as in Copenhagen rules.
4) Victory conditions
For black : capture the king or surround all white pieces (as in Copenhagen)
For white : place the king on a corner square.
Difference with Copenhagen: the edge fort is not a winning condition for white.
Reason: decrease white’s potential to equilibrate the odds, and the rules are more elegant as the concept of edge fort is not explicitly introduced (but it is not discarded, see "repetitions" below).
5) Stalemate and repetitions
5.1) Stalemate
If one side has no more legal move available, he loses (as in Copenhagen).
5.2) Repetitions
After 3 repetition cycles, white must change his move, except if the repetition concerns only the king and the king has no other possible move than the one leading to the repetition. If black does not break the repetition cycle, it is an agreed draw.
Reasons:
In Copenhagen, the identification of the “aggressive player” may not be straightforward in some situations. As far as I understand, the “aggressive player” is the one who wins if the other player does not respond. It is often easy to see who wins in an endgame repetition, but this is not the case in middle game. A very skilled AI may know for instance that some response is forced because she would compute a lot of variations and seeing only one reliable, but then she would need to explain why the move is forced to the opponent in order for him to agree upon the repetition situation… My point is that this rule seems to require the knowledge of who’s winning in any given repetition position, which I guess is not even computable in general. So in my opinion this rule lacks of elegance, although I agree that it works in practice.
The obvious rule regarding repetitions would be that white cannot repeat or he loses (I have seen Hagbard proposing this in some thread). While this is simple and seems to equilibrate the game, there are two major inconvenients:
i/ The edge fort is lost.
ii/ White may be put in a situation where the repetition is forced or the king is captured (in particular when the king is surrounded on the edge).
This is why I introduced the exception that the repetition may concern the king only. This reintroduces edge forts (upon the assumption that any edge fort may be reduced to an edge fort where only one move is possible), and prevents the aforementioned cases where the king is captured by breaking the repetition cycle.
Note that the central forts are not reintroduced as I keep the winning condition of complete surround for black.
Finally, I personally find this rule about repetitions more elegant than the explicit mention of the edge fort in the Copenhagen rules, as the edge fort is implied here by a generic and easily explainable rule. It reminds me a lot about the game of Go, where the rule is : “any completely surrounded group is captured”, and the consequence is “make two eyes to live”. The concept of eye (= fort) is not invented in itself but contained in the more fundamental rule. It’s like in physics: you don’t say “fluids exist in nature”, but rather “particles exist in nature and move like that”, and then you discover that the particles may assemble into molecules and then the molecules may have a specific emergent behaviour that you call “fluid”.
Hope you'll find this interesting and not straightforwardly stupid!
Best regards
Ytreza