Rule variant between "Old hnefatafl" and Copenhagen

Tafl rules
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Rule variant between "Old hnefatafl" and Copenhagen

Post by Ytreza » Tue Aug 27, 2019 7:30 pm


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.


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

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by sqAree » Thu Aug 29, 2019 5:22 am

A few remarks:

1.) As far as I recall the consensus among the top players is that actually black has the advantage. I'm not surprised the data tells otherwise as it's definitely easier to pull off a win with white (one mistake as black is an instant loss). Anyway, you can ignore 99% of the games played on this site, because the players are simply not strong enough to yield valuable data.
2.) The edge fort winning condition is a beautiful rule that definitely enriches the game. Not going to write an essay about it now, you will understand after having played hundreds of games with some of them maybe having exploited the edge fort winning condition.
3.) As far as I understand you, an edge fort will ultimately be a draw using your rules? I think there's a large part of the player base who is strictly against draws whatsoever, maybe not even agreeing with the current state of the rules when it comes to that aspect. ^^ However, what happens in case of an edge fort (with only one square for the king to move to) but black breaks the repetition cycle? Your rules don't really seem to treat this case.
4.) I am very glad to see someone thinking about the rules, BECAUSE even if I may not agree with your propositions, there's definitely something wrong with the rules as is. I don't think we really need to change the mechanics (as in the spirit of the mechanics) or the balance of the game, but some more elegant rules could be useful. In particular:
a) There are way too many rules in the first place.
b) Repetitions are nebulous as you already mentioned.
c) 6b's wording is a bit ambiguous.
d) Rule 10 incarnates the absence of elegance. That rule is kind of my fault, and I still think it's necessary as otherwise there are many game states with no well-defined winner.
e) Yeah, there must be a way to get rid of rule 8b because there's like only one specific situation where it applies.

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by Ytreza » Thu Aug 29, 2019 2:49 pm

Thank you for your reply.

1) Good point. I have the feeling that if white manages to put strong stones on the edges in the opening, black has a much harder time as he cannot just close the corners, and the odds are quite balanced.

2) I agree that the edge fort is a beautiful rule. In my opinion it does not have to be a winning cond in order to enrich the game, but simply a way for white to find a draw if all corners are closed.

3) Yes, an edge fort would be a draw. I don't see objective problems with draws, in chess for instance many games end in draw (well, in the other hand not having draws is surely a strength of go, but I don't think seeking a no-draw game is so important). Black can break the repetition cycle but it is pointless, the game can continue forever, which amounts to an agreed draw. It is a bit like in go were the loser can still put stones in all areas instead of passing, or in chess were a player can keep playing forever even in an obvious draw position. Also note that as the board and the number of pieces are finite, black will eventually close a (huge) repetition cycle, so the rule is theoretically applied (and in pratice all players should agree that edge fort = draw as it is a pratical consequence of the theoretical rule).

4) a) I enjoy to play various rules but I agree it is important to set some "official rules" if one wants to promote the game nowadays. Then the other rules would be kept as variants.

4) b) For me this is the bigger problem of the current rules.

4) d) Maybe 100 moves is a bit small. In go we usually play 200-300 moves. Also, the lack of expertise on "theoretical draws" as called in chess may cause most of these kind of infinite games. Like if in chess you have your king and one knight against a lonely king and you continue to play trying to mate, not realizing it is not possible. Btw, that makes me realize that the variant where white loses if he doesn't win would probably encourage white to keep playing, hence discouraging agreed draws which seems not good.

4) e) I think I don't understand rule 8b. In the show diagram, white needs to move the king in order to protect his upper pawn, then black can do whatever move, then white is in zugzwang as any of his moves leads to a capture. Am I missing something?

In any case, having a "repetition power" for the king takes a lot of exceptions into account in a simple rule, and completely solves the ambiguity of the current rule about repetitions.

In fact, after some days thinking about them, I realize that my variants are still very close to Copenhagen: the threat of shieldwall capture of the king is very rare after all, as well as the edge forts. The main difference is probably the handling of repetitions.

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by sqAree » Thu Aug 29, 2019 6:19 pm

1) When I started out I always felt very unsafe playing black because it's indeed never possible to close every corner. But at some point I realized that a corner is already relatively safe with just one additional piece of black on a 3rd or 2nd row. In my experience it's very easy to defend any corner, the difficulty lies in deciding which corner needs protection the most / the most urgent.
More generally, I really like the balance of "one player has the theoretical advantage, but the game is easier for the other one". It reminds me of other completely unrelated boardgames, and the resulting mentality will be one player trying to "trick" his opponent which allows for way more options such as unconventional moves, creating chaos and mess etc. contrary to the player defending his theoretical victory by having to play very accurately.
(this is not really related to our topic, I just felt I could praise the game balance as I really like it ^^)

2) This, I can't say anything against it, I'm just one of the people who really dislike draws so I would still not like such a rule.

3) Yeah, this is a very subjective matter. You will certainly find players who like draws, and some who don't. For me personally a draw is something very unsatisfying (just psychologically speaking, if I happen to be concerned). I also think having no draws at all will lead to more interesting games being played, generally, as you can never really "rest", it's either loss or win so you have to fight to the death. I think many players will also happily embrace this mentality as a kind of viking mentality, adding to the lore and the historical part of the game.
It probably also depends on the frequency of draws. Chess, let's face it, has too many draws, and there are more and more players you consider chess somewhat boring thanks to this. There are beautiful games like TwixT where draws are theoretically possible but are so rare that they can only happen every few thousand games and under very certain circumstances ; something that makes you feel like you actually accomplished something as the players when it occurs, something that qualifies as a well-deserved outcome for both opponents after a bloody and heated fight, as opposed to chess where many draws (admittedly not all of them) can feel more like "no one accomplished anything, no one risked anything, just nothing really happened".
Regarding your handling of repetitions, the huge repetition cycle is not something we want to see in the game, but when in practice everyone agrees to make an edge fort an immediate draw that's fine ; it just has to be outlined in the rules. I prefer to have a rule a little bit less elegant than a pighead newbie delaying a game for thousands of moves because the rules count on the player's common sense.

4a) There was a misunderstanding. I rather wanted to refer to the amount of regulations within the Copenhagen rules, not to the diversity of different rulesets such as Berserk, Tablut, Old Hnefatafl etc. Either way I agree with what you said.

4b) I acknowledge that your proposed rule fixes this problem. In general I haven't seen a situation on a board where black was initiating a repetition. However, if we consider the rule that white cannot repeat or he loses, the two inconvenients you mentioned would only really come up if we also follow your other proposed rules. My point is, if the only thing we change in Copenhagen rules now is to make the repetition rule applying to only white, it would be a valid fix as well. Furthermore the rule is just as easily explainable as yours.
Obviously there's still the problem of large repetition cycles.

4d) Agreed! I'm sure there are many positions where one player could win but it'd take him more than 100 moves, or even more than 200 etc. This might not even be related to the question of the repetition rule. I can't think of a way to fix this, at least not before the computers solved Tafl strongly.

4e) White doesn't have to react to the pawn threat as his king will reach the upper right corner if black really captures it. So in that position white will just move his king up and down repeatedly. But when white has only three pieces and his king left, the rule won't apply, and there are some situations that can only be resolved via the 100-moves-rule.

Now about shieldwall and king captures on the edge: This would probably destroy the game balance. Positions with the king on the edge completely surrounded are frequent and part of many winning combinations by white. This should definitely stay as it is now.

Now, what I personally wanted to see in the rules was a kind of "if white doesn't win (by corner escape or edge fort) he loses", which would simplify the rules a lot, while not having an impact on the mechanics, strategy or balance whatsoever. But under the current rules draws are still really rare, they can effectively only happen when both players lose a lot of pieces and they enter an endgame position where no one can accomplish anything. Then again, I already played a game (offline) with way over 300 moves where white finally pulled of a win with only two pieces left after both players' armies got completely wrecked in the course of the game. Something else to think about is that it might already be enough to destroy the balance to set edge forts a draw instead of a win.

So no, I'm still not a fan of your propositions, even if we ignore that I don't like draws. I'm still in favor of simplifying the rules and making them more elegant, but what be careful not to change the game too much in the process.

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by Ytreza » Thu Aug 29, 2019 7:42 pm

I like your way of thinking about the balance :) It never came to my mind and seems very attractive as somehow intrinsic property of asymmetric strategical games. Actually it is almost enough to convince me to forget the capture of the king on the edge, and with your other arguments (balance actually in favor of black at high level and opens winning combinations for white) I realize that I should agree with Copenhagen on this point. In fact I played a game yesterday and realized that the immobilization of the king on the edge by the attackers was an interesting strategy leading to nice continuations for both sides.

Thanks for the explanation of rule 8b. Under my proposals, the diagram would then be a draw. I then see two possibilities to handle repetitions and forts:
i/ as already mentionned, if the repetitions only involves the king it is a draw.
ii/ any repetition leads to a loss for white (white has to change his move after 3 rep or resign), except if it is not possible for black to win (i.e. capture the king or surround white's force) in that case it leads to a draw.

Actually ii/ seems better in terms of formulation, easier to explain and removes more draws. In particular it gives conditions for theoretical draws:
ii/ => ii.1) edge fort is a draw.
ii/ => ii.2) if all corners are closed, white has too few pawns to build an edge fort and black has too few pawns to enclose white, it is a draw.

Of course ii.2) does not miraculously solves the issue of infinite games, it can be tricky in practice to identify such situation but it gives a good starting point as a theoretical rules which needs some pratical shortcuts (again, as in go: rule = surround, shortcut = make eyes, and there is no issue at identifying the end of the game and the territories).

Here in particular one needs to define:
- "closed corner", which is not straightforward when white pieces are part of the enclosure (but black has some continuation leading to a complete black closure if white moves these pieces). In first place one could minimally impose a full black enclosure (if it not possible to do so and not possible to win in another way, black should then ask for a draw).
- number of pawns required to build an edge fort = 4
- minimal number of pawns required to enclose white = put white's force in the most compact shape and count the surrounding squares.

Actually... This means that #W (number of white) < 5 (counting the king) => #B < 8 => the corners cannot be closed... Hence ii.2) is not possible. Hence all corners closed + white has too few pawns => black can enclose white, hence it is theoretically possible for black to win, hence, according to ii/, white loses and I can conclude:

ii/ => if all corners are closed and white has 3 or less pawns, white loses (he should resign because otherwise he would be forced to complete the theoretical huge repetition cycle which cannot be broken by definition).

This is just to show that a generic rule is always preferable to a list of exceptions (because more elegant but more importantly because more useful in practice). The exceptions and sub "pratical" rules should all be consequences, with identification of "theoretical endgame draws", "theoretical endgame losses for white" and so on.

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by sqAree » Thu Aug 29, 2019 9:22 pm

Glad you like my way of thinking! :D It's a property I first encountered in a symmetric game though.

I think it's a little hypocritical to let someone lose because it's theoretically possible to lose, ignoring that he could avoid losing by just playing normal moves. Although in the position with a lonely king vs 12 black pieces in the corners, black can force a win anyway because corner protection is not important if white has too few pieces. It's a different story if white has his king and three more pieces.

There's something else coming to my mind. There are actually two different kinds of repetitions. The perpetual repetition as described in rule 8a. And the board position repetition as described in rule 8b. The former applies to both players currently, the latter only to white. That bugs me.
Reminds me of this old position ( White's king is immobile, he can never corner escape nor build an ede fort. And yet, the position would be a win for white if black hadn't constructed an edge fort (moving H11-I11 hence and forth). Now 8b only applies to white, so black can move hence and forth, and it would be difficult to define who is the attacking player in such a case for the threefold repetition.

It's especially for those kinds of positions that I like your latest proposition on handling repetitions (that position would be a direct draw).

Should probably still say that an edge fort wins for white. Winning conditions in this game can already not be summarized in a sentence, one additional point on the list of winning conditions won't undermine the elegance significantly. ^^

So, with all that let's try to summarize.

1. White can win by:
a) corner escape
b) an edge fort
c) black being immobile

2. Black can win by:
a) capturing the king
b) completely surrounding the white pieces as in rule 7b
c) white being immobile
d) white doing 3 repetitions in a row, while it's still theoretically possible for black to accomplish a, b or c

3. It's a draw if:
a) a position is three times repeated but black couldn't accomplish 2a, 2b or 2c anymore

Well, the position in 8b in that case would be a draw indeed. Seems fine to me. I wouldn't even mind if there's a position where black can win by forcing white to repeat (for example by threatening his king a few times). Only thing that still bugs me is the subjectivity when it comes to deciding if it's theoretically possible for black to still win. Because as I already mentioned, it shouldn't be only a matter of how many pieces he has, and would still come down to a calculation. The point is, the decision who wins in a particular situation is not always an easy to see consequence of the general rule. Still, it would be awesome to merge rules 8a, 8b and 10 into just one.

I haven't thoroughly thought this through however, will eventually try to find something cooler after your next input. ^^

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by Ytreza » Thu Aug 29, 2019 10:19 pm

If you want to keep the edge fort as winning condition, I would suggest to rephrase the winning condition for white as:
"White wins if he managed to put his king in a safe position, i.e. in a position where it cannot be captured nor enclosed". This encodes both the win on corners and by building an edge fort, and is somehow preferable in terms of "viking spirit": the goal is not to escape but to be safe!

Anyway, about repetitions I think that the idea is here but my formulation ii/ is bad. In particular I just realized that if the repetition is the kind where black always blocks the king from a direct escape path (the most often seen in my games), then black cannot actually win! (if he tries, he loses because white escapes). A good illustration of this is actually the diagram 8b.

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by sqAree » Thu Aug 29, 2019 10:44 pm

That's indeed an elegant formulation of white's winning conditions! Nice.

What we could do with the repetitions is maybe something like that:
"After repeating three times, white has to play a different move. If he doesn't, the board is frozen. Black will then win if it's theoretically possible for him to win (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."

Which kind of contradicts my previous point about the hypocrisy of having to actually pull off a victory and not only being able to. But at least it would solve every other problem I think.

The rule has the advantage of not only being a theoretical determiner on the outcome, but in practice if the players don't agree they can just let black play both pieces and see if he manages to win.

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by Ytreza » Fri Aug 30, 2019 12:27 am

I was also seeking a procedure in this line of thought (it is like in go, if there is a disagreement about the life of a group, both players can continue to play locally to prove its life or death). However the procedure you mention is not correct if I understand it well. Black could destroy an edge fort for instance, with legal moves. The continuation should include clever white's answers.

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Re: Rule variant between "Old hnefatafl" and Copenhagen

Post by sqAree » Fri Aug 30, 2019 1:27 am

That can't be the solution, as it would just mean to keep playing the game (given there is no such thing as a local battle in Hnefatafl contrary to Go). So again we would need a 100-move rule or something similar.

But if the edge fort is defined as an instant winning condition earlier (which can be achieved by just mentioning the different winning conditions before the repetition rule for example), my proposed procdure would work.

Well, the problem of drawish positions without any threefold repetitions are not resolved by this anyway, I just realize. :/

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