From: eadengle@watcgl.uwaterloo.ca (Ed "Cynwrig" Dengler)
Subject: Re: defects in abstract games
Organization: University of Waterloo
Date: Wed, 23 Dec 1992 17:27:47 GMT

In article <kleber.725061503@husc.harvard.edu> kleber@husc11.harvard.edu (Gwydden) writes:
>
>Ed Dengler proposes Hnefatafl (sp?) (that's NEF-tof-ul, sort of) as an
>abstract game with no flaws, and Nate Smith asks for details on what
>it is.
>

Well, the pronunciation (as far as I can find out, not being an Old English
expert) is NUF-A-TAF-UL (ie. the A is proncounced).

>In reverse order:  Hnefatafl is a Viking board game; don't remember what
>century, but old.  There are two players, one attacking, one "defending",
>or more accurately trying to escape.  Players start with lots of
>pieces in a specific arrangement on a large square board-- sizes and
>placement of pieces vary; in the 23x23ish range; with the defending pieces
>mostly towards the center of the board (but a few on the outsides), and
>the attacking pieces genearlly surrounding them.
>

Actually, while a Viking board has been found, the only rules to date are
from a Saxon manuscript (this is also where the name is found).

The original manuscript used an 18x18 board which the pieces were placed
on the points (thus, it can easily be played on a GO board). The layout
looks as follows (. is an empty point, K is the king, k are the king's
men, and o are the attackers):

. . o . . o . . . . . . . o . . o . .
. . . . . . . . . . . . . . . . . . .
o . . . . o . . . . . . . o . . . . o
. . . . . . . o . o . o . . . . . . .
. . . . . . o . k . k . o . . . . . .
o . o . . o . . . . . . . o . . o . o
. . . . o . . . . k . . . . o . . . .
. . . o . . . . k . k . . . . o . . .
. . . . k . . k . k . k . . k . . . .
. . . o . . k . k K k . k . . o . . .
. . . . k . . k . k . k . . k . . . .
. . . o . . . . k . k . . . . o . . .
. . . . o . . . . k . . . . o . . . .
o . o . . o . . . . . . . o . . o . o
. . . . . . o . k . k . o . . . . . .
. . . . . . . o . o . o . . . . . . .
o . . . . o . . . . . . . o . . . . o
. . . . . . . . . . . . . . . . . . .
. . o . . o . . . . . . . o . . o . .

>Players alternate moving a piece; all pieces move like chess rooks.
>Captue is by placing two pieces of yours on either side of a single
>enemy piece, all in one line (XOX captures the O).  The one special
>piece is the "defender" king, which starts in the center, and must be
>surrounded on all four sides to capture-- with certain exceptions.
>See below, on why I don't think this is a perfect game.
>

This capture (the XOX) is known as a courier capture. The reason I consider
the capturing rules consistent stem from the fact that I belong to the
Society of Creative Anachronism, and I am an authorized fighter in the
society. In a "real" fight (or as real as Society fighting can get), if
you get into a position where one fighter has engaged you (and you are
thus facing him and fighting, giving rise to the position XO.), and another
fighter comes up behind you (giving rise to the position of XOX), then you
are in 99% of the cases dead meat (the fighter coming up behind you can easily
foul your weapon, thus allowing the front man an easy shot at you). This
explains why the courier capture kills the centre man easily. If the extra
fighter came orthogonally to the first one (giving rise to a position such as
                                     .
                                    XO.
                                     X

then in "real" fighting the O fighter can usually survive (I will admit that
this usually requires the O person to be super defensive, but it can be done
since I have done this on battlefields).

If however, there are two fighters in front of you (such as X.X), you can
usually split them by going between them. Since you know that you are
going into this postion, you can usually stave off their attacks even if 
both of them try to kill you. This is why Hnefatafl does not consider a
piece moving voluntarily into a courier capture position to be captured. 

The exception to this is that extremely good fighters can easily turn around
and engage the man who came up from behind, and not die. Since kings are
supposed to be excellent fighters, this requires that you completely
surround him so that at least one of the fighters has a shot at fouling his
weapon from behind.

Now, about the throne. This is the only obstacle on the entire board.
In many "real" fights, the winner is the one who usually goes offensive
(you can't kill somebody if you never swing your sword), so the concept
is that if you are blocked on one side, and are engaged by a fighter
coming from the other side, then you can be quickly killed since you
have no room to retreat. This is why an empty throne is considered to be
the opposite man in an attack.

Also, being the special symbolism of the king, no piece would want to 
place themselves on the throne. A more practical reason is that unless
you are a very good fighter, putting youself at a disadvantage of having to
negotiate furniture in the space you are fighting in usually means that
you will trip and fall, thus an easy mark for your opponents (try fighting
out in some woods and see how awkward fighting around a tree is). This is
the reason (IMO, since I do not know what they would be thinking when they
came up with the game) that only the king is allowed on the throne, since
he is the only "excellent" fighter of all the pieces, and can thus not
suffer the penalty of fighting around a throne.

>The goal of the attackers os, of course, to get the king; the goal of the
>defender is to get his king to an edge of the board.
>
>Now, why I don't think this is an unblemished game.  First, it has a
>nontrivial starting position, though I can get over that one.  Second,
>the rules exceptions I mentioned above:  (1) no "attacker" piece can
>ever land *on* the center square where the King starts (I've never
>understood the reason for this rule); (2) as a result, the King could
>stand adjacent to this square and be immune from capture, so if he's
>adjacent to that square, you only need to surround him on three sides;
>(3) similarly, if the king is adjacent to one of his own men, you
>can surround the pair of them (with six guys) and win.  This rule
>really needs to be generalized, in something like a go-type way.
>

For case (1), no piece except the king may occupy the throne (this goes for
attackers and defenders alike). For case (2), since the throne is an
obstacle, and thus counts as the opposite man on the attack, the king can
be captured by three attackers and the throne. For case (3), this is not
a capture of the king, since the king is NOT surrounded by four attackers.
The attacking player would have to kill of the extra man, and then capture
the king.

>Nope, this one has too many impurities for me.  I second the nomination
>of Go for the most perfect abstract game, with "mental jujitsu"
>(the perfect-knowledge bidding card game) pretty high up there too.
>
>--Michael Kleber                 I don't have an overactive imagination...
>  kleber@husc.harvard.edu        I have an underactive reality...   --EG

I hope I have explained to you why I do not consider the points you have
made to be impurities. After doing fighting in armour, and in some instances
with obstacles in the way (such as fighting in woods and on bridges), I
consider Hnefatafl to be a very accurate simulation of real fighting given
the simple rules it has.

(Source for these rules: A History of Board Games (Other Than Chess) by
H.J.R. Murray)

Ed

P.S. There are more variants for this game, unfortunately, I am soon
     leaving for Christmas vacation. I will do a post of all the
     variants I know about with sources when I come back in the new
     year. Merry Christmas to everyone!

P.P.S. As I will not be around for about a week, and this university kills
       posts in this newsgroup within a day :-(, if anybody has a response
       to this, could they e-mail me a copy so I don't miss anything?