hist-games: chess-board w/ playing-cards

Christian Joachim Hartmann lukian at Null.net
Fri May 15 05:02:40 PDT 1998


At 08:45 14.05.98 -0600, Chas wrote:
>
>Is there any pattern to the 1-12 numbering? I was trying to see if the each quarter of the 
>board had a complete 1-12 sequence to match the corresponding quadrant of the circle, 
>but it looked to me that there were numbers repeated in some quarters (2 "9" and "10's" 
>in the upper right quarter for example)
>
>Chas

Yesterday evening, I occupied myself with the pattern of the numbering,
the distribution of the cards and the orientation of them.
I learned a whole lot of things about the board -- but this
hasn't necessarily brought me closer to the game played with it!


It is clear to see that both the symmetry of the board and the
numbering from 1 to 12 is very regular.

The distribution of the cards however seems irregular and accidental,
but the designer of this board tried to make an irregularity that
seems to be even.

For example:
- No two squares with the same suit touch each other
  exept for the 7 and the deuce of leaves.
- Never are two squares of the same rank of card adjacent to one
  another.
- No two court cards are adjacent. The courts are evenly distributed
  on the board.


Here are some patterns in detail:


1. The orientation of the squares:

There are 48 numbered squares equal to 48 cards.
Twelve each are orientated towards one side of the
board.
There are 16 unnumbered squares which are orientated
4 each along the main diagonals of the board.

I've drawn a sketch of the board with the orientation
of the squares designated:
<http://www-public.rz.uni-duesseldorf.de/~hartmanc/public/orient.gif>



2. The distribution of the numbers:

The numbering begins with "1" next to the single
large leaf and continues in groups of four along the
edges and then into the centre.

Sketch two:
<http://www-public.rz.uni-duesseldorf.de/~hartmanc/public/distrib.gif>

Whether this 'movement' along the edges and into
the centre is the track of a racecourse, as proposed,
I cannot say.



3. The distribution of the cards:

Each of these groups of four contains one card
of each suit. If one writes down the ranks of each suit
that are in a certain group, you'll get the following
table:

[D = Deuce/Daus; K = King; O = Over; U = Under; X = Flag/Banner/10]

  (Acorns, Leaves, Hearts, Bells)
 # |  Ac Le He Be  |  Group
---+---------------+-------
 1 |  D  K  6  8   |    a
 2 |  7  U  9  4   |    b
 3 |  X  3  5  O   |    c
 4 |  6  D  8  K   |    a
 5 |  4  9  U  7   |    b
 6 |  3  O  X  5   |    c
 7 |  5  X  O  3   |    c
 8 |  8  6  K  D   |    a
 9 |  O  5  3  X   |    c
10 |  U  4  7  9   |    b
11 |  9  7  4  U   |    b
12 |  K  8  D  9   |    a

Upon closer examination, it'll become evident that 
there are only three different combinations of
card-ranks to be found in the above table.
I've labelled them 'groups'.

The numbers 1, 4, 8, 12  (Group a) contains always 6, 8, K and D.
The numbers 2, 5, 10, 11  (Group b) contains 4, 7, 9, U.
The numbers 3, 6, 7, 9  (Group c) contains 3, 5, X, O.


If I arrange these three groups taking
the Deuce as a simple two, I get this:

Rank of the card:  D 3 4 5 6 7 8 9 X U O K

Group a            D       6    8          K
Group c              3   5           X   O
Group b                4     7    9    U

I think I can see at least traces of a pattern.


If one colours the squares in the DISTRIB.GIF
sketch according to the three groups they belong to,
one gets this:

<http://www-public.rz.uni-duesseldorf.de/~hartmanc/public/groups.gif>

A truely fascinating diagram. For example, all the
4s, 7s, 9, and Unders (Group b) are to be found on
the blue squares!

Or

Of the three groups, only the red one (c) has a
symmetrical distribution. Due to that, all the
ranks from this group (3, 5, X, O) are to be found
in ALL four orientations, which is mostly NOT the
case with the other ranks.


---


What of all this?

Not much. I believe I discovered how the designer of this board,
down in the 17th century, achieved an irregular but even
distribution of the cards, but I haven't come closer to the rules
of the game that have been played with this irregular layout
created like this --
or has anybody an idea how these 'structures' can be put to use for gaming?


Greetings,


**       Christian Joachim Hartmann 
**       lukian at Null.net
**       christian.hartmann at uni-duesseldorf.de

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