Wednesday, 10 October 2012

The game of the Four Seasons: making 7-sided dice

 

Medieval dice


Seven-sided dice, which are used for the Game of the Four Seasons, called the World are not common medieval dice. Common medieval dice are six-sided dice, just like ours. The book of Alfonso X the Wise describes how they are made, and how they should look like:

f. 84v: Showing the seven-sided dice.

"And we say that dice should consist of three squared shapes of six equal sides, all equal in size and perfectly square because otherwise they will not roll as often on one side as another and it would be trickery more than luck. And thus this is the first of the ways of cheating, as we will later tell17, in which those who wish to cheat make crooked dice.
And it is to have on each one of the six sides, pips in this manner: on the one side six, and on the other five, on the other four, on the other three, on the other two and on the other one, so that twenty-one pips come on each die, and so that sixty-three pips come on three dice.
And the pips should be placed in this manner: opposite the six-side, the one; and opposite the five, the two; and opposite the four, the three. And these dice can be made of wood, or of stone, or of bone, or of any metal, but especially are best the ones made of bone, the heaviest to be found, more than any other material and they fall more equally and more squarely on any type of surface."

Indeed most unearthed medieval dice are made of bone, antler, jet, clay or wood. However, in medieval times the positioning of the pips could be different from Alfonso's description (or the from Roman or Modern times). The second system, only found during the Middle ages, was 1 opposite 2, 3 opposite 4 and 5 opposite 6 (instead of the opposite sides totalling 7). Medieval dice are small, compared to modern ones, sizes between 9-12 mm are common. False medieval dice also existed. A London find did contain a whole set of false dice. Some were weighted, or had more sixes or ones.













Left: Bone dice from Amersfoort, the Netherlands dating from the 14th century.  Right: Two systems of arranging pips from 12/13th century dice made of jet from York, UK. 11079 is our current system, while 11078 uses the alternative medieval system.



Two sets of Roman six-sided dice, currently on auction (14 October) at Hermann Historica (starting bid 3-400 Euro for 20 dice which are also perfect for medieval re-enactment). You can see the concentric circles of the pips, which are also very common during medieval times. Some have two concentric rings, other only one (left photo). The right photo shows some dice with sides that are rounded off and decorated. White dice are made of bone, the black of horn.

Seven-sided dice


There are several games in the "Libro de los Juegos" that make use of 7-sided dice, like Decimal chess, 4-season chess, and the game of the four seasons called the world. Folio 84 describes how the 7-sided dice are made. The book also describes an eight-sided dice, which looks like our modern one (used e.g. in fantasy roleplaying games).

"[f. 84]
And these dice are made like this: they have seven sides and the side with the highest number of pips is seven. They could not be made in another way for this game.
Because the shape of this die is uneven it falls edge up, with two sides showing. The side closest to the shooter is his. If they fall so that it cannot be determined which face to use, they are to be thrown until it can.

.....
There are other seven-sided dice than the ones we describe above. And this is how they are: they have two flat ends, the upper end with seven and the lower with six. The sides have five faces and because the sides are odd in number they cannot help but fall edge up. And for these five sides the play is the same as we described before. And this is their diagram and how they are made. [f. 84v]"

Making the seven-sided dice


I had some antler at home, which was at the basis solid white like bone. This made it very suitable for to make my 7-sided dice. Antler is worked similar like bone. First, I cut an 12.5 mm thick slice from the antler and ground it flat using sandpaper.


Left: The piece of antler, the two slices cut of (for two 7-sided dice) and two test 6-sided dice. Right. Sanding the slices of antler on a 150 grit sandpaper.

Then I glued a paper pattern of the pentagon on the antler slice with water-soluble glue. Then I used a hand held rotary tool (Dremel) with a ceramic cutter to cut the (remaining four) sides of the die. These sides were also sanded to have an acceptable die with equal squares. My first 7-sided die had squares of 12.5 mm, which made the pentagon side disproportionate large. My second die had rectangles of 11 by 12.5 mm, which gives a better proportion in comparison with the pentagon side.  





 Left: Laying out the pattern on the antler slice. Right: The roughly cut seven-side die.

The blank die being ready, the next step was to drill the pips. King Alfonso told that the 6 and the 7 were on the pentagon, but no mentioning was made for the arrangement of the 1 to 5 pips. I decided just to use the 1 to 5 order on the rectangles. The second problem was to drill the concentric circles for the pips. In medieval times this was done with a pump drill with some sort of toothed drill bit. I did not have these tools, so I had to improvise. For the concentric circle I used a sanding drum holder for my rotary hand tool and sharpened the edge. For the central dot, I used a cutter from the dentist (They use them only once and you can get them for free at your yearly visit). I also devised a jig to make the positioning of the dice under the drill stand easier (one-dimensional instead of two-dimensional), and another to hold the pentagon.



Left: The concentric ring drill bit made from a drum sander. Another drum sander is next to the pliers. Right: The bench clamp holding the the die moves along a fixed ridge, making the positioning of the drill easy and one-dimensional. First, all circles were drilled for this position, then the circle bit was changed for the dental cutter. After that, the ridge was moved to a new position to start again with some new pips.


Left: The bench clamp holding the jig for the pentagon. For the drilling of the rectangular sides, the die is just held in the clamp with some rubber protective edge. Right: Positioning of the die under the drill. First the concentric ring, then the centre dot.  






Left: A circular drawing by pencil is made on the pentagon, which is in turn dived into six parts. This shows the points where the pips should be drilled at equal distance. Right: The pentagon in the jig,  Pips can be drilled in sets of two, before the ridge has to be moved in a new position. This side will have seven pips, the middle three are finished, the two left pips only have the concentric circles. 


Left: The two seven-sided dice on the game board of the Four Seasons, called the World. Right: A close up of the dice.

f. 85v: A game of Decimal Chess using seven-point tables, seven-sided dice and seventeen pieces on each side. Alfonso is named as one of the players here.

The seven-sided dice throw reasonably fair, considering the fact that the pentagon sides are (slightly) larger. Next post will on making the game counters for the Game of the Four Seasons, called the World.

9 comments:

  1. to make the dot-and-ring design of the pips, which are also used on ornaments, art, sculpture and coinage, i made my own drill bit.

    Take a nail or similar metal, and flatten the end. then sharpen it with a file so there are three points, one in the center and two equally apart from it. Then put this into your drill.

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    1. Well, that also solves centring the point in the circle. Thanks!

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    2. Very nice game! Wonderful work! Say, please, how to identify winning number on a 7-sided dice?
      Margarita, Russia

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    3. For the numbers six and seven it is obvious. They sit on either side of the pentagons and fall flat on the table. The side that is above is the number that you throw. The numbers one to five, however, are on the squares sides of the die. If two of the squares are up, you choose the side which is directed most towards the person who has thrown the dice. You have thrown that number. If you can not decide which side to choose, you have to throw again.

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    4. for my two dice shown on the photo, you would have thrown a 7 and a 2 (assuming the one throwing the dice sits behind the computer)...

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    5. Thank you very much! I understand everything

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  2. I'm impressed but your work got me thinking.
    Maybe I'm completly wrong, but according to http://en.wikipedia.org/wiki/Regular_polygon
    are the area of an 5-sided polygon 1.72 times bigger then one of the sides.
    This should give that the height should be 17.2 millimeters so all sides of the dice have the same area.(and in my mind roughly the same probability to land on)
    Out of my own curiosity, have you tried if the probabilities of your dice is correct?

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    Replies
    1. Both my 7-sided dice have different dimensions. I did not calculate if the areas of the rectangular and polygonal sides were equal (i thought of this after the first one was made and corrected it a bit for the second die), and hence the probabilities are not correct. Nevertheless all pip numbers do show up eventually; the 6 and 7 appear more often.
      But equal areas are not the only thing to consider for the 7-sided dice, also the angle between the sides plays a role. An 90 degree angle rolls less, than the polygonal angles.

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  3. Hi,

    I was wondering how you made the drill bit from the drum sander? I am looking at making my own dice and I was not sure how you made your drum sander concentric drill bit.

    Thansk!

    ReplyDelete