Twelve square cards

[remod]

Following @breakmov indications, I've created the design for a square card that would directly generate a hexagram with his moving lines (with three coins probabilities)

The front/back sides of each card are the following:



To cast a hexagram, you mix, shuffle, and rotate 12 of those cards, then you lay them out preserving the orientation and alternating front and back as shown in the following picture:

etc.

until you stack all the twelve cards and you'll get the entire hexagram with the moving lines (the red dots).



If a card with lines appears on one of the "white" sides, the curve in the middle will help determining which line you got:



the card on the left side represents a broken line, and the card on the right side is a solid line. You will turn the card 90 degrees clockwise to make it directly show the line on the bottom.

These cards could be created very easily with a marker. Those artistically talented could add other graphical elements to enrich the visuals.

I hope it is close enough to what @breakmov had in mind.

 

[breakmov]

Yes, the idea turns out to be equivalent to that. I liked the graphic option you used to replace the numbers and this whole option test

breakmov

 

[remod]

I simply can't stop thinking about it until I've exhausted all the possibilities
An alternative design that can use only 6 square cards is the following:



The red lines represent moving lines.

So, after having shuffled, rotated, and mixed the six cards one could lay them out as follows to instantly get a hexagram and its moving lines (with three coins probabilities).



Just another option (possibly more portable and easy to use).

P.S. Note that you could use just one of these cards to cast hexagrams line by line. You rotate and flip at will and then pick a side. That's your line. Repeat six times for your hexagram.
Think how portable this method is, the card can be tucked into your favorite I Ching book so that you have it at your disposal any time!

 

[breakmov]

It's curious how thoughts multiply and often in resonance like this case... in the previous option, I imagined this solution that you left, filling the free sides by duplicating the lines, to solve the problem of one side of the card appearing without a line, due to rotation.
...I'm thinking how to do something similar, without the rotation component, maybe with an equivalent, for rectangular cards.

breakmov

 

[remod]

Square cards are more "powerful" because they are equivalent to an 8-sided die and considering that there are 8 trigrams and that the probabilities for three coins are multiple of 1/8, there are many possibilities.

For example, you can split the eight trigrams on the back and front of a square card


and use two of them joining them along a side to get a hexagram with a probability of 1/64. (you are left with the problem of moving lines, though).




Rectangular cards, instead, are equivalent to a 4-sided die (considering flipping back/front and rotating up/down) so you need at least two of them. Freely mixing and matching two cards gives you 32 possibilities which are enough to accommodate either the three coins probabilities or the yarrow stalks probabilities (as multiples of 1/16).

Using more cards quickly gives you more outcomes, with three cards you have 384 possible outcomes, with four cards 6144, and so on.

The challenge is to find the right simplification to make some of the outcomes to collapse, leaving the user with fewer outcomes to manage.

For example, by using three cards, only one face for each card, and allowing rotations, the number of possible outcomes drops to 48.

The seven (or two) cards I use at the moment cut the 32 possible out to 16 by "compressing" two 4-sided dice on each card. You can simply join the long side of one card with the short side of the other. Or the upper left corner with the upper right corner and so on.

There is a method to cast a hexagram all at once using three rectangular cards marked as follows:


You flip, shuffle and rotate the cards and then lay them down, sum up the left upper corner of each card and add 1. That's the number of your hexagram.

For example this is the hexagram 28 (3+8+16+1):



And this is the hexagram 6 (1+0+4+1)



Feasible but quite impractical, I think.

What do you think?

P.S. Of course this can also be done with 6 rectangular, single faced cards market (0,1) (0,2) (0,4) (0,8) (0,16) (0,32). They are just binary numbers. It's more additions, though.

 

[my_key]

Hi remod
There are some interesting ways of exploration Yi casts outlined here.
This sounds like it is holding a possibility of a new casting ritual using cards. In the past when I have explored I Ching divination with cards I have just picked 2 cards. A primary and a relating hexagram are produced and there is never a scenario for an unchanging hexagram. This certainly looks to be a possibility using your square cards. Am I correct in that statement?

I'm wondering though what are the probabilities in your method for lines representing yin, yang, old yin and old yang. Especially when looking at how they compare with the probabilities of the more common divination methods of yarrow, coins and marbles.

Do you have any insights about this?

 

[remod]

This sounds like it is holding a possibility of a new casting ritual using cards.

Thanks, @my_key.

I assume you're talking about the initial idea from @breakmov in the two incarnations I proposed:

and

right?

If this is the case, they can generate hexagrams with any number of moving lines, from 0 to 6.
They are exactly equivalent to the three coins method where the probabilities for lines are:

6 -> 1/8 7 -> 3/8 8 -> 3/8 9 -> 1/8

It is easier to see it in the second version (the one using 6 cards). Out of the 8 possible outcomes, 3 are yin, 3 are yang, 1 is old yin and 1 is old yang. Hence, the odds are the same as the three coins method.

For the method using 12 square cards (the first one presented) it's slightly more complicated.
The cards, after having been shuffled, are laid out alternatively front/back/front, etc as shown in the picture



The front card has 1 possibility out of 4 (i.e. 25%) to have the red dot in the lower left corner meaning that there is a 25% chance for a line to be moving.
The back card provides yin or yang lines with a probability of 50% (1/2) each.

So, the possible outcomes are:
1/4 * 1/2 -> 1 /8 -> old yin
3/4 * 1/2 -> 3/8 -> yin
3/4 * 1/2 -> 3/8 -> yang
1/4 * 1/2 -> 1 /8 -> old yang

The same as the three coins method.

I hope I've been clear enough. Please tell me if it's not the case.

Personally, I prefer methods that generate lines with the yarrow stalk probabilities that's why I've devised methods that use two, three, four, five, seven, or eight cards that generate lines with yarrow stalks probabilities.

Many of them are described in this thread and this thread but there are others.

I could also adapt this design with square cards to make them generate yarrow stalks probabilities (but you need seven or twelve of them). Let me draw them down and I'll make a new post in this thread.

Happy to see this topic piqued your interest!

 

[remod]

To generate lines with yarrow stalks probabilities (or, better, the marble ones), one can use twelve square cards whose front/back is designed as follows:



You shuflle and rotate them (without flipping them!) and then lay them out in pairs as shown here:

(and so on for the other pairs)

You look at the upper right combination to determine the nature of the line (in the picture above they are 7 and 8). You then use the back of one of the cards in each pair to record the line and form the hexagram.

(and so on).

The table below shows why this produces lines with yarrow stalks probabilities.
Corners are marked with 2,3,3, and 3 red dots.
Sides are marked with 4,5,5,6 black dots.
Summing up a corner and a side, out of the 16 possible outcomes, 1 is a six, 7 are eights, 5 are sevens and 3 are nines.

You can use only seven of them by pairing them two at a time and recording the line with one of the cards (then you may reshuffle or not, at will).

 

[remod]

Wondering if using numerals would be clearer:


Maybe with numerals is easier to focus on using always the top pair of numbers:



What do you think?

 

[my_key]

Hi remod
I have been drawn by the visual impact the cards make. I also like that the card methods certainly add some contemplation time with the required shuffling actions.

The considerations of the probabilities is an important consideration, and whilst I am not a probability expert you have clearly relayed how probabilities for yarrow, marble and coins are maintained. There has always been a slight mismatch between coins and yarrow / marble methods - that for me is the main reason I chose to use marbles.

Yarrow / marble Coin
6 – moving yin: 1 in 16 [2 in 16]
7 – static yang: 5 in 16 [6 in 16]
8 – static yin: 7 in 16 [6 in 16]
9 – moving yang: 3 in 16 [2 in 16]

One further query is how do you keep the appropriate ratio of probabilities if you are pulling two lines at a time (per your diagram) or using some of the cards to stack and show each line you have drawn to build the hexagram. With marbles I always have to return the marble I have just selected back into the bowl to maintain the integrity of the probability of the next selection.

You may already have this one covered, or I may have missed it in the above posts.

The dots appear more authentic the numbers are easier to do the sums. Numbers also less prone to miscounts.

 

[remod]

I also like that the card methods certainly add some contemplation time with the required shuffling actions.

I do also agree that a certain amount of "manipulation time" is needed for better focus on the issue one is asking about.

The considerations of the probabilities is an important consideration, and whilst I am not a probability expert you have clearly relayed how probabilities for yarrow, marble and coins are maintained. There has always been a slight mismatch between coins and yarrow / marble methods - that for me is the main reason I chose to use marbles.

I do prefer the yarrow stalks/marble probability exactly because them being asymmetric. It reminds me that nothing is ever perfectly balanced and that is this imbalance that generates changes.

One further query is how do you keep the appropriate ratio of probabilities if you are pulling two lines at a time (per your diagram) or using some of the cards to stack and show each line you have drawn to build the hexagram.

The diagram was just an example, you pair the cards and from each pair, you get a line with marble probabilities.
To get a single line, the process is to

• pair two cards,
• count the dots (or do the sum),
• use one of the cards to record which line you received (by laying down the card with that line at the bottom).

For example, if, after shuffling and rotating the cards, you get the following outcome:


You use one of the two cards to record the line you got (9):



Then you pair other two cards and, for example, you get:

You lay one of these cards on top of the previous one to record the fact you got a 7:



Pair other two cards and, say, you get 8:


Again, you pick one of these cards and lay it on top of the previous ones:



Continue this way to get the other three lines and complete the hexagram.

If you start with seven cards, you do the pairing, lay down one of the cards to record the outcome, and use the other card for the next pairing.
If you start with twelve cards, you can do six pairs after the shuffling and then flip them to see the outcome.

I would probably prefer to start with seven cards, but that's just my preference.

The probabilities only depend on the fact that you use two cards, as long as you have enough of them, the odds are safe. I hope it's clearer now.

With marbles I always have to return the marble I have just selected back into the bowl to maintain the integrity of the probability of the next selection.

I never managed to keep marbles together (the ones I used had the tendency to get lost every time) so I string them in a sort of bracelet (or rosary) with beads of one or two colors. A couple of examples:



I prefer the version with beads of the same color and made a lot of them, but I kept losing them as well.
So I moved to cards (which I seem to be better at not losing ) and I've found them to be very comfortable to use.

The dots appear more authentic the numbers are easier to do the sums. Numbers also less prone to miscounts.

I'll put together images that can be used to properly print these cards (both versions) with a print-on-demand service (it will be really cheap to print them as business cards).
I'll make them available here, just in case someone wants to try them.
Any suggestion on the graphic to use (more elaborate? Simpler? ...) will be welcome.

 

[remod]

I've thought, actually, that starting with 12 cards is better. It allows you to keep track of the received hexagram and the relating one at the same time.
To get the hexagram, you do the pairing and use one card to track the received line and the other to track the changed one (or the same if it's not a moving line).

At the end you'll have the full answer in front of your eyes.




The following two images are big enough to be printed at 300dpi on a 6,9x6,9cm square business card. I've been careful to stay in the printing "safe zone" but you should check if you ever decide to print them. You can download them by first clicking on each of them, then right-click on the larger image that appears, and selecting "save image as ...".




To stay cheaper I've opted for a 5.5x5.5 format and ordered 100 for 21€ (taxes and shipping included). Some of my friends will soon roll their eyes and say "again?!?!" when I'll give some to them .
I hope you like the image at the center ...

If anyone is interested in the version with dots instead of numbers, just let me know and I'll make them as well.

 

[remod]

And here is the version with three coins probabilites (closer to initial @breakmov idea, I believe).
These are even easier to use as you simply shuffle, flip, mix and rotate them at will and lay down the first six cards by sliding them upwards to form the received hexagram. Use the other six cards to record the relating hexagram.




(or use only six of them for increased portability).

If you want to make them yourself, here is a PDF (600K) that should help you doing so.

PS: I forgot to mention that these cards can also be useful just to keep track of your casting when using other methods (say, three coins). You can use all twelve to track separately the received hexagram and the relating one, or just six (red moving lines are a good enough indicators, I think).

 

[remod]

My "business cards" have just arrived. The last picture is for the set of 12. Still quite portable, I think.

Yes, there is the risk of losing or damaging some cards but I have 100 of them now. Good for a lifetime

It might be worth considering just 6 of them to be used as a tracker, it seems a pretty easy way to keep track of the outcome.

 

[remod]

Just a note on printing cards as business cards instead of playing cards.
You get a lower price but you also get lower quality. Especially for the cut, not only the cards I got are slightly off-center in an inconsistent way. Some of them are slightly shifted on one side and some on another side.
This never happened with the playing cards printing services I used.

Nothing that really bothers me but I thought you may want to know if you want to print them.

 

[remod]

I just figured out that also the version that I labeled as "three coins probabilities" can be used for obtaining lines with yarrow stalks probabilities. Again, using the same "trick" that @breakmov illustrated in his dice chain.

To get yarrow stalk probabilities, you consider the black lines as "non-changing" and the red lines as "potentially changing". To confirm that a red line is, indeed, changing, you pair it with another card and look at the second card. If the line is of different nature (regardless of the color) the line is really a changing line.

For example, these two are changing lines because the second card is showing a line of different nature.



While these ones are non-changing lines because the second card confirms the nature of the received line:

 

[breakmov]

could you please explain better how you create the difference in probabilities between yin lines and yang lines?

breakmov

 

[remod]

You are right @breakmov, I described it wrongly: for the yang lines, the black lines are those that can potentially change, not the red ones! Sorry for the confusion.

Let me go step by step.
These are the front/back of each card:



Let's assume we have 12 of them and that we'll focus (after flipping, rotating, and shuffling) on the bottom line for each card.

The procedure for getting a line with yarrow stalks probability is the following:

1. Pick two cards and pair them so that the two bottom lines are visible.
2. The first of the two lines determines the nature of the line (yin/yang)
3. If the first line is a yin (broken) line, to determine if it is changing:
   • If it is red and the second line is a yang (solid) line of whatever color, it's a changing line
   • Otherwise, it is unchanging
4. If the first line is a yang (solid) line, to determine if it is changing:
   • If it is black and the second line is a yin (broken) line of whatever color, it's a changing line
   • Otherwise, it is unchanging

Let's calculate the probabilities.

First of all, let's note that the probability to get a yin or yang line from a card (regardless of the color) is 1/2 since there are exactly 4 yin lines and 4 yang lines among the 8 possible outcomes.

To receive a changing yin (broken) line, the first line must be a red yin line and this happens with probability 1/8 (there is only one red yin line among the eight).
So, the probability to get a changing yin line is the probability that the first line is a red yin line and the second is a yang line which is 1/8 * 1/2 = 1/16.

To receive a changing yang (solid) line, the first line must be a black yang line and this happens with probability 3/8 (there are three black yang lines among the eight).
So, the probability to get a changing yang line is the probability that the first line is a black yang line and the second is a yin line which is 3/8 * 1/2 = 3/16.

To receive an unchanging yin line, you must receive a yin line that is not changing (of course). The probability is: 1/2 (the probability of getting a yin line) minus 1/16 (the probability that is a changing yin line). Which is 8/16 - 1/16 = 7/16.

To receive an unchanging yang line, you must receive a yang line that is not changing (of course). The probability is: 1/2 (the probability of getting a yang line) minus 3/16 (the probability that is a changing yang line). Which is 8/16 - 3/16 = 5/16.

Hope it is clearer now. Please feel free to ask if something is still too vague.

My bad for not having described the method correctly in the previous post!

 

[breakmov]

yes that was the idea ...I don't use these probabilities precisely because of the lack of symmetry in them.

The two colors you use play the role of the numbers I use on my YiDragon

I leave an image of the yarrow probabilities for each pair of dice





PS- for the normal yang line:
where it says "when 3 appears on the left die..." it should include

"when 3 appears on the left dice and 1 does not appear on the right dice"....


breakmov

 

[remod]

I like your YiDragon a lot

From the picture, the dice seems to be made of metal so you probably can't change the number of dots on their faces.

If you could change them, marking all the left side dice with 3,4,4,4 and all the right side dice with 3,4,4,5, just by summing the two dice you would get 6,7,8, and 9 with yarrow stalks probabilities.

Marking the left side dice with 3,4,4,3 and the right side dice with 3,4,4,5 will provide 6,7,8, and 9 with three coins probabilities.

The YiDragon would not change, it would just be easier to read.

P.S. here are the tables that show how the marking produces the desired probabilities:

 

[breakmov]

Thank you.
I assigned the option of using the numbers 1, 2, 3 ,4 due to the metaphysical meaning of these numbers and their sum...
1+2+3+4 = 10
But the main reason has to do with simplicity and with just a simple glance noticing which lines change.

It is no longer possible for me to edit the post #, but maybe I should have left a simpler explanation/image like this one....



But back to your topic...

I loved that simple 12 cards aspect in post #12....and with the natural option to use yarrow stalks or coin odds what more could you ask for?

ps -I'm gathering material to make a square deck inspired by that simple look that you left in the 12 cards..I found material that is resistant (acetate) and thin enough (50 micron ....+/- 0.05mm) to make the deck of cards, with Zhou Yi attached, with a total width of 19.2 mm ( ... 0.756 inches)

breakmov

 

[remod]

I would love to have a look at your deck. The thin material could help achieving your goal.
Please post it when you'll have a prototype, I'm curious!