Wednesday, 29 June 2016

Three cards

One of the drawbacks of using just one or two cards is that when shuffling them it may be possible to keep track of their orientation and position even without looking; it could take quite some time before losing track of which face is which.
Using three cards (considering only one face and two orientations) provides 48 combinations which make the result dependant on the orientation and the position of each card (and it is much more difficult to keep track of three cards at the same time).

I designed the following three cards (these are scanned images as I lost the original jpg!):







where each card can result in being yin or yang depending on both the other two cards.
They are to be used as follow:
  1. Shuffle the three cards at will; remember to rotate one of two of them from time to time while shuffling (it is important!);
  2. Turn the cards and look at the three ideograms on the upper left corner;
  3. If the same sequence appears on the left of one line, draw that line. Otherwise draw the other line. Note that any ideogram can be placed where a red circle appears.
  4. Repeat steps 1-4 other five times drawing the hexagram from bottom to top.
 The following  pictures show some examples.

Result: yin (broken line) as the sequence of the three upper ideograms doesn't appear at the left of any line

Result: moving yin (broken line) as the sequence of three upper ideograms appears at the left of any line (the red circle can be replaced by any ideogram)

Result: yang (solid line) as the sequence of the three upper ideograms appears at the left of any line

Result: moving yang (solid line) as the sequence of the three upper ideograms doesn't appear at the left of any line

Note that if you hold them in your rught hand is even easier to read them as your hand will cover the right side of card which is not relevat for the result.

Probabilities

The lines and the ideograms are set to provide exactly the same probabilities of the sixteen marbles method:

Prob(6) = 1/16
Prob(8) = 7/16
Prob(7) = 5/16
Prob(9) = 3/16
Prob(yin) = Prob(yang) = 1/2


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