*Liubo*but I didn't know it was related to the I Ching or to divination in general.

Sven Christensen sent me a very interesting article where a parallel between games and divination is drawn and some light on the relationship between Liubo and the I Ching is shed.

Liubo rules are long lost and they were most probably not directly related to divination with I Ching, so the best I can do is to make up a method for casting hexagrams using the same principles that Chris devised for his "One Die Method".

The picture[1] below shows a Liubo dice wich is a 14-sided irregular polyhedron. Since the symbols are repeated twice, it is actually a 7 values die.

A possible method for casting a line (directly inspired to Chris' method) could be the following:

- Throw the die and look at the face on the top:
- If it contains lines, draw ;
- If it contains a symbol, draw ;
- If it is empty, throw the die again and look at the face on the top:
- If it contains lines, draw ;
- If it contains a symbol, draw ;
- If it is empty, restart from step 1
- Repeat steps 1-4 until you have drawn all the lines from the bottom to the top of the hexagram.

#### Probabilites

Let's begin by noticing that the steps 1-4 above could not produce any line: the probability of such event and the probability of, instead, getting a line are:
Prob(

Prob(

*no line*) =^{1}/_{7}*^{1}/_{7}=^{1}/_{49 }Prob(

*line*) = 1-^{1}/_{49}=^{48}/_{49 }The probability for each possible outcome (conditioned to the event of actually getting a line) is:

Prob(6) = Prob(9) = (

Prob(8) = Prob(7) =

Prob(

^{1}/_{7}*^{3}/_{7}) *^{49}/_{48}=^{1}/_{16}= 6.25%Prob(8) = Prob(7) =

^{3}/_{7}*^{49}/_{48 }=^{7}/_{16}= 43.75%Prob(

*yin*) = Prob(*yang*) =^{1}/_{2}It is interesting to note that this methods has something in common with the Yarrow Stalk method (probabilities as multiple of 1/16, 49 possible outcomes from throwing) and something in common with three coins method (same probability for 9 and 6).

To enahance the fairness of the die, if you decide to build it, I suggest you alternate the symbols so that the the same symbol appears once on a square face and once on an hexagonal face.

3D printed Liubo dice are availble on Shapeways.

[1] http://www.livescience.com/52806-tomb-ancient-board-game-photos.html

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