Sunday, 15 May 2016

One die (1d6)

 

Sven Christensen recently shared a method he devised for casting hexagrams using just one regular die. The method proceeds as follows:

  1. Throw a six face die;
  2. Depending which line you're drawing, look up in the following table (re-throwing the die if needed):
  3. Draw the line that corresponds to the number you got;
  4. Repeat step 1-3 drawing the hexagram from the bottom to the top line.
You can find the original pdf file on Sven's site.

Probabilites

This method is very peculiar in that it does not assign the same probability to all the 64 hexagrams. With most of the other methods, each hexagram has 1/64 probabilities to be the outcome (1.56%); with this method, the most probable outcome is hexagram 64 (3/6 + 1/6 * 3/6)6 = 3.94% and the least probable hexagram is 63 (2/6 + 1/6 * 3/6)6 = 0.52%.

The probability of the other hexagrams can be calculated using the following values:

Prob(6) = Prob(9) = 1/6 * 3/6 = 1/12 = 8.33%
Prob1,3,5(8) = Prob2,4,6(7) = 3/6 = 50.00%
Prob2,4,6(8) = Prob1,3,5(7) = 2/6 = 33.33%
Prob1,3,5(yin) = Prob2,4,6(yang) = 3/6 + 1/6 * 3/6 = 58.33%
Prob2,4,6(yin) = Prob1,3,5(yang) = 2/6 + 1/6 * 3/6 = 41.67%

where Prob1,3,5(x) means "Probability of x for the line 1, 3 or 5" and similarly for Prob2,4,6(x).

It would be interesting to understand what difference this makes (if any) in the interpretation of the outcome.

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