## Sunday, 15 May 2016

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.