Sunday, 23 January 2022

Two Coins
 Another method, with only two coins, I learned from Clarity

  1. Throw the two coins.
        If they both show head count 2 otherwise count 3
  2. Throw the two cons again
        Count 2 for each head and 3 for each tail.
  3. Sum it all up and draw the resulting line according the following table:
    6 7 8 9
  4. Repeat steps 1 and 2 other five times drawing the resulting lines from the bottom to the top of the hexagram.

Probabilities

This method generates lines with the same probabilities as the yarrow stalk method because the odds of getting 2 in the first throw are 1/4.

For each of the possible eight outcomes, probabilities are:

2+2+2 = 6  1/4 * 1/2 * 1/2 = 1/16
2+2+3 = 7  1/4 * 1/2 * 1/2 = 1/16
2+3+2 = 7  1/4 * 1/2 * 1/2 = 1/16
2+3+3 = 8  1/4 * 1/2 * 1/2 = 1/16
3+2+2 = 7  3/4 * 1/2 * 1/2 = 3/16
3+2+3 = 8  3/4 * 1/2 * 1/2 = 3/16
3+3+2 = 8  3/4 * 1/2 * 1/2 = 3/16
3+3+3 = 9  3/4 * 1/2 * 1/2 = 3/16

 

 Meaning that:

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


1 comment:

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