To cast an hexagam, proceed as follows:

- Shuffle the deck
- Pick a card;
- If the suit is
*spades*(♠), write down**2**; Otherwise, write down**3**; - Pick another card;
- If the suit is
*black*, write down**2**; Otherwise, write down**3**; - Pick a third card;
- If the suit is
*black*, write down**2**; Otherwise, write down**3**; - Sum up the numbers and draw the line according the following table:

6 7 8 9 - Reinsert the three cards in the deck
- Repeat steps 1-9 other five times drawing the resulting lines from the bottom to the top of the hexagram.

**Probabilities**

The calculations are simple, just a little bit tedious. The diagrams below summarize all the possible events and their probability:

By multiplying and then summing up the above probabilities we get:

Prob(6) = 5.88% (-0.37%)

Prob(8) =

Prob(7) =

Prob(9) =

Prob(

Prob(

Prob(8) =

^{ }43.75% (+0.86%)Prob(7) =

^{}31.25% (+0.12%)Prob(9) =

^{}18.14% (-0.61%)Prob(

*yin*) = 50.49%Prob(

*yang*) = 49.51%Compared with the yarrow stalks method (see the numbers between parenthesis) this methood is less likely to produce moving lines. Also, it slightly (0.5%) favours

*yin*lines over

*yang*lines.

#### Getting Yarrow Stalks probabilities

If the cards reinserted in the deck the actual probabilities are exactly the same of the yarrow stalks method.- Shuffle the deck
- Pick a card;
- If the suit is
*spades*(♠), write down**2**; Otherwise, write down**3**; - Reinsert the card and reshuffle the deck
- Pick another card;
- If the suit is
*black*, write down**2**; Otherwise, write down**3**; - Repeat steps 4-6 once again
- Reinsert the card in the deck
- Sum up the numbers and draw the line according the following table:

6 7 8 9 - Repeat steps 1-9 other five times drawing the resulting lines from the bottom to the top of the hexagram.

#### Getting three coins probabilities

The more logical variation to get the three coins method probabilities, is to always assign 2 to black cards and 3 to red cards:- Shuffle the deck
- Pick three cards;
- For each black suit, count
**2**; for each red suit, count**3**; - Sum up the numbers and draw the line according the following table:

6 7 8 9 - Reinsert the three cards in the deck
- Repeat steps 1-5 other five times drawing the resulting lines from the bottom to the top of the hexagram.

Prob(6) = 11.76% (-0.74%)

Prob(8) =

Prob(7) = 38.24% (+0.74%)

Prob(9) = 11.76% (-0.74%)

Prob(

Prob(8) =

^{ }38.24% (+0.74%)Prob(7) = 38.24% (+0.74%)

Prob(9) = 11.76% (-0.74%)

Prob(

*yin*) = Prob(*yang*) = 50%Where the numbers in parenthesis represent the discrepancy from the three coins methods. The chance of getting a moving line is lower; the probability of getting

*yin*or

*yang*is 1/2.

Again, reinserting the card at each step (and reshuffling) would give exactly the three coins method probabilities.

Cards images: Atlasnye

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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