Using coins will quickly reveal some problems: while shaking the coins in cupped hands, it's hard to know whether they are truly being tumbled; when flipping the coins, they tend to bounce and scatter. It's much easier to use a die as a coin-equivalent: if an odd number of pips shows, it counts as "heads"; if an even number of pips shows, as "tails." Obviously, the 50/50 probability is preserved — and rolling dice turns out to be easier and quicker than flipping coins. Thus the three-coin method will use three dice.
Dice can also be used for the two-coin method. It is best to use two pairs of dice, each pair having its own color — e.g., a pair of blue dice and a pair of white dice, such as are commonly found in backgammon sets. One pair can then be designated the "first toss" in the two-coin method, and the other the "second toss." One roll of four dice will then determine a line, with probabilities matching the yarrow-stalk method.
The number values on a single die can also be used to determine the hexagram's lines. Designate odd numbers as yang, even numbers as yin, and roll a six-sided die once for each of the six lines. Roll the die a seventh time to determine the moving line. This method mimics Zhou court divinations in which yarrow stalks were used in a two-stage divinatory process, first casting the hexagram, then designating one line as moving (see Shaughnessey, 1996, pp. 7–8).
Since a single toss of three distinct coins allows for eight possible combinations of heads & tails, the three-coin method's probabilities can be duplicated with a single eight-sided die, rolling it once to generate each line. Use an odd and an even number on the die, 1 and 8 for instance, to designate a moving line when either number is obtained. This preserves the equal 1/4 chance that a given yin or yang line will be moving.
A similar distribution to yarrow stalks is possible using two dice, 1 eight-sided (1d8), and 1 twenty-sided (1d20). Roll both of them at once per line.
- If the 1d20 is an even number
- if the 1d8 = 1 -X- moving yin (1/16 probability)
- if the 1d8 = 2 - 8 - - yin (7/16 probability)
- If the 1d20 is an odd number:
- if the 1d8 = 1 - 5 ––– yang (5/16 probability)
- if the 1d8 = 6 - 8 -0- moving yang (3/16 probability)
Another duplication of the yarrow stalks' probabilities can be done by taking the total of two eight-sided die rolls (2d8; odd totals indicating yang lines and even totals indicating yin), to produce each hexagram line. The 1:1 distribution of yin and yang is preserved, and the chances of obtaining certain totals will be used to match the yarrow stalks' weighted distributions of moving yin and yang lines.
The 2d8 roll provide four possible instances where the total is either two or four, which equates to the yarrow stalks' chances of a yin line being moving. This can be demonstrated by mapping all totals on an 8x8 grid, each axis representing the numbers on one die. The chance of an even (yin) total being two or four (moving) is then 4/32, equaling 1/8. Weight the distribution of moving yang lines similarly, by using totals that equate to a 3/8 (or 12/32) chance of obtaining that result among the 32 odd possibilities, such as seven and 11 (which can likewise be diagrammed on the 8x8 grid). So a total of two, four, seven or 11, when yielded by one 2d8 roll, can indicate that the resulting yin or yang line is moving.
A very simple method on casting the I Ching whereas one has only one changing line for the hexagram would be using a single six-sided die. Even numbers are yin, odd numbers are yang. Roll six times to create the hexagram, a seventh time to determine the changing line. 1 is the bottom line, 2 is the second line from the bottom, 3 is the third line from the bottom, etc...
Other articles related to "dice":
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Famous quotes containing the word dice:
“The dice of God are always loaded. The world looks like a multiplication-table, or a mathematical equation, which, turn it how you will, balances itself.”
—Ralph Waldo Emerson (18031882)
“Often beneath the wave, wide from this ledge
The dice of drowned mens bones he saw bequeath
—Hart Crane (18991932)
“When God throws the dice are loaded.”