Probability of Change
So I'm curious about the probability of receiving a changing line in a casting.
From the wikipedia page is a nice chart with probabilities:
With both coins and milfoil there is a 50% chance of getting a yin or yang line. With both coins and milfoil there is a 25% chance of getting a changing line. Within a changing line:
With coins it is equally probable for the change to be yin-to-yang or yang-to-yin. However with milfoil it is more probable for a yang line to change than for a yin line to change.
So it would appear that different casting methods draw on different principles to calculate change.
Milfoil appears to use the principle that it is more likely for yang energy (firmness/substance) to change and become used and form yin. While on the other hand it is less likely for yin receptivity to cultivate enough stillness within its field for what is in motion to settle and gather back into firmness / yang.
While with coins it would appear just as likely for a yin to settle into yang as yang to settle into yin.
I know a lot of people prefer to use coins as milfoil takes much longer. However given the above differences, I wonder if we can really consider these methods to be interchangeable.
Earlier I was also reading about the marble method for casting, which appears to duplicate the probability of milfoil castings while making the process much simpler. Marbles are nice and simple, but any objects could work once marked appropriately, like these.
I am curious if others have explored this difference in principle behind change within casting methods.
I added customizable variance to my program and ran it from +- 1 through +- 10 (e.g. stack size / 2 +- 1, etc.). The results are unexpected.
Variance: 1
Permutations: 8
Yang (old) percent: 25.000000
Yang (young) percent: 25.000000
Yin (old) percent: 0.000000
Yin (young) percent: 50.000000
Variance: 2
Permutations: 64
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 3
Permutations: 216
Yang (old) percent: 16.666667
Yang (young) percent: 33.333333
Yin (old) percent: 8.333333
Yin (young) percent: 41.666667
Variance: 4
Permutations: 512
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 5
Permutations: 1000
Yang (old) percent: 20.000000
Yang (young) percent: 30.000000
Yin (old) percent: 5.000000
Yin (young) percent: 45.000000
Variance: 6
Permutations: 1728
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 7
Permutations: 2744
Yang (old) percent: 17.857143
Yang (young) percent: 32.142857
Yin (old) percent: 7.142857
Yin (young) percent: 42.857143
Variance: 8
Permutations: 4096
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 9
Permutations: 5832
Yang (old) percent: 19.444444
Yang (young) percent: 30.555556
Yin (old) percent: 5.555556
Yin (young) percent: 44.444444
Variance: 10
Permutations: 8000
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Here is the average percentage if the split variance is between 1-5 stalks: Yang (old) percent: 19.834
Yang (young) percent: 30.166
Yin (old) percent: 5.166
Yin (young) percent: 44.834 And here is the average percentage if the split is between 1-10 stalks: Yang (old) percent: 19.272
Yang (young) percent: 30.728
Yin (old) percent: 5.728
Yin (young) percent: 44.272 I think these last numbers are the most accurate for real world use.
Variance: 1
Permutations: 8
Yang (old) percent: 25.000000
Yang (young) percent: 25.000000
Yin (old) percent: 0.000000
Yin (young) percent: 50.000000
Variance: 2
Permutations: 64
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 3
Permutations: 216
Yang (old) percent: 16.666667
Yang (young) percent: 33.333333
Yin (old) percent: 8.333333
Yin (young) percent: 41.666667
Variance: 4
Permutations: 512
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 5
Permutations: 1000
Yang (old) percent: 20.000000
Yang (young) percent: 30.000000
Yin (old) percent: 5.000000
Yin (young) percent: 45.000000
Variance: 6
Permutations: 1728
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 7
Permutations: 2744
Yang (old) percent: 17.857143
Yang (young) percent: 32.142857
Yin (old) percent: 7.142857
Yin (young) percent: 42.857143
Variance: 8
Permutations: 4096
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Variance: 9
Permutations: 5832
Yang (old) percent: 19.444444
Yang (young) percent: 30.555556
Yin (old) percent: 5.555556
Yin (young) percent: 44.444444
Variance: 10
Permutations: 8000
Yang (old) percent: 18.750000
Yang (young) percent: 31.250000
Yin (old) percent: 6.250000
Yin (young) percent: 43.750000
Here is the average percentage if the split variance is between 1-5 stalks: Yang (old) percent: 19.834
Yang (young) percent: 30.166
Yin (old) percent: 5.166
Yin (young) percent: 44.834 And here is the average percentage if the split is between 1-10 stalks: Yang (old) percent: 19.272
Yang (young) percent: 30.728
Yin (old) percent: 5.728
Yin (young) percent: 44.272 I think these last numbers are the most accurate for real world use.
