Comparator of casting methods
Coins, yarrow stalks and 16 tokens
Press Cast to simulate 50,000 lines and compare the three methods with their exact distribution.
There are several ways of generating a line, and they do not all give the same. The three coins split the four outcomes symmetrically; the yarrow (49 stalks) does not. And the 16 tokens (a modern simplification) are built to reproduce the yarrow exactly. Here are the three distributions and a simulator that converges to them live. What matters for anyone actually consulting: coins and yarrow are not interchangeable.
heads = 3, tails = 2; the sum of three coins.
the ancient method; see the experiment on the ritual of the 49 stalks.
a modern simplification: 16 tokens in the proportion 3/7/5/1; it reproduces the yarrow by construction.
| Method | 9 yang▪ | 8 yin | 7 yang | 6 yin▪ | χ² (3 df) |
|---|---|---|---|---|---|
| Three coins | – | – | – | – | – |
| Yarrow (49 stalks) | – | – | – | – | – |
| 16 tokens | – | – | – | – | – |
simulated percentage (theory in brackets) · χ² below 16.27 = compatible with the theory at p > 0.001 (3 degrees of freedom)
The practical conclusion: if you consult with coins believing it is equivalent to the yarrow, you are wrong. The two share P(yang) = 1/2 and P(mutates) = 1/4, but they split the direction of the change differently (see coins against yarrow and the Markov chain). The 16 tokens, on the other hand, are an exact substitute for the yarrow: same distribution, verified.
Three casting methods with their exact distributions: P(mutates) = 1/4 in all three; the equivalent modern method of 16 tokens (3, 7, 5, 1) reproduces the yarrow by construction, whereas the coins are different.
verificar_sorteoThe 16-token method is named as an equivalent modern method; its authorship remains to be verified (section D of the evidence document).
The types of claim and the full bibliography (APA) are in Foundations.