Technical detail for the curious:

The simulation follows the traditional Yarrow Stalk algorithm (Da Yan). The core of this algorithm relies on modulo-4 arithmetic on the stalks remaining after a random split.

To make it physically realistic, I used a Box-Muller transform to simulate the user splitting the stalks with a Gaussian distribution (since humans naturally tend to split near the middle), rather than a uniform random split.

I was worried this 'human bias' might skew the modulo probabilities, so I ran a 1-million-run Monte Carlo simulation to verify.

The Result: The remainders [0,1,2,3] still emerged with a near-perfect 25% distribution (deviation < 0.05%).

So, the app simulates the physics of human imperfection while preserving the mathematical perfection of the probability distribution (where Old Yin is 1/16).

Stack: Next.js + Tailwind css

Happy to answer any questions about the math or the hexagrams!