Life & fun · December 14, 2025
I Ching simulator with accurate Yarrow Stalk probabilities
I built this because I wanted a digital I Ching that honors the original math, rather than just Math.random(). 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…
In plain words
This I Ching simulator uses the traditional Yarrow Stalk algorithm (Da Yan) rather than simple random number generation. It models how humans actually split stalks by applying a Gaussian distribution through Box-Muller transform, simulating the natural bias toward middle splits. The creator verified through Monte Carlo simulation that this realistic approach maintains the original mathematical probabilities, with remainder distribution staying within 0.05% of the expected 25% for each outcome. It's designed for users seeking authentic I Ching divination grounded in both traditional methods and computational precision.
written from the facts on this page · September 2026
From the sources
In the maker’s words, at launch
I built this because I wanted a digital I Ching that honors the original math, rather than just Math.random(). 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!
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