Show HN: I Ching simulator with accurate Yarrow Stalk probabilities

(castiching.com)

55 points by jackzhuo 2 days ago

46 comments

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!

nestorD 5 hours ago

Fun fact: archaeological evidence on I Ching divinatory records shows an hexagram distribution different from the one produced by the yarrow stalk method. Meaning that, while it is now considered the traditional method, it was likely not the original approach.

  • jackzhuo 37 minutes ago

    That's a really cool fact about the archaeology!

    To be honest, my reason for picking this method was simple: I was reading a book about the I Ching that described the different ways to cast hexagrams.

    The Yarrow Stalk method stood out to me because it felt more mysterious—in the past, it seemed like a secret method known only by a few experts.

    Also, from a coding perspective, this algorithm was just much more interesting to build than a simple coin toss!

  • z2 4 hours ago

    Naive question: could this have been survivorship bias? Could certain ones not have been written down or kept with the others?

    • nestorD an hour ago

      I doubt it. The I Ching does not really have bad / low interest hexagrams. Also historians who studied the topic seem pretty sure that the yarrow stalk method is a recent introduction (by I Ching standards, we are talking about a bronze age divination tool...).

egypturnash 7 hours ago

Some kind of text on what the resulting hexagrams mean along with their names would be nice for those of us who haven't memorized the meaning of all sixty-four.

  • jackzhuo 42 minutes ago

    You are right—there is no detailed text yet.

    To be honest, I haven't added it because I'm hesitating. I planned to use AI to generate the interpretations, but I'm not sure if that's a good idea.

    I feel like letting AI explain the I Ching might kill the 'traditional vibe'.

    I'm still deciding: should I use AI, or just use the classic book text? What do you think?

  • ohbleek 5 hours ago

    I believe that is what is listed at the bottom of the page.

helterskelter 7 hours ago

I'm curious, and I figure you would know more about this than I do: when using real yarrow stalks for the I Ching, how do you split them into groups? I mean like, roughly equal? Don't think about it too much and just split? Just separating them into, say, groups where one group is just a single stalk doesn't seem random.

I guess it's a question of philosophy, either split into groups based off of your intuition, or aim for a truly random split in the pile.

Anyway, I wasn't sure if this is something that's a settled matter or what.

  • jackzhuo an hour ago

    OP here. This discussion is exactly why I implemented the Box-Muller transform!

    You are right that humans don't split perfectly randomly (Uniform Distribution). We tend to aim for the middle but miss slightly.

    In my code, I modeled this 'human splitting action' using a Gaussian (Normal) distribution centered at 50% of the pile, with a standard deviation. This simulates the user trying to split the stalks roughly in half, rather than just picking a random number from 0 to 49.

    Interestingly, my Monte Carlo simulations showed that even with this human bias (splitting near the middle), the final modulo-4 probabilities remain stable. So the algorithm is robust even against our 'imperfect' hands.

  • ksymph 6 hours ago

    Functionally it makes no difference whether you split near the middle or not -- a truly random selection would sometimes end up with a pile of one, and that's totally fine. As long as you're not trying to game the system by, say, specifically counting out the sticks to get the outcome you want, it makes no difference. (and if you're doing that, then what's the point?)

    Splitting closer to the middle does make it easier to avoid unintentionally counting though. If you make the same splits every time, you'll get the same outcome of course.

    Philosophically / spiritually speaking, "don't think about it too much and just split wherever feels right" is the simple answer. Keep in mind the question you want to ask when you make the split and let whatever happens happen. Close your eyes if it helps you focus.

    • helterskelter 3 hours ago

      > Functionally it makes no difference whether you split near the middle or not -- a truly random selection would sometimes end up with a pile of one, and that's totally fine.

      Yeah I just mean I would be very conscious of splitting with a single stalk in one group and would wonder if that was really a 'fair' selection or something I did intentionally since I know the exact number of the yarrow in one hand. In practice, I can't imagine anyone would make a selection like that, even though in a truly random system it would happen not infrequently.

      • ksymph 33 minutes ago

        Having a certain number in one hand is still a couple steps removed from getting a specific outcome, so there isn't anything inherently 'unfair' about it. My point was more that it's the intention that matters. If you make a split because it feels right, with your question in mind, then it's fine if it's totally uneven and/or you're aware of how many there are. Splits like that do happen from time to time, it's all part of it.

jmkd 4 hours ago

I got a result using coins but could find no link to the hexagram so had to look it up on another site. While I was clicking around your site trying to find the hexagram then I lost my reading and back button didn't work, so changing lines etc were lost. I would love to use this more but not in current state.

  • jackzhuo 28 minutes ago

    Thanks for the honest feedback!

    You are raising a critical UX issue. Currently, I haven't implemented user accounts or a database because I wanted to keep the app simple and login-free.

    However, that shouldn't mean losing your data on a refresh! I will prioritize a fix using Local Storage so your current reading persists even if you hit the back button.

    I'll also make the result link much more obvious so you don't have to hunt for it. Really appreciate you trying it out despite the rough edges!

  • [removed] 28 minutes ago
    [deleted]
NooneAtAll3 6 hours ago

Any chance to make Enter or Spacebar press the button when Yarrow Stalk thing progresses?

It got tiring and boring to click and click and click with the mouse with no explanation for how it works

blastro 6 hours ago

As a fellow iChing developer - this is nice! Thanks for sharing.

  • jackzhuo 26 minutes ago

    Thank you! Always happy to meet a fellow developer in this niche.

    Have you built a web app or a mobile app? I'd love to check out your work if you have a link!

Jimpulse 7 hours ago

Any sites that give nice barebones explanation of the results? I imagine filling more of the blanks myself instead of AI is part of the exercise, but a nice starting point can help.

  • thefaux 6 hours ago

    The canonical western text is Richard Wilhelm's german interpretation, translated to english by Cary Baynes. This site has the hexagram descriptions from that translation: https://www.iching.online/wilhelm.php

    I recommend buying the book though. It is fascinating whether or not you buy into it.

    • Jimpulse 3 hours ago

      Dang a Jung forward. Will have to pick it up! Thanks.

    • mistrial9 3 hours ago

      Carl Jung's Synchronicity text, published at the end of his life, uses I Ching as one testing ground..

dvh 6 hours ago

> "What should I use for 15V 150mA DC power supply?"

Original Hexagram 45. GATHERING TOGETHER (MASSING) (Ts'ui)

Transformed Hexagram 17. FOLLOWING (Sui)

Ok.

  • jackzhuo 23 minutes ago

    Asking the Oracle for circuit design specs... I love it!

    My interpretation for your power supply:

    Gathering (45): You need to gather some capacitors? (or maybe a heat sink for the 'massing'?)

    Following (17): Clearly it's telling you to use a Voltage Follower. :D

joeframbach 7 hours ago

Please consider improving the color contrast. The text is gray-on-gray and impossible to read.

calebm 5 hours ago

The I Ching contains all 6-bit patterns.

  • roadside_picnic 4 hours ago

    The hexagrams can be modeled with only 6-bits, but this does not contains enough information for a proper reading of I Ching which also need to account for line changes. So there are really 4 lines: young yin, old yin, young yang, old yang.

    A fundamental part of I Ching reading is the implication that each present state is in the process of transforming to another.

    • jackzhuo 4 minutes ago

      Spot on! This is exactly why a simple Math.random() > 0.5 binary flip isn't enough for a proper simulation.You are right that we are mathematically dealing with base-4 logic (6, 7, 8, 9), not just base-2.While there are only 64 hexagrams ($2^6$), there are actually 4,096 possible casting results ($4^6$) when you account for the moving lines. My algorithm is designed specifically to capture the distinct probabilities for all 4 states.

n0um3n4 4 hours ago

i wonder if a query to thise quantum random bumber generator machines would help

lawlessone 5 hours ago

Now i feel like i need to read The Man in the High Castle again.

vessenes a day ago

I can’t get this to work on iOS at all - question - coin or yarrow choice - then what? No links seem to be hot/working. A little tutorial would be great. Fun project!

  • jackzhuo 21 hours ago

    Hi, thank you so much for reporting this!

    I just identified the issue (it was a specific mobile browser compatibility bug). I have deployed a hotfix and it should be working now on iOS.

    Could you please give it another try? Sorry for the trouble!

  • AnonHP a day ago

    Same here. It just doesn’t work on Firefox Focus on iOS, even after I disabled content blockers.

    • dang a day ago

      I put this post in the SCP (https://news.ycombinator.com/item?id=26998308) - will temporarily bury it until the author confirms it's working. Sorry for the inconvenience!

      • jackzhuo 21 hours ago

        Hi Dan, thanks for the heads up. I have fixed the mobile bug and deployed the update. It should be working for everyone now. I've also replied to the users above.

      • typpilol a day ago

        Not working on edge on android either

    • jackzhuo 21 hours ago

      Thanks for flagging the Firefox Focus issue. I've just pushed a fix for mobile browsers. It should be loading correctly now. Let me know if it works for you!