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Open in hackernews

Show HN: I Ching simulator with accurate Yarrow Stalk probabilities

https://castiching.com/
63•jackzhuo•1mo ago
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!

Comments

vessenes•1mo 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!
AnonHP•1mo ago
Same here. It just doesn’t work on Firefox Focus on iOS, even after I disabled content blockers.
dang•1mo 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!
typpilol•1mo ago
Not working on edge on android either
jackzhuo•1mo ago
Thank you! I found the bug causing issues on mobile/Edge. Just deployed a fix. It should be working now.
thenthenthen•1mo ago
Seems to work on iOS safari!
jackzhuo•1mo ago
Great to hear! Thanks for verifying.
jackzhuo•1mo 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.
jackzhuo•1mo ago
sorry, I will check it now!
jackzhuo•1mo 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!
jackzhuo•1mo 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!

egypturnash•1mo 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.
ohbleek•1mo ago
I believe that is what is listed at the bottom of the page.
jackzhuo•1mo 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?

goopypoop•1mo ago
why throw mud into the water?
jackzhuo•1mo ago
Point taken.

I'll keep the water clear. Sticking to the Wilhelm/Baynes text.

joeframbach•1mo ago
Please consider improving the color contrast. The text is gray-on-gray and impossible to read.
mapontosevenths•1mo ago
To be technically accurate, it would actually need to be a suffusion of yellow for all answers above four.

https://www.urbandictionary.com/define.php?term=A+Suffusion+...

jackzhuo•1mo ago
Thanks for pointing this out!

I probably stared at it for too long on my own monitor and got used to it. I will bump up the contrast in the next update to ensure it's readable for everyone.

Jimpulse•1mo 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•1mo 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•1mo ago
Dang a Jung forward. Will have to pick it up! Thanks.
mistrial9•1mo ago
Carl Jung's Synchronicity text, published at the end of his life, uses I Ching as one testing ground..
helterskelter•1mo 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.

ksymph•1mo 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•1mo 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•1mo 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.
jackzhuo•1mo 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.

helterskelter•1mo ago
Very cool, thanks for the response. Neat project btw.
jackzhuo•1mo ago
Thanks!

Speaking of 'neatness', I just pushed an update that lets you generate a visual Result Card of your reading.

So now you can get a nice downloadable souvenir of that Gaussian-distributed hexagram. :D

blastro•1mo ago
As a fellow iChing developer - this is nice! Thanks for sharing.
jackzhuo•1mo 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!

v0id_p•1mo ago
Hey Jack, I built an I Ching tool earlier this year using arrow.js. I tried to stick with vanilla JS at first but it proved difficult to maintain. My tool uses a casting method that results in the same probabilities as when one uses the Yarrow Stalk method, but doesn't include a yarrow stalk simulation. I briefly considered creating a 3D simulation of the yarrow stalk casting method but never got around to it. I find it interesting that someone had a similar idea.

My I Ching tool is located at classicofchanges.com

jackzhuo•1mo ago
Always happy to meet a fellow developer in this niche!

I checked out your site—having the full index on a single page is actually super handy for quick referencing.

And I totally relate to the 'Vanilla JS vs Framework' struggle. I ended up choosing Next.js precisely because managing the state for the complex probabilities (6/7/8/9) was giving me a headache. Respect for sticking to the raw math!

langitbiru•1mo ago
Hello there. I'm also an I-Ching developer.

https://neoching.com

jackzhuo•1mo ago
Thanks for sharing neoching.com!

It is really cool to see how different developers interpret the same ancient text. I noticed your approach is very direct and efficient with the results.

Keep going!

NooneAtAll3•1mo 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

jackzhuo•1mo ago
OK, I will fix it.
dvh•1mo 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•1mo 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

dvh•1mo ago
>Transformed Hexagram

toroid transformer?

jackzhuo•1mo ago
LOL, I completely missed that pun!
nestorD•1mo 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.
z2•1mo ago
Naive question: could this have been survivorship bias? Could certain ones not have been written down or kept with the others?
nestorD•1mo 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...).
jackzhuo•1mo 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!

calebm•1mo ago
The I Ching contains all 6-bit patterns.
roadside_picnic•1mo 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•1mo 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.
roadside_picnic•1mo ago
This is a great project btw! I've long been fascinated by the 易经 especially the different probability distributions associated with the different methods of generating the lines. It's been a while but I used to have an actual set of yarrow stalks!
jackzhuo•1mo ago
Thank you! That means a lot coming from someone who appreciates the probability mechanics behind it.

Since you have experience with the actual stalks, I think you'll like the update I just pushed: I’ve fully integrated the classic Wilhelm/Baynes text to ensure the reading has that authentic, traditional grounding you mentioned.

I also added a way to generate a visual card of the result—trying to bring back a bit of that 'tangible artifact' feel of the physical ritual. :)

lawlessone•1mo ago
Now i feel like i need to read The Man in the High Castle again.
jackzhuo•1mo ago
You absolutely should!
n0um3n4•1mo ago
i wonder if a query to thise quantum random bumber generator machines would help
jmkd•1mo 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•1mo 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!

jackzhuo•1mo ago
OP here with a massive update!

I spent the last 24 hours implementing the feedback from this thread. Thank you all for the harsh (but fair) critique.

1. Ditched AI for the Classics Many of you pointed out that AI interpretations felt "soulless" or risky. I agreed.

Now: The app directly displays the canonical Richard Wilhelm / Cary Baynes translation (Foreword by Carl Jung) for the Primary Hexagram, Moving Lines, and the Relating Hexagram. It's mathematically precise and respects the source material.

2. No More Lost Readings (Persistence) @jmkd mentioned losing a reading on refresh.

Fix: The latest reading is now auto-saved to Local Storage.

Privacy: Still no login required. Your data stays in your browser.

3. Shareable "Result Cards" Since the hexagrams look so cool, I added a feature to generate a downloadable image card. It captures the visual pattern and the key judgment text.

Give it another spin and let me know if the "Moving Lines" logic feels right to you now!

LargoLasskhyfv•1mo ago
My Reading, Yarrow Stalks results:

_____ (black bar, 7)

_____ (black bar, 7)

__.__ (grey bar, marked by green dot in the middle, 9)

__ __ (two short black bars with gap in the middle, 8)

__.__ (grey bar, marked by green dot in the middle, 9)

__ __ (two short black bars with gap in the middle, 8)

Primary Hexagram 6. CONFLICT (Sung)

Relating Hexagram 20. CONTEMPLATION (Kuan)

Reverse engineer the question :->

jackzhuo•1mo ago
Let me reverse engineer the stack trace:

You were likely asking: 'Why is this code throwing an error and fighting me?'

The transition from Conflict (fighting the code) to Contemplation (Observing/Viewing) suggests the solution isn't to type more code, but to step away and look at the logs (or the documentation).

Did I debug the user intent correctly?

LargoLasskhyfv•1mo ago
No :-)

Edit: Or maybe yes, if you mean the 'code of life'.

Because the question has been:

Why did I lose the supernatural powers I had in my youth, which I've lost as I've gotten older and older?

jackzhuo•1mo ago
This is a profound question, and looking at your specific moving lines (Lines 2 and 4), the answer is almost startlingly precise.

It’s rare, but both of your moving lines start with the exact same verdict: 'One cannot engage in conflict' (不克讼).

Line 2 says: Retreat and return home. (Don't fight the reality.)

Line 4 says: Turn back and submit to fate. (Acceptance brings peace.)

The Oracle seems to be validating your feeling of loss, but advising that this isn't a battle to be won against time (Conflict). It’s a transition to be understood.

You are moving from Hexagram 6 (Fighting) to Hexagram 20 (Contemplation/Viewing). The 'supernatural power' of youth is active energy; the power of age is perspective. You aren't losing the code, you're just moving from 'Writing' to 'Architecting'. :)

LargoLasskhyfv•1mo ago
Maybe. But I'm not at (birth and growing up) 'home'. Which would be Bonn Bad Godesberg at the Rhine in Germany. Instead about 8800km west, somewhere high up in the Rocky Mountains, rather comfortably.

The power of youth aside, I had real supernatural powers. Which I've used to heal some early love affair of mine from a bad traffic accident, by impossible means.

I could also see the future of my personal experiences, and that way general development up to about 2024 and some 2025, but from the latter just some trickles, from 1982 on.

Actually some years earlier, but not that clearly.

Another short flashback from around 2050, me still living well in the Rockies, with the same woman, but no general clue about what's happening in the world, or what happened up to then. Or how the skies would look.

And another from about 2075, similar to the above, with me crashing in some experimental plane with an early prototype of a new energy source and engine.

Breaking one of my front teeth while I'm running away from the wreck as fast as I can, and the shockwave of its explosion throws me facedown onto a small rock in the desert. Blacking out in pain.

Getting collected by SAR Helo-like thing, tilt-rotor, but different from the ones which are flying now.

Laughing hysterically after having forced the female medic to give me 'the good suff', and she's stumbling into my lap/beween my legs because of some turbulence.

"Whoa Babe! Not so fast!"

Being annoyed at arrival, because I don't want to be wheeled in.

So I walk. Much commotion and protest. I just grumble "STFU!"

Being numb while having my rather stiff flight suit removed, and the few splinters which made it trough the back.

Hrrm, actually, writing this down, I 'premember' some supernaturalness there, while being checked up in some hospital in LA. Still same wife, having sex with her in the ICU, disabling all machines and cams by just wishing so, to the concern of the personell, but shooing them away. Gash in my upper lip gone after sex. And flown in from elsewhere stepdaughter healing the other patients currently in that wing. My security forcing all personell to NDA, gag-ordering them to NOT talk to anyone about this.

Something very strange and extraordinary happened to me while 'making love' for the first time to that early love affair of mine, in a strange place.

Which wasn't even my first sex, btw. Just very, very lovely, and unbelievably intense.

Something even stranger, and more extraordinary happened during a little celebration held for her return back to life in good health, which I've been invited to, because I did enable her return.

Shortly after that I rejuvenated some old nun, 90+, eaten up by cancer, waiting to die under morphines.

Told to try by the then acting chief nun, after she 'got wind' of me having sex with some of the girls they housed, and watched over.

When I explained myself, that she shouldn't blame me, they should feel blessed by my touch and semen.

As could be seen by the smile of one of them, whole again, because before one frontal tooth was broken off halfways. Also slimmed down her belly and hips a little. The other one was just right, maybe a little bit too horny. But youth, hormones kicking in hard! (Giggle)

So chief nun took me by my words, and I 'delivered'. I made that old nun free of cancer, and returned her to about 25 years of biological age, with all her memories still intact, and not addicted to morphine, clear minded.

Very sexy.

Which in turn led to a little celebration, and an orgy in their chapel. Which a few days later led to a meeting with some Jesuits near there, where they lived in cozy appartments below the ruins of an old castle tower.

Why? Because one of the assholes tried to exorcise the devil out of me. Which ended very bad for him, but I healed him too, after I messed him up, to be my messenger to the pope, or whoever is really pulling the strings in the Vatican.

Message more or less:

"I'm back, and I really don't like your ways! Change, or else...!"

I still don't like their ways, btw. Though they changed a little, mainly opening their archives which is very important to me!

Anyway, much sex ensued, most just joyful with sweet girls of my age, some slightly older, but still young woman, some middle aged female teachers, sometimes in orgies again, sometimes healing and/or rejuvenating(just one older) them.

Also got to know some female nurses, and took care of their needs. Which in turn led me to heal the complete intensive care wing of a child hospital. With the exception of a child born without a brain, and being that way for all of its about 10 years of existence. Nothing to heal there, I can't make brains up. Just gently stopping its heart. Didn't even shiver. No parents that would care, either.

Left my home.

Fuckery continued in several places, sometimes in orgies. Where sometimes some supernaturalness ensued again during said fuckery.

Moved on, tried to live a more normal life, got experience in several fields. Wasn't really for me, could be considered a failure. Moved on several times again.

'Invented' something very technical, but not really, was just a rehash of old ideas, brought up to current technological standards, and combined where it made sense. With patents long expired, some not so long, but still.

That got noticed, and so I've been snatched up to where I am now, by ways of which I'm not at liberty to talk about :-)

With all that said, I don't see why I should turn back home and submit to fate?

What would that even be? Being exorcised? Crucified?

I've been 40+ years gone from there, and don't miss it that much, TBH.

I live very well where I am now, have cats, sexy women, (legal)drugs, and am healthy.

Just lacking the supernaturalness. (For now?)