Divination and Decisions
Probability in divination, dithering on the wheel
Divination tools and decision tools look like two different species, but they grapple with the same thing: uncertainty. The former wraps randomness into an interface for stopping and facing yourself — divination is a random source plus a symbolic mapping table, a personality test is a structured self-report plus norms, a mindfulness trinket is a ritualized attention anchor, though only in the middle one do the numbers actually mean something; the latter works in reverse, reducing vague dithering to something comparable, with its limits set precisely by what the reduction throws away. This piece takes both groups apart: first the arithmetic inside the occult, then the arithmetic inside decisions.
Occult Arithmetic: Randomness, Scales, and Ritual
Three Parts
The technical structure of any divination system breaks into three pieces. The random source — shuffling, tossing coins, shaking a stick cylinder — is at bottom sampling from a finite set under some distribution. The mapping table: the drawn result corresponds to a fixed piece of symbolic text, a tarot card’s meaning, a hexagram statement, a fortune-stick number. The interpretive frame: the step that stitches the symbolic text to your situation, done by a person or by your own brain.
Of the three, only the first is a math problem; the second is a literature problem, and the third is a psychology problem. Almost every argument about divination criticizes the second and third with the standards of the first, or the other way around. Looked at separately, there is nothing left to argue about.
Tarot, One Narrative Out of 450,000
Cyber Tarot is the full 78 cards: 22 major arcana, the Fool through the World, and 56 minor arcana, 14 in each of four suits. Drawing three cards for past, present, and future is the most common spread.
Work out the scale first. Three ordered, non-repeating draws give 78×77×76 = 456,456 possibilities. Multiply by upright and reversed, and it passes a million.
That number matters. The spread’s state count far exceeds the complexity of any single person’s situation, so you can always find an interpretation that fits. Whether it is accurate is another matter; its expressive capacity is simply too large.
The quality of the random source, on the other hand, can be checked seriously. An ideal shuffle is a uniform random permutation, and the standard algorithm is Fisher-Yates: walk from the last position backwards, swapping each with a random position at or before it. Correctness requires each step’s random number to be uniform within the current remaining length, written as Math.floor(Math.random() * (i + 1)). Written as * n instead, it becomes the classic biased shuffle, where some cards land in some positions noticeably more often. This bug is extremely common in real projects.
The demo above is a problem at another level. Pseudorandomness is not as simple as “more random is better.” The top row is two runs of a linear congruential generator fed the same seed, bit-for-bit identical output, which is called determinism. The bottom row scatters pairs of adjacent random numbers: an LCG falls onto a recognizable family of lattice lines, while xorshift128+, which modern engines use, scatters with uniform, structureless coverage, which is called statistical quality.
A divination tool should at minimum differ on every run. But differing every run and being uniformly distributed are two different things.
The mechanism that actually makes tarot seem accurate is not in the cards but in the reader. The Barnum effect — Forer’s 1948 experiment — has subjects rate a personality description that fits everyone highly, mistaking it for something written for them alone. Add confirmation bias: you remember the hits and forget the misses.
So the most honest thing about Cyber Tarot is that it says outright it is for entertainment only. It admits to being a random prompt generator.
Six Lines, Where the Hexagram Is Uniform and the Change Is Not
This section is the hardest part of the piece. It turns a mystical question into pure arithmetic, and the first conclusion contradicts the popular claim.
Toss three coins once to get one line: heads counts 3, tails counts 2, and the sum of the three falls on 6, 7, 8, or 9.
| Result | Name | Combinations | Probability |
|---|---|---|---|
| 6 | Old yin (changing line) | 1 | |
| 7 | Young yang | 3 | |
| 8 | Young yin | 3 | |
| 9 | Old yang (changing line) | 1 |
A single line’s distribution is plainly uneven. Many people infer from this that the sixty-four hexagrams have different probabilities, that some are rarer. That step is wrong.
The total probability of a yang line is , and yin is as well. The six lines are independent, so any specific hexagram’s probability is . The primary hexagram is perfectly uniform over the sixty-four, and Qian is no rarer than Jiji.
The real unevenness lies in change, that is, in the moving lines. Old yang and old yin each take , so a single line is moving with probability , and the number of moving lines follows a binomial distribution .
A still hexagram with no moving line has probability . Exactly one moving line, , is the most common. Exactly two comes to about . All six moving — the extreme transformation of Qian into Kun or Kun into Qian — is about .
Treat the primary hexagram and the resulting hexagram as one joint event, and the unevenness becomes clearer. Let the two differ by lines, the Hamming distance; then
The probability depends only on how many lines changed. A one-line change is times more common than a five-line change. That fixes the information structure of the system: the hexagram is uniform, and how it changes is what carries weight. It favors stability, because three quarters of all lines never move.
The demo above is the cleanest visual version of this. 3d6 and 1d20 both have an expected value of 10.5, but 3d6 collapses toward the center with , while 1d20 spreads flat with . Summing multiple dice necessarily produces a bell-shaped distribution, a direct consequence of the central limit theorem.
The six-line method sums three coins and inherits exactly that shape. It turns a uniform binary into a weighted four-valued variable, and the gap between and is the information source of the whole changing-hexagram system.
However many hexagram statements there are, and however mystical they read, the part that does the work is still arithmetic.
Scales, and Why You Borrow Someone Else’s Questions
Psych Test Toolkit holds a dozen or so scales, and their credibility levels are not remotely comparable; they have to be stratified first.
The first layer is clinical screening scales. GAD-7 has seven items scored 0-3 each, total 0-21, with thresholds at 5, 10, and 15 for mild, moderate, and severe. PHQ-9 has nine items, total 0-27, with thresholds at 5, 10, 15, and 20.
Those two scales’ scores can be used directly because of three things. Norms: the percentile a score maps to comes from a large population sample, not from guesswork. Reliability: internal consistency usually above 0.8, plus test-retest reliability. Validity and criterion: with clinical interview as the gold standard, they can report sensitivity and specificity, that is, how many of the ill are caught and how many of the healthy are falsely flagged.
Without norms, a score has no frame of reference. A homemade anxiety test hands you 47, and that 47 means nothing, because there is no population distribution behind it.
The second layer is personality typology. MBTI is the most popular and the most questioned in psychometrics. It slices four continuous dimensions into two classes at the midpoint, so slightly introverted and extremely introverted get the same letter. In several test-retest studies, nearly half of respondents change type when retested a few weeks later. The person did not change; the score sat near the cutoff, and noise was enough to cross the line.
The Big Five keeps the dimensions continuous, and its test-retest stability is far better. Holland’s RIASEC is a six-dimension model of vocational interest with a clear purpose: matching interests, not diagnosing personality.
The third layer is pure entertainment. Lightweight self-reports like Personality Test hand out a rough label at the end, and their value is giving you a vocabulary for describing yourself.
This stratification matters because misuse causes real harm. Scoring moderate or above on GAD-7 or PHQ-9 means the right move is to see a doctor, not to screenshot it for social media and announce a diagnosis. Conversely, treating an MBTI type as a career ceiling turns an entertainment tool into a verdict.
The Three Ritual Ones
The remaining three tools have nothing to do with prediction; they address attention and mood, and their mechanics are fairly clear.
Cyber Wooden Fish taps once, chimes once, merit plus one. It has no functional output at all, yet it lands precisely on the need to fight anxiety with tiny rituals. The mechanism splits into two parts. It cuts continuous anxiety into completable units, each tap a closed action. And it gives meaningless repetition a positive feedback, which is that plus one.
Breath counting, prayer beads, and walking meditation in mindfulness training use the same structure. Attention anchors on one simple repeated action, and when it wanders you pull it back. Tapping the wooden fish just drops the cost of pulling it back to zero.
Life Reboot Simulator gets its laughs elsewhere. It runs a whole life from randomized starting attributes, with rare talents at absurdly low probability, which is really gacha odds in another costume. You are born ordinary; the odds of being a child of destiny are some small decimal. It lets you see directly that initial parameters shape the trajectory far more than effort does, and having laughed through it, you find it easier to make peace with your situation.
This is a legitimate use of gamified narrative. Externalizing the uncontrollable part as probability is healthier than pretending it is controllable.
Random Quote is pure breathing room. A short line does not solve anything, but it interrupts one round of rumination. The effect comes not from the words but from the act of pausing on purpose.
Four Questions
Next time you see a personality test or an AI fortune teller, ask four questions in order.
Are there norms — where does the score’s population distribution come from, and how large is the sample? Are reliability and validity reported — only something that can state its alpha coefficient, test-retest stability, and sensitivity and specificity deserves the name of a scale. How is the score used, screening or diagnosis — the former can be self-administered, the latter requires a professional. Who does the interpreting — in divination the interpretation is always completed by you, which is not a flaw but how it works.
Tarot and the six lines fail this yardstick, but they do not need to pass — their numbers never have to answer for an outcome. The next group holds no such exemption: the scores decision tools produce get used for real.
Laying Out the Indecision: Wheels, Weights, and Error Bars
Half the drain in daily life comes not from doing things but from recurring low-value decisions: whether to, what to eat, how to choose. Individually they are trivial, but they keep occupying the same patch of working memory, and the accumulated fatigue far exceeds the tasks themselves.
Three Kinds of Trouble
There are really only three reasons decisions get hard, and each calls for a completely different tool.
Too many options, such as what to eat today: use What to Eat Today or Random Kit; the essence is sampling. Too many dimensions, such as whether to change jobs: use SWOT Analysis; the essence is a weighted sum. Uncertain outcomes, such as whether to take a risk: use Life Simulator or an event tool; the essence is a Markov decision.
The first kind of trouble has experimental backing. In Iyengar and Lepper’s jam study, the stall with 24 varieties drew more passers-by who stopped, but its purchase rate was only 3%, while the stall with 6 varieties converted 30%. More options raised attraction and destroyed the ability to decide at the same time. This is the most cited evidence for choice overload.
The Wheel, Where Randomness Stops the Search
What to Eat Today has a mechanism so plain it needs no explanation: candidates go into equal sectors, you spin, and wherever the pointer stops is lunch. Two implementation details: font size steps down automatically once there are more than 20 sectors, and the spin’s tail pins the animation’s last frame off-screen, so there is no argument about the pointer landing right on a line. Neither is the point.
The point is this sentence: the real function of randomization in decisions is not to pick the optimum but to terminate the search.
A classic psychological mechanism confirms it. Toss a coin while you are oscillating between two options, and the instant it lands you suddenly know which side you were hoping for. If the result disappoints you, you already had a preference, and the dithering was just reluctance to admit it. If it relieves you, the two options really are close in utility, and either will do.
What randomization does here is run a cheap test of your actual preference.
Formally, randomness is necessary in exactly one case: mixed strategies in a zero-sum game. Rock paper scissors must be random, or you get exploited. The vast majority of life decisions are not zero-sum, so randomness is not optimal; it is only a stop-loss valve for when the cost of deciding exceeds the benefit.
That yields one rule of use. If you want to spin again after it lands, you have a preference: stop spinning and do the one you were secretly rooting for.
Weighted Scoring, Turning SWOT from a Sticky Note into a Model
SWOT Analysis is usually treated as an exercise in drawing four boxes, but its original design is strategic matching. Strengths and weaknesses are internal and controllable, opportunities and threats are external and given; pairing them yields four kinds of strategy: use strengths to seize opportunities, shore up weaknesses to meet opportunities, use strengths against threats, and contract to defend.
The most typical misuse is adding the four quadrants together directly. My execution is strong, plus 3, but the industry is declining, minus 5, so net minus 2. That arithmetic is meaningless: S/W is what you can change, O/T is what you cannot, and the units do not match.
The right approach is layered. Use S/W first to establish the boundary of capability, what I can do. Then use O/T to establish the environmental window, what is worth doing. The intersection is the strategy.
If you really want a quantitative comparison, you need weights, that is, a decision matrix.
Here is the weight of criterion and is option ‘s score on it. The hard part is not the arithmetic but where the weights come from. Assigning weights by feel hides your bias inside a formula that looks objective. The rigorous route is AHP: compare every pair of criteria for importance, build the judgment matrix, take the principal eigenvector as the weights, then check whether your pairwise judgments contradict each other with a consistency ratio .
The greatest value of weighted scoring is not the number it produces but that it forces you to write down what you care about as line items that can be argued with. The score is a by-product; the weight table is the deliverable.
Life Simulator, a Minimal Markov Decision Process
Life Simulator is a turn-based mini-game: each day you allocate points across five meters — hunger, fun, energy, social, money — and a meter hitting zero or running out ends the run. It looks like a casual game; it is actually the smallest playable version of a Markov decision process.
State is the current value of the five meters; on the site they all start at 70 and are clamped between 0 and 100. Action is where today’s time goes. Transition is the change the action produces plus a random event each day — money up, energy down, social and fun rising together, and so on. Reward is living longer with higher meters.
The standard solution maximizes discounted cumulative return , where is the discount factor. A small means living in the moment; a large one means tolerating short-term pain for long-term gain. That parameter is precisely the mathematical definition of short-sightedness. The moment in the game when I know I should sleep but scroll my phone for two more hours is temporarily set to 0.5.
One more thing is widely misunderstood. The five meters competing for the same budget creates the illusion that life is zero-sum. But real life is full of positive-sum moves: sleep enough and energy rises, energy improves efficiency, efficiency saves time, and the saved time can go to socializing. The game makes the interaction terms negative for difficulty; in reality they are often positive.
Mistaking the game’s feel for a law of reality is the most dangerous way to use this kind of simulation.
Calories, a Number That Must Come with Error Bars
Food Toolkit is probably the only tool in this batch with a hard formula. Basal metabolic rate comes from the Roza-Shizgal revision of Harris-Benedict.
is weight in kg, is height in cm, is age. Multiply by an activity factor for total daily expenditure: sedentary 1.2, light 1.375, moderate 1.55, intense 1.725, extreme 1.9. Macronutrients convert by Atwater factors — protein and carbs at 4 kcal/g each, fat at 9 kcal/g — so a 30/40/30 split of protein, carbs, and fat can be inverted straight into grams.
This algorithm has one boundary that must be stated: it is a regression fit, not a physiological law.
The original formula came from a small-sample calorimetry study in 1919; the revision was published in 1984; its explanatory power is around 0.7, and individual error commonly runs plus or minus 10% to 15%. Someone computed at 1800 kcal may truly sit anywhere between 1550 and 2050.
That does not make the formula bad. Predicting metabolic rate from height, weight, and age simply does not carry enough information; what actually determines BMR is fat-free mass, and the formula has no such term.
So the correct use is to treat it as a starting point, calibrate against two weeks of weight change, and never as a verdict. By the same token, scaling a recipe is a strictly linear transform — every ingredient times 1.5 — and unit conversion is an affine transform, with an offset for temperature but none for weight. Those two things can be exact; metabolic rate cannot.
Knowing which numbers are computed and which are estimated is the precondition for using any tool.
Multiplayer Scenarios
Beyond single-player tools there is another class that handles how a group divides things. Script-Murder Judge Assistant deals out secret roles, tracks day and night phases, and records elimination votes. Its core is not randomness but information isolation: a role is visible only to its holder, and the judge is the one neutral node.
Random Kit does something more interesting in a group. Board games, team picking, and lotteries use it; on the surface it seeks fairness, in substance it makes the result unarguable. A random number has no position, so nobody can welch on it. That is a classic idea in mechanism design, whose most elegant form is the cake-cutter who takes the last piece: separate the right to divide from the right to choose, and selfishness constrains itself.
Tools externalize; they do not take responsibility for you. Filling in SWOT will not resign for you, and spinning the wheel will not eat for you. The only thing they do is turn “I feel awful” into “here are four boxes, I can fill them one at a time.” Dithering is unstructured attention occupation; you cannot stop thinking about it, but you can write it down, spin it, fill one box. After that step, even with exactly the same conclusion, the mental load is different.