Three Changes Make One Line: Old Yang, Old Yin, Young Yang, Young Yin — Probability Distribution and Complete Calculation Tables • TIMEACTOR

Why Three Changes for One Line — One Change Is Not Enough, Two Are Not Enough, Three Are Just Right

Nine, Six, Seven, Eight — Four Numbers That Decide Whether Your Hexagram Is Alive or Dead

The Dayan method passes through three changes to produce each line. After three changes, you do not simply get yin or yang. You get one of four possible line states: Old Yang (9), Old Yin (6), Young Yang (7), Young Yin (8). Nine and six are changing lines — Old Yang transforms into Young Yin. Old Yin transforms into Young Yang. Seven and eight are stable lines — Young Yang stays Young Yang. Young Yin stays Young Yin. The difference between your original hexagram and the transformed hexagram is determined entirely by the nines and sixes. Wherever a nine or a six appears — that is where the hexagram moves. And — the probabilities of nine and six are naturally different. Old Yang's probability is triple Old Yin's. Yang is active — it changes frequently. Yin is still — it changes rarely. The ancients designed this algorithm so that even the probability distribution aligns with natural law.

Old Yang (9) probability ~19%: yang at its extreme — about to change. Old Yin (6) probability ~6%: yin at its extreme — the smallest probability — things at maximum stillness rarely change on their own. Young Yang (7) probability ~31%: stable yang — does not change. Young Yin (8) probability ~44%: stable yin — the highest probability — more things in the world are still than are moving.

Have You Truly Understood Old and Young Yin-Yang? Four Self-Test Questions

You can explain why three changes are needed for one line. One change yields only two possibilities (5 or 9). Two changes yield four combinations, but mapping to (49 minus sum of all remainders) divided by 4 still cannot reliably separate all four line states. Three changes yield eight combinations — enough to map stably to four line states. One step fewer is impossible. One step more is redundant.
You can calculate from memory which of the eight three-change combinations maps to which line value. (5,4,4) → Old Yang 9. (5,4,8) → Young Yin 8. (5,8,4) → Young Yin 8. (5,8,8) → Young Yang 7. (9,4,4) → Young Yin 8. (9,4,8) → Young Yang 7. (9,8,4) → Young Yang 7. (9,8,8) → Old Yin 6. Formula: (49 minus sum of the three remainders) divided by 4 equals the line value.
You can explain why Old Yang (9) appears at roughly triple the rate of Old Yin (6). The first change produces 5 at probability 3/4 and 9 at probability 1/4. First-change-5 is the norm (75%). First-change-9 is the minority (25%). Old Yang requires a first change of 5. Old Yin requires a first change of 9. This 3:1 asymmetry, compounded across three changes, yields final probabilities of roughly 3/16 for Old Yang versus 1/16 for Old Yin.
When interpreting a hexagram, you actively assess the changing-line ratio. Out of six lines, typically 0 to 3 are changing. All six lines moving is extremely rare. All six lines stable is also rare. One or two changing lines is the norm. If you draw a hexagram with four changing lines — the hexagram is telling you: your current situation is highly unstable. Multiple things are simultaneously reaching a tipping point.

Common Breakers

Thinking 7 and 8 are unimportant and only fixating on 9 and 6. Changing lines are indeed central to interpretation — 9 and 6 tell you where the movement is. But stable lines — 7 and 8 — tell you where the stability is. In your destiny, what changes is always the minority. What stays the same is the majority. Obsess over the one or two changing lines and ignore the four or five stable lines in the background — your interpretation skews. Example: your relationship hexagram has only one changing line, five stable. Your relationship foundation is steady. One variable is moving — maybe your partner's job change. Do not let one changing line negate the stability of five unchanging lines.
Equating Old Yang with good and Old Yin with bad. Yin and yang have no moral valence. Old Yang means yang has filled to the brim and must tip over — fullness overflows. You hit the peak of your career. The hexagram gives Old Yang — it is not congratulating you. It is telling you: you are at the top. Downward comes next. Old Yin means yin has reached its deepest point and the rebound is near — extreme yin returns. You are at the lowest point of your life. The hexagram gives Old Yin — it is not piling on. It is telling you: you have hit bottom. The bounce is coming. Nine and six are both extreme points. Extreme points are turning points. The direction of the turn depends not on the number but on your situation and your question.

Old Yang, Young Yin, Young Yang, Old Yin: Probability Wisdom for Career, Relationships, Personality, and Health

Career & Wealth

The probability distribution carries a practical lesson for career questions. Every time you cast a line, there is roughly a 19% chance of Old Yang (change) and 6% of Old Yin (change) — combined about 25%. On average, one in four lines changes. Six lines per hexagram — average 1.5 changing lines. In career terms: one out of every four decision nodes in your life is a turning point. Not every decision alters your destiny. But one in four does. The skill to build is not 'identifying every node.' It is identifying the node that is most likely a turning point. How? A node is likely an Old Yang turning point when three conditions converge: your accumulated momentum has peaked, the external environment has opened a window, and you feel a strong gut sense you will regret not acting. When a node meets none of these — you are in a deep rut, everything feels stuck — wait. Old Yin (6) has only a 6% probability. True stagnation is itself rare. It will not last long. The rebound is close.

Love & Relationship

The relative probabilities of Old Yang and Old Yin in relationships reveal a harsh truth. Old Yang (9) — 19%. Old Yin (6) — 6%. Yang actively changes. Active relationship changes — confessing, breaking up, reuniting, marrying — are naturally about three times more frequent than passive waiting. If you are the type who says 'I will wait for them to make the first move' — you are betting on a 6% probability. They are not incapable of speaking. Their probability of speaking is simply lower. If you feel a relationship needs to change — your probability of acting is roughly triple theirs. This is not a gender issue. It is yin-yang attributes: yang initiates. yin receives. Young Yang (7, 31%) and Young Yin (8, 44%) together account for 75%. Most of the time, your relationship is in a stable state — calm, routine, day after day. That does not mean something is wrong. Precisely the opposite — 75% of the time should be stable. The remaining 25% are turning points. If you believe every day should be earth-shattering, you are fighting probability.

Personality

Are you a 9-type, a 7-type, or an 8-type personality? Old-Yang-type personality (~19%): your life changes frequently. Switch jobs, switch cities, switch directions. You are used to change. You may even enjoy it. Stability makes you restless. Young-Yang-type personality (~31%): you have stable yang energy — initiative, decisiveness, drive — but you do not change direction frequently. You found a direction and you push. Young-Yin-type personality (~44%): you are naturally steady. You do not change easily. You dislike surprises. Your strength is persistence, not explosion. Most people are Young-Yin types. That is not a flaw. The world runs on Young-Yin types. Old-Yin-type personality (~6%): you are the rare few. You accumulate power in the deepest silence. When you explode, the force is immense — but the intervals between explosions are long. You do not need to envy people who are always moving. Your rhythm is slow and deep.

Health

The probability distribution's health lesson is straightforward. Your body's 'changing lines' occupy roughly 25% — fever, injury, cold, stomach bug, insomnia. These are the body's nines and sixes — short-term anomalies. The body is signaling. The remaining 75% is your body in Young Yang 7 or Young Yin 8 state — running smoothly. Your task: when the body produces a changing line (anomaly), do not panic. Probabilistically, it is expected — roughly one anomaly per four cycles. Catching a cold twice a year is completely normal (2/12 ≈ 17%, near the changing-line ratio). Catching a cold twice a month — your system is producing changing lines at an abnormally high frequency. Check the fundamentals — sleep, diet, stress. You are not treating a cold. You are adjusting the probability distribution. Conversely, if you have not caught a cold in three years — your body may be missing the changing-line signals it needs. Occasional minor illness is your immune system running drills. A system that never produces changing lines is fragile — because it has never drilled.

Nine, Six, Seven, Eight: The Deeper Meaning of the Four Numbers

After You Understand Probability, You Gain an Extra Dimension in Hexagram Interpretation

Memorize the Eight Three-Change Combinations as a Chant: You do not need to calculate (49 minus sum) divided by 4 every time. Memorize it. Chant: 5-4-4 Old Nine — (5,4,4) → 9. 9-8-8 Old Six — (9,8,8) → 6. 5-8-8, 9-4-8, 9-8-4 all Young Seven — (5,8,8) → 7, (9,4,8) → 7, (9,8,4) → 7. 5-4-8, 5-8-4, 9-4-4 all Young Eight — (5,4,8) → 8, (5,8,4) → 8, (9,4,4) → 8. Remember: only (5,4,4) gives Old 9. Only (9,8,8) gives Old 6. The remaining three combinations each map to Young 7 and Young 8. When you operate, you hold three remainder values in your hand. Silently chant the chant. You know the line type instantly. No math needed.
Use Changing-Line Count to Assess a Hexagram's Dynamism: After casting six lines, count the number of changing lines. Zero changing lines: your current life is in extreme stability. No major shifts in the near term. The hexagram result describes your current state more than it predicts the future. One to two changing lines: the most common state. The hexagram has movement but is not chaotic. Study where the changing lines sit — first line (start phase)? Third line (mid-process)? Top line (end phase)? Position matters more than count. Three to four changing lines: your situation is in intense flux. Multiple matters are turning simultaneously. Do not rush decisions. Wait for the storm of changing lines to pass. Let the situation stabilize first. Five to six changing lines: extremely rare. If you draw this — skip interpreting the original hexagram. Go directly to the transformed hexagram. All six lines changing means your situation will completely overturn. The probability is vanishingly low. Take it seriously.
Compare Your Life's Major Decisions Against the 9-6-7-8 Probabilities — Build Probability Intuition: Run a small experiment. Review the ten most important decisions you made in the last five years — job changes, moves, breakups, startups, investments, habit changes. Label each decision with a line value. Labeling rules: you actively initiated the change → 9 (Old Yang). Change was forced on you by circumstances → 6 (Old Yin). You proactively acted but did not change direction → 7 (Young Yang). You continued by inertia → 8 (Young Yin). Then count the proportions. If your 9s exceed 30%, you may be an over-active changer — constantly self-revolutionizing even in good periods, creating unnecessary instability. If your 6s exceed 10%, your life is often pushed by external events — you lack proactive planning. If your 8s exceed 50%, inertia dominates too much of your life — you fail to move when you should. The ideal ratio is roughly: 7 at 30%, 8 at 50%, 9 at 15%, 6 at 5%.

Three Changes Make One Line FAQ

Q:Why does the first change only produce 5 or 9? Can it not produce other numbers?

The proof is simple. After Suspend-One in the first change, the left and right piles total 48 stalks (one stalk was suspended, leaving 48 from the original 49 operating stalks). After Count-by-Four on both piles: left remainder r1 (1 to 4), right remainder r2 (1 to 4). Since 48 is a multiple of 4, r1 + r2 must be a multiple of 4. The (r1, r2) pairs satisfying this condition: (1,3), (2,2), (3,1), (4,4). The first three pairs sum to 4. The last pair sums to 8. Add the suspended 1 stalk: 4+1=5 or 8+1=9. Mathematically, no third result is possible. The ancients may not have used modular arithmetic terminology. But they knew the result could only be 5 or 9 — because this mathematical property follows from the total being 48, which itself derives from Heaven-Earth numbers 55 minus 7 (the five center elements plus the two Heaven-Earth starting points).

Q:The three-change remainders (5,4,4)=13 map to Old Yang 9. (9,8,8)=25 map to Old Yin 6. How exactly do you get from the sum to the line value?

The formula is direct. After three changes, the number of stalks remaining in your hand — those not set aside as remainders — equals 49 minus the sum of all three change remainders. Divide that remaining count by 4. That quotient is the line value. Example (5,4,4): sum of remainders = 5+4+4 = 13. Remaining stalks = 49 - 13 = 36. 36 ÷ 4 = 9 → Old Yang. Example (9,8,8): sum = 9+8+8 = 25. Remaining = 49 - 25 = 24. 24 ÷ 4 = 6 → Old Yin. Verify the range: minimum sum is 5+4+4=13 (Old Yang 9). Maximum sum is 9+8+8=25 (Old Yin 6). The full range spans 13 to 25, with intermediate values mapping to 7 and 8. All four values (6, 7, 8, 9) appear. Complete coverage.

Q:Old Yang ~19%, Old Yin ~6% — was this asymmetry deliberately designed or a coincidence?

The ancients did not compute probability. But they cared about frequency — they performed thousands of divinations and knew which results appeared often and which appeared rarely. Old Yang being roughly triple Old Yin's probability is not coincidence. From a design perspective: first-change-5 has probability 3/4. First-change-9 has probability 1/4. The 3:1 ratio comes from (1,3)+(2,2)+(3,1) being three combinations versus (4,4) being one combination. Why this design? Yang is active. Yin is still. Among changing lines, yang should appear more frequently than yin — matching nature, where growth (yang) is more common than death (yin). Take it one step further: across the sixty-four hexagrams, changing lines are dominated by Old Yang. So transformed hexagrams tend to lean yang — more active, more generative, more forward-moving. This matches the Yijing's foundational spirit: 'ceaseless generation is what the Yi is.' The entire system's tone is toward life, not toward death.

Q:When casting, I often lose track of which change I am on. Any simple tracking method?

Simplest method: take a sheet of paper. Draw three horizontal lines representing the three changes for the first line. After each change, record the remainder sum on the line — 5 or 9, 4 or 8, 4 or 8. After three changes, write equals and the line value. Example: 5, 4, 4 = 9. Then draw three more lines for the second line. Continue. If you prefer no paper — count on your fingers. After first change: thumb up = 5, index finger up = 9. After second change: use the other hand's fingers. After third change, glance at your hands and decode. But honestly — use paper. After the full hexagram is cast, you can look back. Which line's number combination surprised you? That line is likely what the hexagram wants you to notice most.