1% risk · 2R reward · ~40% win — positive expectancy under randomness
E = P×R − (1−P). If E > 0, the system survives.1% risk · 2R reward · ~40% win — the minimal viable setup that keeps E positive.What it does: A single rule that decides long-run survival under randomness.
Equation: E = (WIN_RATE × AVG_WIN) − (LOSS_RATE × AVG_LOSS)
Worked example: 0.40 × 2R − 0.60 × 1R = +0.20R → positive expectancy.
Plain meaning: When E > 0, the average outcome per trade is positive, so the system survives over time.
Equivalent threshold: R > (1−P)/P. At P = 0.40 you need R > 1.5; the baseline uses 2R for margin.
12 metrics across Distribution, Efficiency, Robustness, and Capital — the operational health of 1240.
| Domain | Metric | Symbol | Formula | Interpretation |
|---|---|---|---|---|
| Distribution | Stability Index | S | σₘ / μₜ | Average deviation stability (0–1) |
| Volatility Density | Vd | σ / MAD | Noise uniformity ratio | |
| Signal Consistency Ratio | SCR | Nvalid / Ntotal | Behavioral precision rate | |
| Efficiency | Expectancy Coefficient | Ec | (W×R) − (L×1) | Expected return per risk |
| Risk–Reward Efficiency | RRE | mean(R) / mean(1) | Risk–return harmony index | |
| Systemic Cost Ratio | SCR₂ | (slip+comm+behav)/gross | Systemic frictional cost | |
| Robustness | Max Drawdown Ratio | MDDr | Dmax / Epeak | Depth of capital contraction |
| Recovery Factor | RF | Net / Dmax | Recovery resilience ratio | |
| Behavioral Durability Index | BDI | Nplan / Ntotal | Psychological consistency index | |
| Capital | Flow Velocity | CFV | Cturn / Etotal | Capital turnover rhythm |
| Compounding Growth Rate | CGR | (Eend/Estart)^(1/n)−1 | Rate of compounded survival | |
| Capital Persistence Ratio | CPR | Tabove / Ttotal | Continuity of capital stability |
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PCI = (D + E + R + C) / 4 · PCI ≥ 0.70 → Survival Zone · 0.50–0.70 → Adaptive Drift · <0.50 → Collapse
Defines the cognitive linkage between Pure12 domains and canonical fields of 1240.
| Field | Concept |
|---|---|
| F1 | Mathematics — probabilistic logic |
| F2 | Physics — capital as energy |
| F3 | Behavior — psychological control |
| F4 | Time — temporal averaging |
| F5 | System — boundary constraints |
| F6 | Evolution — adaptive logic |
| F7 | Data Awareness — feedback loop |
| F8 | Inner Balance — entropy control |
| F9 | Outer Balance — environmental fit |
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