When can you stop working?

1. Bitcoin follows a power law. Giovanni Santostasi’s model (2024) fits 15+ years of daily price data to a log-log regression: log10(price) = a + b × log10(days since genesis). R² exceeds 0.95 — one of the strongest long-term fits in any financial asset. This is not a trendline drawn through noise; it is a statistical regularity with a physical basis in network adoption dynamics. Through network adoption, there are structurally more buyers than sellers at floor price levels — which is why the floor has held for 15 years and counting.

2. Log residuals mean-revert. The distance between the actual price and the power law trend (measured in log10 space) behaves like a spring: large deviations pull back toward the trend. This is modeled as an Ornstein-Uhlenbeck process — a well-studied mean-reverting stochastic process from physics. The implication: bubbles deflate, crashes recover, and the trend reasserts itself over time.

3. Volatility decays across regimes. Each Bitcoin halving cycle shows measurably lower volatility than the last. We calibrate separate residual distributions per cycle (2012–2016, 2016–2020, 2020–2024), each fitted with Student’s t-distribution (heavier tails than Gaussian to capture extreme moves). The trend is unmistakable: as Bitcoin matures, the swings shrink. Future cycles are projected to continue this decay.

4. Monte Carlo with power-law-specific design. We don’t use generic stock-market Monte Carlo. Every simulation parameter is derived from Bitcoin’s specific behavior: the OU mean-reversion speed, per-cycle t-distribution shape, and a hard downside clamp at −2σ (the empirical floor). Innovations are drawn from the fitted t-distribution, not a normal distribution — this preserves the fat tails that define crypto while respecting the mean-reversion that defines the power law.

5. 100,000 simulated price paths. Each path runs month-by-month from the user’s retirement age to life expectancy, deducting inflation-adjusted expenses and tracking stack depletion. 100,000 paths produce stable percentile estimates (p5 through p95) with minimal sampling noise. The probability you see in the ring is not a guess — it is the fraction of paths where your stack survives.

6. Floor-based math — the most rigid framework possible. The floor is defined as 0.42× the power law trend: the absolute worst-case price at any given date. Bitcoin has never traded below this level in its entire history. All retirement projections use the floor, not the trend or median. If the model is even approximately correct, this is the harshest assumption we can make. Measured from the floor, all volatility is on the upside.

7. The core inequality: stack × floor_growth > yearly expenses. This is the floor freedom test. When the floor’s annual growth alone exceeds your living costs, you never need to touch principal — even under the worst-case price path. The projection table shows this ratio climbing year by year. Once it crosses 100%, the floor alone sustains you indefinitely, and all volatility becomes pure upside.

8. Near-zero risk of ruin through first principles. Three compounding tailwinds work in your favor: (a) volatility decays cycle over cycle, (b) the floor rises deterministically via the power law, (c) your expenses in BTC terms shrink every year as the floor grows. The Monte Carlo confirms what the math predicts: for adequate stacks, 99%+ of all simulated futures survive to life expectancy. We cap displayed probabilities below 100% because finite simulations cannot prove absolute certainty — but the first-principles argument is even stronger than the simulation.

Verify it yourself. The full model — power law fit, residual distributions, per-cycle volatility histograms, and all 100,000 simulated price paths — is open for inspection at btcpowerlaw.nl. Every number on this page traces back to that data.