The bedtime-story calculator problem

You take two Bitcoin. You take €30,000 annual living costs. You type "20% BTC CAGR" into a calculator and it spits out: "in 20 years you'll have 8 BTC and three houses."

That's pretty. It's also self-deception.

Bitcoin is not a savings account. The annualized log volatility has been around 70% since 2017. Translated: over two years the 1-sigma confidence interval for BTC's price runs from "×0.4" to "×3". Over ten years from "×0.05" to "×40". A single number as the answer to a question about two decades is mathematically borderline.

We've added two risk modes to the Bitcoin Lifestyle Calculator. Both run on the same input scenario, both show the three strategies (Humble V0 / Tiger V1 / Dragon V2) in parallel — but they answer different questions.

Mode 1 — Stresstest (Free): the three canonical BTC paths

The Stresstest asks: what happens to your plan on the three classic Power Law paths — Lower, Fair, Upper?

Power Law is the trend line that has described Bitcoin since 2010 with surprising accuracy. Lower bound = Fair / 2.5, upper bound = Fair × 2.5. Historically ~95% of all daily BTC prices have fallen inside that corridor.

Concrete setup for our example user Sebastian, 35:

2 BTC starting holdings
€30,000 annual living costs (with 2% inflation)
20-year horizon
Loan: 5% interest, liquidation LTV 83%, V2 leverage 3×

What the Stresstest delivers: a 3×3 matrix. Three strategies × three paths. Per cell: final BTC-net, liquidation year if triggered, peak LTV.

How to read it:

• Lower bound: BTC stays glued to the pessimism trend line for 20 years. V0 (Humble) holds out longest because he sells gradually and isn't pressured by debt growth — but he ends up with markedly less BTC. V1 (Tiger) and V2 (Dragon) get liquidated with high probability because their debt keeps growing while BTC value stagnates.
• Fair: classic BTC Power Law growth. V2 builds the most BTC, V1 holds steady, V0 loses substance to inflation.
• Upper bound: bull case. All three run extremely well, V2 becomes absurdly rich.

The most important takeaway from the Stresstest is not "which strategy wins", it's which strategy fails in which path?. If V2 already liquidates in the Fair path, your plan is not robust under normal assumptions. Period.

Three paths. Three stories. Readable in a single matrix.

Mode 2 — Monte Carlo (Pro+): a thousand random worlds

The Stresstest gives you stories. The Monte Carlo gives you statistics.

We take the same input scenario but roll the dice. Specifically: a Geometric Brownian Motion model with historically calibrated volatility (σ ≈ 70% annualized, three profiles selectable from Low 0.5× to High 1.5×). From that we generate 100, 500, or 1000 random BTC price paths over your horizon. For each path we run all three strategies.

What you get at the end — per strategy:

• Survival rate: in what % of paths did you still have BTC at the end (V1/V2: not liquidated; V0: BTC not depleted).
• Median final BTC: the middle outcome.
• P10–P90 bracket: the spread. How far apart are worst and best case?
• 10% worst-case: what did the worst 10% of paths deliver on average?
• Spaghetti chart: 50 randomly sampled paths as faint lines plus the P10–P90 ribbon.
• Histogram: distribution of final BTC values. Liquidated paths collect as a red bin on the left.

Optional: black swan toggle. When active, every path has a 10% probability of getting one-time −50% crash injected at a random step. Brutal but realistic — the Mt.Gox 2014, March 2020, and FTX 2022 drops are underrepresented in historical σ.

How to read the numbers — and where most people fall in

In Monte Carlo there's a trap. The thick line in the spaghetti chart is the median across all paths, including those already liquidated or depleted (= 0 BTC). Once 50% of paths have failed, the median snaps to zero. That's not "the typical surviving path" — it's "the 500th-worst out of 1000".

Without that knowledge, you read survival rate 35% and think: "ah, in two-thirds of cases I win." Wrong. In two-thirds of cases you're out. In the remaining third you can win — and there the spread between P10 and P90 typically runs by a factor of 5.

The right reading order:

1. Survival rate first. If it's below 80%, your plan is too aggressive for your risk appetite — regardless of how good the median looks.
2. 10% worst-case second. That's the value you have to plan with under pessimism. If it's below "livable", you have no risk management, you have hope.
3. Median and P90 last. They're pretty, but that's the reward for the risk, not the plan.

Stresstest and Monte Carlo together — why both

The Stresstest gives you three narratively tangible stories: "What if BTC stays bearish? What if fair? What if bullish?". That's communicable. You can take the result to lunch and explain it to your partner.

The Monte Carlo gives you 1000 data points from which probabilities can be derived. That's statistically honest — you don't see three stories, you see the distribution. You recognize whether your plan happens to shine in a bull path, or whether it holds in the middle of the distribution too.

Combined, they answer two different questions:

• Stresstest: "Where does my plan break?"
• Monte Carlo: "How likely is the break?"

You need both. A strategy that looks stable in the Stresstest may have 30% survival rate in Monte Carlo (because most random paths don't stay in the Power Law corridor). A strategy that fails in one Stresstest path may still have 95% survival in Monte Carlo (because the bearish Power Law path rarely hits exactly that way).

Takeaways

• A single number output for 20 years on BTC is mathematical self-deception.
• Stresstest shows three canonical stories — narrative and communicable.
• Monte Carlo shows the distribution over 1000 random worlds — statistically honest.
• Read survival rate before median. Read 10% worst-case before P90.
• The thick line in the spaghetti chart is not your typical path. It's the median including liquidations.
• Three strategies (V0/V1/V2) in parallel — you instantly see which Stresstest each survives and which Monte Carlo survival rate each has.

Both are live in the Bitcoin Lifestyle Calculator. Stresstest is Free, Monte Carlo Pro+. Input once — both lenses applied — plan stands or falls.

Direct link to Stresstest → Direct link to Monte Carlo →