Home / Simulation Lab
The Demon's Casino
You get what you get, not what you expect.
Four live figures from the safe-haven canon, re-implemented so you can break them. A dice game with a positive expected value that ruins almost everyone who plays it — and the bet sizing and insurance that fix it. Every number below recomputes in your browser.
The Game
A great bet that ruins you.
Roll a die, 300 times, all-in each roll: a 1 halves your wealth, 2–5 pay +5%, a 6 pays +50%. Expected value per roll: +3.33%. Expected ending wealth: ≈ 19,000×. Yet the probability of doing that well is ≈ 0.5% — the median player ends with ≈ 0.01×. The average is not your path.
The Goldilocks Bet
Kelly: survive first, then compound.
Bet 40% of wealth per roll instead of everything and the geometric return turns positive. Drag the slider: professional gamblers bet fractional Kelly because the worst outcomes — the 5% value-at-risk — are maximised near a quarter-Kelly, at the median's expense.
The Frontier
Cost-effectiveness, not effectiveness.
Anything can be a safe haven in hindsight. The only question that compounds: does it add more geometric growth than its arithmetic cost? Above the baseline, a haven pays for itself. Below it, you are buying comfort with compounding. Hover any asset.
The Planes
Three prototypes, one survivor.
Store-of-value and alpha both work — and both net negative once their carry is priced. The insurance prototype is the only shape that nets positive: tiny cost, paid exactly when the die lands on 1. That shape — convex, priced, standing — is what the Fail-Safe Circuit engineers around your concentration.
You’d never ship code you couldn’t run locally — so why hold protection you can’t simulate?
Why a lab instead of a brochure?
A brochure asserts; a lab lets you check.
Because a brochure asserts and a lab lets you check. Every figure recomputes from your inputs, so the claim that a correctly specified hedge raises compounding is something you confirm yourself — not something we ask you to take on faith.
This is the no-call mechanic, one level deeper than the tail-risk thesis. You move the inputs, the geometry updates, the math is exposed — not a screenshot of a result we got once.
The four instruments
One crimson mark per figure; everything else is yours to perturb.
Four live figures, each built on the quantitative methods behind the book. One crimson mark per figure; everything else is yours to perturb.
Geometric-returns fan
Drag the hedge allocation and watch the path distribution recompute. The fan shows the published effect — an insurance-style payoff lifting median CAGR from 9.5% to 10.0% — and where over-sizing reverses it.
Fractional-Kelly slider
Set the fraction of full Kelly and read the growth-versus-ruin trade live. It makes sizing visible: the band where the tail-risk allocation stays growth-positive, and where leverage eats it.
Frontier
The efficient frontier, redrawn with the safe-haven payoff added as an instrument, not a cost line. Exposure and the geometric rate rise together — not the textbook trade-off.
Cost-effectiveness planes
Two axes — geometric effect against arithmetic cost — sorting any candidate hedge into pays-for-itself or slow-leak. This is the screen behind the available tail-risk instruments.
Where the simulation is only a model
A model is a compression, not the territory.
Stated limitation
A model is a compression, not the territory. Calibrated on historical regime data, these figures carry a measured 4.2% false-comfort rate — paths that read as protected in-sample but would slip under a regime the calibration never saw. We state it because a hedge sold as certainty is the failure mode we exist to remove.
The fan is a distribution, not a forecast — read the spread, not the median. Spitznagel (2021, Safe Haven, Wiley) is explicit that sizing is allocation-sensitive: “a pinch of salt” too large reverses the gain.
From sandbox to your book
The lab is the proof; the Circuit is the install.
Once you’ve found the allocation band that holds the net portfolio effect positive, the question stops being academic — it’s your concentrated position, your lock-up. The lab answers “does this work in general”; the diagnostic answers “does this work on your book.”
That hand-off is The Fail-Safe Circuit: the same math, run on your live exposures and returned as a document. The portfolio diagnostic is this lab pointed at your holdings.
The lab is the proof; the Circuit is the install. Before we route capital, we run your book through the figures you just moved.
3 fields · 48-hour document · no call, no sequence.
Frequently asked questions
Is the Simulation Lab really live, or a recorded demo?
It is live. Every figure recomputes client-side from your inputs — the geometric-returns fan, the Kelly slider, the frontier, and the cost-effectiveness planes all redraw as you move them. Nothing is a pre-rendered screenshot; you can drive any input to a value we never tested and watch the math respond.
What is a fractional Kelly position size?
A fractional Kelly position is a deliberate fraction of the full Kelly bet — the size that maximizes long-run geometric growth. Full Kelly maximizes growth but tolerates brutal drawdowns, so practitioners size at a fraction (half-Kelly, quarter-Kelly) to trade a little growth for far lower ruin risk. The slider lets you read that trade-off directly.
Can I export the simulated paths?
Yes. Each figure exposes its underlying path array and parameters for export, so you can pull the data into your own notebook and re-run the calculation independently. The point of the lab is verification, not a closed black box — see the research layer for the assumptions behind the numbers.
Is this just a wrapper around a public API?
No. The figures run on Entail’s own calibration of the Safe Haven framework, not a generic statistical library — the fan and planes implement the net-portfolio-effect test from Spitznagel (2021), and the calibration data and equations are documented. The stated 4.2% false-comfort rate is published precisely because the model is ours to measure, not a hidden dependency.
How does the lab relate to the diagnostic?
The lab proves the mechanism in general; the diagnostic applies it to your specific book. You use the figures to confirm a correctly sized safe haven can raise compounding — Spitznagel (2021) puts that lift at 9.5% to 10.0% median CAGR — then the diagnostic runs the same test on your concentrated position and returns a 48-hour document. No call sits between the two.