Practice instruments — ten simulators for the arithmetic of risk

In-labRuns entirely in your browser — no server, no accounts, nothing stored. Every simulation is seeded, so the same inputs always give the same worlds.

Sizing is the decision most traders make third, after entry and exit. It is the one that determines whether the other two ever get to matter — and the arithmetic that shows why is genuinely hard to believe until you watch it happen.

Pure-TypeScript simulation core with no framework dependencies, hand-drawn canvas charts, and 180 tests pinning every numeric claim the interface makes. Where a closed form exists it is used instead of a simulation: the terminal distribution after n bets is exactly binomial, so nothing about it needs sampling.

1. 01Every path gets its own seeded RNG, so moving the sizing slider re-runs the SAME worlds with one decision changed. A shared generator would confound every comparison with luck.
2. 02Yes/no drill questions are graded on the Brier score, not on correctness — marking on correctness would train exactly the overconfidence the Kelly instrument shows turning into 5x sizing.
3. 03Drill questions are generated FROM the simulators, so answers are computed rather than authored and the bank cannot drift out of sync with the maths.
4. 04No worked company case ships with it. Constructing one from the filings is where the learning is; the valuation instrument reads a CSV you author instead.

• Believing you win 60% while actually winning 52% puts full Kelly at exactly 5x true Kelly. Overconfidence does not shade the bet size; it multiplies it.
• A genuine 52/48 edge, sized correctly, still finishes underwater 57% of the time over ten bets. Ten bets is not a sample, and most people quit inside one.
• Six positions at 0.6 average correlation behave like one and a half. A book is only as diversified as its correlations, never as its line count.
• Win 50% or lose 40% on a fair coin: expected return +5% a flip, growth rate −5.1% a flip. Both numbers are correct, and only one of them happens to you.
• Win 50% or lose 33.3% and the geometric mean is exactly 1.0 — you compound at zero forever while the spreadsheet reports a healthy +8.3% expected return.
• The variance-drag shortcut (growth ≈ mean − variance/2) is a second-order truncation, so it throws away skew. On a lottery-shaped payoff exact growth is about −9% and the shortcut reports about −175%: wrong by a factor of nineteen, and wrong in the pessimistic direction.
• Detection scales as roughly the inverse SQUARE of the edge, so halving the edge quadruples the sample you need. That is the honest reason nobody has a 60/40 edge — an edge that large would be provable inside months, so it would be found and competed away. The edges that survive are the ones too small to demonstrate.
• When three of five positions carry 86% of the risk in a single theme, a put on that theme is a sizing decision rather than a trade — which is the one place long options genuinely fit.
• Buying more time on an option costs roughly the square root of it: doubling the days does not double the price, and does not come close to free either.
• A tornado chart ranks inputs by the RANGE you chose for each, not by any intrinsic importance. Narrow the swings and the ordering flips, so the chart is a statement about your own uncertainty and is only as honest as the ranges are.

Live and compounding, and short of shipped by exactly one criterion: the code is not public. The instruments run in the browser, the core is pinned by its own test suite, and the findings above are stated — but the repository this build lives in is private, so there is no source link to give you. Checked 2026-09-05: github.com/menfem/menfem-vercel returns a 404 to anyone not signed in. A plausible-looking link would clear the bar without clearing the point of it, so there is none.

• 2026-09-05Graded against the shipped bar — three of four, short only a public repository