Practice instruments — ten simulators for the arithmetic of risk
Most explanations of position sizing are a paragraph and a formula. The formula is memorable and the consequence is not — it only lands when you can hold the edge fixed, move the bet size, and watch the same two thousand worlds end differently. Ten linked instruments: Kelly and sizing, small-sample horizons, compounding drag, volatility targeting, portfolio risk decomposition, calibration, valuation, options, thesis falsifiability, and a Brier-scored drill that tests whether any of it stuck.
Related research
Knowledge BaseWhere it runs
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.
Live demo
Kelly & position sizing
A real edge, sized wrong, still ends at zero.
Presets
Each one makes a specific argument.
The process
What is actually true about your edge.
A 52% win rate at even money is a realistic ceiling for a skilled discretionary trader.
Your estimate
The edge you think you have — where the real damage starts.
Off — you are assumed to know your edge exactly. Nobody does.
Sizing
The only variable most traders set last.
Betting 0.00% of wealth per bet.
The run
Same seed, same worlds.
Dead below 1.0% of stake.
Expected log growth against bet size
The peak is Kelly. The second zero is the cliff. Everything red is an edge you really have, sized into certain ruin.
The same worlds, this bet size
2,000 paths over 250 bets. Change the sizing and these are the identical 2,000 worlds — only your decision moves.
Where it all ended
Log-binned, because a linear histogram of wealth is one bar at zero.
What actually happened
The numbers behind the picture.
Reality check — the edge you think you have
Overestimating your edge does not scale your bet a little. It scales it by the ratio of the two Kelly fractions.
What if I'd sized differently
One Monte Carlo per multiple, across the whole range.
Runs 40 separate simulations. Takes a second or two.
Simulated results from a seeded pseudo-random generator. Nothing here is a forecast, a recommendation, or a claim about any real instrument — it is a machine for developing intuition about the arithmetic of risk. Anything you type stays in your browser.
Stack
The problem
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.
The approach
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.
Decisions & trade-offs
- 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.
- 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.
- 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.
- 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.
Where it stands
Live and compounding. The instruments already produced findings worth keeping: believing you win 60% while actually winning 52% puts full Kelly at exactly 5x true Kelly; a genuine 52/48 edge sized correctly finishes underwater 57% of the time over ten bets; and six positions at 0.6 average correlation behave like one and a half.
The running diary appears here as /notebook entries once the build starts.