A crash-game study, and the limits of the evidence

Correction, 24 October 2026: This post was originally titled “Proving a crash game is fair (and why I bothered)”. That title and its conclusions overstated what the analysis could establish. The original publication date and URL are retained. The figures below are historical reported outputs, not results independently reproduced for this update.

There's a genre of online game — the "crash" or "multiplier" game — where a number climbs from 1.00x and you have to cash out before it crashes. It can feel as though there should be a pattern. I explored that hypothesis with an AI-assisted personal analysis project.

So I built a small pipeline: a Playwright bot that scraped about a thousand rounds, an SQLite store, and an analysis stage. Then I tried, honestly, to break it.

What the study could ask

A sample can help investigate narrower questions:

1. Distribution fit: how well do specified models describe the observed sample?
2. Dependence: do specified tests detect particular kinds of serial structure in that sample?

Neither question is a complete fairness audit. Sampling gaps, changing game rules, fitted parameters, multiple comparisons, and limited statistical power all affect the interpretation.

The distribution

The original analysis reported a log-normal fit with a Kolmogorov–Smirnov p = 0.49 and an estimated house edge of 10.7%. A non-significant goodness-of-fit result does not confirm that model, and a p-value needs appropriate calibration when parameters were fitted to the same observations.

A house-edge estimate also needs the actual payout rules, observation process, and uncertainty. The reported estimate is not a verified statement about the operator's current game.

The independence

The original report described the following outputs:

• Autocorrelation (ACF) — no clear pattern reported at the examined lags.
• Ljung–Box — reported p > 0.08.
• Streak / runs tests — reported as non-significant.
• GARCH — no useful volatility structure reported under the fitted specification.

Failing to detect dependence is not proof of independence. It does not rule out every predictive pattern or establish that a strategy is executable.

Under the probabilities and payouts assumed in the original Kelly criterion calculations, the reported recommended stake was zero for the examined targets. That is a conditional model output, not a universal proof that no edge can exist.

Why bother

The useful outcome was a reason not to automate a strategy on the available evidence. A stronger study would freeze its evaluation period, candidate tests, comparison policy, and stopping rules before inspecting held-out data, then report uncertainty, missing observations, losses, fees, nonfills, and execution limitations.

That is the lesson worth preserving: validate before automating. An honest negative or inconclusive result is useful; calling it proof of fairness is not.