How we calibrate

What PatternSight does — and what it cannot do

A fair lottery is, by design, maximally random. Uniform draw probabilities maximize Shannon entropy — the mathematical way of saying no number is more likely than any other and the draw carries no exploitable signal. Our default belief about every game is therefore fairness: absent strong evidence to the contrary, the forecast for every number stays uniform. We never inject a preference for a number because it is "due" or "running hot" — that would mean inventing information the data does not contain.

PatternSight is a quantitative research terminal for lottery analytics: distributions with quantified uncertainty, calibration against actual frequencies, bias and anomaly detection, and ROI backtests against random — all with mandatory multiple-comparison correction. It does not predict which numbers will win, and it never claims to improve your odds. In many jurisdictions, claiming you can predict gambling outcomes is a consumer-protection violation, not just a credibility risk. What you do with the numbers, and the outcomes, are yours.

Why our backtest edge is ≈ 1.0 — and why that is correct

A lift of ≈ 1.0 (no edge over random) is not a bug we tune away; it is what theory predicts. Three independent reasons: (1) the entropy maximum — a fair draw has no signal to extract; (2) the Cramér-Rao bound— detecting a bias as small as p = 0.105 vs 0.095 would need impractically many draws, so small-sample "edges" are statistical noise; (3) our own complexity gate — if an advanced model does not beat a plain Dirichlet-Multinomial baseline after correction, we demote it. Order of magnitude: detecting a 1%-high number in a 6/49 game needs roughly 20,000 draws; a Pick-3 digit bias roughly 5,000. Most games never accumulate that history.

Two rigor rules follow. Correct null for the game type: for without-replacement games (6/49-style) the naive χ² distribution does not apply — the asymptotic null is a weighted sum of χ² variables (Genest et al. 2002), so we calibrate those p-values by permutation rather than reading a standard χ² table. Multiple-testing control: across hundreds of games × numbers × features we run a very large number of implicit tests, so every anomaly claim must survive Benjamini-Hochberg FDR or Bonferroni correction. A single isolated hot number is never evidence.

Data pipeline

Draw histories scraped per-jurisdiction from official lottery commission sources, normalized into a SQLite warehouse, and reduced to per-(game, window, ball_kind, number) digests. Public dashboard tables (in Supabase) are refreshed nightly via cron — currently across 16 games, expanding to ~50 in Phase 5-6.

Statistical tests

• Pearson χ² with Wilson-Hilferty p-value approximation for uniformity testing against the discrete-uniform null.
• Kolmogorov-Smirnov for distributional fits (sums, range spreads, gap distributions).
• Bonferroni correction applied for the 16 games × 4 windows comparison surface (α/64 ≈ 0.00078).
• Wilson 95% CI on count proportions (Brown-Cai-DasGupta 2001; normal approximation undercovers at low counts).
• 5-fold walk-forward cross-validation for Bayesian smoothing α and Markov order selection (minimizes held-out NLL per game).
• Cover (1989) sharing-risk adjustment on strategy backtests (a real edge: avoid combinations other players cluster on).
• Percentile bootstrap 95% CI on strategy EV (skewed distributions; normal-theory undercovers).

Calibrated vs Explore modes

Calibrated mode (default) locks all statistical parameters to the per-game values minimizing held-out NLL via cross-validation. This is the scientifically defensible view.

Explore mode unlocks sliders so users can play with hot/cold thresholds, smoothing α, window length, etc. Every chart in Explore mode shows a live df-spentwatermark — the count of degrees-of-freedom the user has spent fiddling. After ~3 slider moves, the watermark begins suggesting that the result is increasingly exploratory and shouldn't be treated as a calibrated finding.

Format-mixed games

Several games have changed ball ranges during their history (Powerball 5/55 → 5/69 in 2015; Mega Millions 5/56 → 5/70 + 1/25 in 2017). When all-time χ² is computed without per-format weighting, these games fail uniformity at p < 0.05 — not because the RNG is biased, but because the format change mixes draws from different distributions. When filtered to a single format, every major game passes. The scorecard marks these as Format-mixed*.

Statistical references

• Cleveland, W. (1985). The Elements of Graphing Data.
• Tufte, E. (1990). Envisioning Information.
• Wilkinson, L. (2005). The Grammar of Graphics.
• Wilke, C. (2019). Fundamentals of Data Visualization.
• Munzner, T. (2014). Visualization Analysis and Design.
• Brown, L., Cai, T., DasGupta, A. (2001). Interval Estimation for a Binomial Proportion. Statistical Science.
• Shannon, C. (1948). A Mathematical Theory of Communication. Bell System Technical Journal. (Entropy is maximized by the uniform distribution.)
• Genest, C., et al. (2002). Goodness-of-fit tests for discrete distributions. (Weighted-χ² null for without-replacement draws.)
• Benjamini, Y., Hochberg, Y. (1995). Controlling the False Discovery Rate. JRSS-B.
• Cover, T. (1989). Do longer games favor the stronger player? AMS.
• Stern, H. (1992). Probability models for lottery games. Statistical Science.
• Suetens, S., Tyran, J.-R. (2016). The gambler's fallacy and gender. JEBO.

Spiritual tradition sources

Each widget cites its primary sources inline. Master list (Phase 3+):

• Agrippa, H.C. (1533). De Occulta Philosophia Libri Tres.
• Wilhelm, R. / Baynes, C.F. (1950). The I Ching, or Book of Changes.
• Bascom, W. (1969). Ifa Divination: Communication between Gods and Men in West Africa. (Referenced; Ifá is closed/initiation-based and not simulated in this product.)
• Aveni, A. (2001). Skywatchers (Maya).
• Tedlock, B. (1992). Time and the Highland Maya. (Living Tzolkin tradition.)
• Pingree, D. (1981). Jyotihśāstra (Vedic Jyotish).
• Ho, P.-Y. (2003). Chinese Mathematical Astrology.

Reproducibility

The complete pipeline (warehouse loaders, calibration scripts, digest builders, and dashboard push code) is at D:/dev/projects/research/lottery-datasets/calibration/ with a pytest suite covering Bug-A (REAL underflow), Bug-B (PostgREST dedupe), timeseries draw-seq invariants, and strategy field stability.