Forecast Observatory

Shape probabilities are exact within each assumed weighted-subset model. Learned parameters and model choice remain uncertain. The number table is ordered numerically; it does not recommend a ticket. Replays filter today’s canonical archive by draw date; later corrections may be present.

Five fixed models start with weights ½ for fair and ⅛ each for the alternatives. Each draw is forecast before its result updates those weights. The final 30% is chronological validation. Promotion needs 200 draws, at least 60 validation draws, log evidence ≥ log(20), and positive Brier improvement. This is an operational gate, not a guarantee of future advantage; searches across games or dates are not corrected.

These paths use the fair independent-draw model and a fixed rule era. The shaded central 80% ranges describe future outcomes, not uncertainty about a mean. Waiting targets are probabilities, not due dates. Horizons count draws, not days.

Demand is inferred from prize tables, not observed sales. A rolling median of the previous 12 log estimates predicts the next record; the last 60 past errors set the band. Recent coverage is scored on up to 30 later records. Dependence, jackpot shocks and missing records can invalidate that band. No forthcoming jackpot amount is assumed.

Population jackpot risk assumes independent uniform tickets. The separate popularity multiplier is your scenario for how often other players choose one line. Popularity changes sharing, never that line’s chance of being drawn. Real correlated or concentrated choices can change the population result.

P(S | w) = ∏(wᵢ : i∈S) / eₖ(w); Pmix(S) = Σⱼ πⱼPⱼ(S)

πⱼ,new ∝ πⱼ,old Pⱼ(Sactual); Brier = mean((pᵢ − yᵢ)²)

P(≥1 in H) = 1−(1−p)ᴴ; E[distinct] = N[1−(1−k/N)ᴴ]

Match-count probabilities are exact under each whole-draw model and mixed using the same forecast weights. The fair case is hypergeometric: P(R=r)=C(k,r)C(N−k,k−r)/C(N,k). Saved lines are read locally; the forecast comparison sends no numbers to the server.

Match-count Brier scores use the whole count distribution: 0 is perfect, 2 is worst. Scores evaluate the forecast, not whether a ticket was bought or a prize was won.

R · Hypergeometric distribution

• Gneiting & Raftery (2007) · Strictly Proper Scoring Rules
• Hyndman & Athanasopoulos · Time-series cross-validation
• Hyndman & Athanasopoulos · Prediction intervals