Research: Mega Millions Simulation — Hot, Cold & Independence

Generated: 2025-12-15T20:19:15.533Z · Lottery: Mega Millions (sample)

Pre-registration

  • Primary hypothesis: Under independence, conditioning on a lagging first block does not make the target appear sooner. (Δ = 0).
  • Primary metric: Primary outcome = ΔmeanWaitToFirstHit (RMST@200) for lagging − control; one-sided direction = lagging sooner (Δ<0).
  • Analysis plan: We report analytic 95% CIs for ΔRMST@200 (primary), plus secondary ΔmeanCount@10 and a bounded ΔpHitWithin(X) using a scenario-specific X chosen to avoid ceiling/floor (baseline near ~0.7). We also show a robustness grid over (cutoff, window, alpha).

Design

  • Mode: target
  • Rules: main 5 of 70
  • Seed: 1; Future draws: 200; Grid trials per cell: 2000
  • Primary horizon (RMST): 200; Secondary meanCount window: 10
  • Grid: cutoff ∈ {50, 100, 200}, windows ∈ {5, 10, 20, 50, 100}, α ∈ {0.01, 0.05}
  • UX pHitWithin window: 16
  • Target mode: random

Primary result (pre-registered)

Mode: target; cutoff=100; alpha=0.05; window=10; RMST horizon=200

Primary outcome: ΔmeanWaitToFirstHit (RMST@200) lagging − control

Definition: draw index of first hit in the future window (1..T), with “no hit” treated as right-censored at T; reported as RMST = E[min(Tfirst, T)].

Estimate: 4.660

95% CI: -0.491 to 9.811

One-sided p (approx): 0.961905

n: lagging=46; control=1939

Note: p-value is one-sided because direction (lagging sooner ⇒ Δ<0) is pre-registered; CIs are two-sided 95%.

Censoring rate: lagging=0.000000; control=0.000000

Secondary outcome: ΔmeanCount in next 10 draws (lagging − control)

Estimate: -0.232

95% CI: -0.444 to -0.021

(Linear expectation metric; not bounded by 0..1.)

Tertiary (bounded / UX metric): ΔpHitWithin(16) lagging − control

Window is chosen to avoid ceiling/floor when possible; still bounded and non-linear.

Estimate: -0.110826

95% CI: -0.254578 to 0.032926

Kaplan–Meier survival curve: probability the target has nothit yet by draw t

Curves should overlap under independence; systematic separation would indicate a real shift in time-to-first-hit.

S(t) draws 0.5 1.0 0.0 Lagging Control

Data verdict (plain language)

Verdict: No evidence of a ‘due’ effect.

  • ΔRMST@200 = 4.660 (95% CI -0.491 to 9.811); one-sided p≈0.961905. Estimate is slightly later, but not reliably different from 0.
  • Interpretation: “Lagging sooner” means fewer expected draws until first hit (negative ΔRMST).

Power / sensitivity (approx)

Approximate minimal detectable effect (80% power; normal approximation; two-sided alpha). Approximate also because the cohort is defined by a binomial-tail conditioning event.

Primary metric baseline meanWait (RMST@200): 13.905

n: lagging=46; control=1939

MDE @80% power(|ΔmeanWait|): 7.358

Secondary baseline meanCount@10: 0.711

MDE @80% power(|ΔmeanCount|): 0.302

Interpretation: effects smaller than the MDE are hard to reliably detect with this cohort selection + sample size.

“Approximate” reflects both the normal approximation and the binomial-tail conditioning used to define cohorts.

Tertiary metric baseline: pHitWithin(16) = 0.697782 · MDE @80% power (|ΔpHit|) = 0.191818

Interpretation notes (important)

  • Independence null: for toy processes (coin/die) the true effect is 0 by construction; any single “significant” result can occur by chance when you scan many cells.
  • Ceiling/floor risk: when baseline pHitWithin is near 1 (ceiling) or near 0 (floor), ΔpHitWithin is a bounded, non-linear metric and can look more dramatic than it is.
  • Preferred quantity: the primary endpoint here is mean wait-to-first-hit (RMST@T), which directly targets “does it show up sooner?” and avoids the ceiling pathology of pHitWithin in high-p regimes.
  • Small cohorts: grid cells with very small cohort sizes (n < 20) are shown for completeness but are not interpretable (often producing degenerate CIs like 0 to 0).

What these results do not show

  • No “compensation” mechanism: a cold streak does not create a forward advantage under independence.
  • No exploitable strategy: statistically significant cells (especially under ceiling/floor metrics or small n) do not imply predictability or an edge.
  • No jackpot implication: this does not change the combinatorial odds of a specific full ticket.
  • No claim about real-world fairness: real lotteries can be tested for bias separately; this report’s main claim is about conditional reasoning under the null.

Robustness grid (lagging vs control)

  • Each row is one (cutoff, α, window). Look for systematic drift away from 0; do not over-interpret isolated “significant” rows.
  • Rows with n(lag) or n(ctrl) < 20 are visually muted and are not interpretable.
mode cutoff alpha window n(lag) n(ctrl) Δmean 95% CI (Δmean) ΔRMST 95% CI (ΔRMST) ΔpHit 95% CI (ΔpHit)
target 50 0.01 5 0 1997 NA NA NA NA NA NA
target 50 0.01 10 0 1997 NA NA NA NA NA NA
target 50 0.01 20 0 1997 NA NA NA NA NA NA
target 50 0.01 50 0 1997 NA NA NA NA NA NA
target 50 0.01 100 0 1997 NA NA NA NA NA NA
target 50 0.05 5 37 1915 0.106 -0.075 to 0.286 -0.314 -0.778 to 0.150 0.124465 -0.035012 to 0.283943
target 50 0.05 10 37 1915 0.223 0.014 to 0.433 -1.199 -2.270 to -0.129 0.247096 0.107048 to 0.387144
target 50 0.05 20 37 1915 0.374 0.064 to 0.683 -3.534 -5.282 to -1.786 0.148684 0.058735 to 0.238633
target 50 0.05 50 37 1915 0.274 -0.247 to 0.795 -5.523 -8.173 to -2.873 0.026632 0.019421 to 0.033843
target 50 0.05 100 37 1915 0.386 -0.538 to 1.310 -5.823 -8.483 to -3.162 0.000000 ≈0.000000 (degenerate CI)
target 100 0.01 5 1 1997 NA NA NA NA NA NA
target 100 0.01 10 1 1997 NA NA NA NA NA NA
target 100 0.01 20 1 1997 NA NA NA NA NA NA
target 100 0.01 50 1 1997 NA NA NA NA NA NA
target 100 0.01 100 1 1997 NA NA NA NA NA NA
target 100 0.05 5 46 1939 -0.229 -0.331 to -0.127 0.398 0.147 to 0.649 -0.175393 -0.274855 to -0.075930
target 100 0.05 10 46 1939 -0.232 -0.444 to -0.021 1.221 0.490 to 1.953 -0.159058 -0.300306 to -0.017809
target 100 0.05 20 46 1939 -0.220 -0.536 to 0.096 2.671 0.827 to 4.515 -0.045810 -0.174018 to 0.082397
target 100 0.05 50 46 1939 -0.477 -0.927 to -0.026 3.634 0.097 to 7.170 -0.018208 -0.077553 to 0.041138
target 100 0.05 100 46 1939 -0.655 -1.424 to 0.114 4.598 -0.462 to 9.658 -0.021223 -0.063379 to 0.020932
target 200 0.01 5 9 1978 -0.151 -0.440 to 0.138 0.119 -0.754 to 0.992 NA NA
target 200 0.01 10 9 1978 -0.170 -0.748 to 0.407 0.760 -1.436 to 2.956 NA NA
target 200 0.01 20 9 1978 -0.119 -0.851 to 0.613 1.977 -2.700 to 6.653 NA NA
target 200 0.01 50 9 1978 -0.444 -1.849 to 0.961 2.742 -6.695 to 12.180 NA NA
target 200 0.01 100 9 1978 -0.099 -1.800 to 1.602 4.112 -8.511 to 16.735 NA NA
target 200 0.05 5 45 1921 -0.151 -0.291 to -0.010 0.320 0.028 to 0.612 -0.125872 -0.244608 to -0.007136
target 200 0.05 10 45 1921 -0.125 -0.356 to 0.106 0.962 0.133 to 1.791 -0.111875 -0.257900 to 0.034151
target 200 0.05 20 45 1921 -0.209 -0.500 to 0.082 1.498 -0.394 to 3.390 -0.051154 -0.181662 to 0.079355
target 200 0.05 50 45 1921 -0.131 -0.709 to 0.447 3.388 -0.812 to 7.587 -0.038036 -0.111299 to 0.035227
target 200 0.05 100 45 1921 -0.423 -1.166 to 0.320 3.573 -1.104 to 8.251 0.000521 -0.000499 to 0.001541

How to Cite This Page

Lucky Picks. “Research: Mega Millions Simulation — Hot, Cold & Independence.”
https://luckypicks.io/research/independence-and-lagging-numbers/mega-millions-simulation/
(Accessed September 2026)

For a non-technical explanation of what these results mean for players, see our Hot & Cold Lottery Numbers guide.