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.

Interpretation: Lagging numbers do not reach their first hit sooner than comparable non-lagging numbers under independence. Shaded areas represent pointwise 95% confidence intervals.

Limitations

Simulation-based
Assumes independence
Not testing real-world rigging

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 December 2025)

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