Test Before You Commit

 BGPT Odds of True

The hypothesis (that MC simulation can distinguish syndicate vs crowd expected returns) is methodologically sound and the underlying analytic predictions are proven with clear falsification criteria; uncertainty reflects only whether model assumptions (no take, equiprobable) hold in the simulated scenario.

 Hypothesis Novelty

MC verification of game-theoretic results is standard methodology; the underlying syndicate-edge theorem (2017) is moderately novel but the simulation approach itself is routine.

 Quick Analysis Plan Copied

 Long Analysis Plan

Analytic Anchors for Monte Carlo Verification

The hypothesis is directly testable against three closed-form predictions from the syndicate-vs-crowd game model: (1) a syndicate betting all 1,000 distinct tickets earns +26.41% expected return against 1,000 independent quick picks; (2) syndicate strategies betting fewer than 583 tickets have negative expected gain; (3) the unique Nash equilibrium is (s=t, q=uniform) with positive syndicate return Lottery syndicate analytic results and Nash equilibrium.

Curve derived from the paper's closed-form expected-gain formula (Formula 15), reproducing the reported anchors at s=583 and s=1000.

What Monte Carlo Adds Beyond Closed-Form

The paper is purely analytic and reports no simulation or empirical verification Acknowledged absence of simulation validation. A Monte Carlo test is therefore the natural falsification tool. The per-draw return for the trump ticket is extremely right-skewed: the syndicate always wins (it covers every number), but the payout depends on crowd duplication K~Bin(1000, 0.001).

Green = profitable draw, red = loss. Mean = +26.41%, SD ≈ 58%. Convergence to ±0.3% precision requires ~37,000 independent draws; ±0.1% requires ~340,000.

Falsification Criteria and Blind Spots

• MC falsification: If simulated mean return at s=1000 falls below 26.41% (or is not positive), the analytic claim weakens Explicit falsification test for syndicate return.
• Model scope: Results assume no take, no carryover, equiprobable tickets, and a single syndicate. Real lotteries have takes of 30–50%, carryovers, and multi-syndicate competition — none fully modeled Practical and structural model limitations.
• Missing control: The model does not compare against a coordinated crowd (which would eliminate the edge), so the result is specifically about coordination asymmetry, not ticket selection skill.

Confidence: High (strong analytic proof, clear falsification path); the 26.41% figure is model-specific and does not transfer to real lotteries without the a/(s+c)−x≥0 condition for take and carryover.