0xRoulette Research https://0xroulette.com/research Reproducible roulette simulation studies with fixed seeds and honest analysis of variance and risk. en Martingale across 100,000 reproducible sessions https://0xroulette.com/research/martingale-100000-sessions A fixed-seed experiment measuring how often a $5 Martingale reaches a $100 target before bankroll or table limits break the progression. Sat, 15 Aug 2026 00:00:00 +0000 https://0xroulette.com/research/martingale-100000-sessions Gambler’s ruin: closed form versus simulation https://0xroulette.com/research/gamblers-ruin-formula-vs-simulation A 140,000-trial check of the gambler’s ruin formula against deterministic simulation on European roulette even-money odds. Sat, 15 Aug 2026 00:00:00 +0000 https://0xroulette.com/research/gamblers-ruin-formula-vs-simulation How many spins does wheel-bias detection need? https://0xroulette.com/research/wheel-bias-sample-size Power calculations for detecting a roulette pocket that lands 0.25 to 2 percentage points more often than the fair 1/37 baseline. Sat, 15 Aug 2026 00:00:00 +0000 https://0xroulette.com/research/wheel-bias-sample-size European versus American roulette: the risk distribution https://0xroulette.com/research/european-vs-american-risk Paired-seed simulation of 20,000 sessions per wheel showing how a second zero changes terminal bankroll, drawdown, and ruin risk. Sat, 15 Aug 2026 00:00:00 +0000 https://0xroulette.com/research/european-vs-american-risk Deterministic RNG design and validation https://0xroulette.com/research/deterministic-rng-validation Frequency, serial-correlation, repeatability, and multi-seed batch checks for the exact two-stage seeded generator used by 0xRoulette. Sat, 15 Aug 2026 00:00:00 +0000 https://0xroulette.com/research/deterministic-rng-validation Five strategies, the same 10,000 seed sequences https://0xroulette.com/research/same-seed-strategy-comparison A paired comparison of Flat, Martingale, Fibonacci, D’Alembert, and Paroli under identical European-wheel outcome sequences. Sat, 15 Aug 2026 00:00:00 +0000 https://0xroulette.com/research/same-seed-strategy-comparison Measuring drawdown and probability of ruin https://0xroulette.com/research/drawdown-ruin-methodology A worked methodology for peak-to-trough drawdown, finite-horizon ruin estimates, and Wilson confidence intervals using 25,000 fixed-seed sessions. Sat, 15 Aug 2026 00:00:00 +0000 https://0xroulette.com/research/drawdown-ruin-methodology