Roulette simulation methodology

A roulette simulation evaluates a specified model. Its output depends on the pockets, payouts, wager rules, random sequence and stopping conditions supplied to it. Read those assumptions before interpreting a chart as evidence about a betting system.

State the game before running it

Our explanatory probability model treats each pocket as equally likely and successive spins as independent. Ordinary European examples use 37 pockets; American examples use 38. Payouts are fixed and outside wagers lose fully on zero unless a calculation explicitly defines another rule.

Record these fields when comparing runs:

• Wheel and zero treatment.
• Starting simulated balance and stake unit.
• Selected wagers and stake-change rules.
• Table minimum and maximum.
• Spin cap and any win/loss stop.
• Treatment of an unaffordable next wager.
• Number of independent sessions.

A cap that truncates a doubled wager changes the strategy. Stopping at an unaffordable next wager and replacing it with a smaller one are different policies.

Separate analytical answers from samples

Single-spin probability and expected value can be calculated exactly from the payoff table. A simulation samples paths through those outcomes. It adds information about finite-session behavior, but its sample mean varies from run to run.

For a binary event observed across n independent sessions, a rough standard error near an observed proportion p is √(p × (1 − p) / n). The division by n happens inside the square root. Around p = 0.5, 10,000 sessions give a standard error about 0.5 percentage points. That describes sampling variation under the model; it does not establish fairness or certainty about the future. Rare-event estimates need enough observed events to support an estimate.

Make a seeded run reproducible

A seed initializes a deterministic random generator. Repeating a seed only reproduces a result when the generator, outcome mapping, strategy, inputs and stopping rules are also identical. A seed alone is insufficient. Unseeded demonstrations can illustrate individual paths but should not be labeled exact replay.

Read the controls and output labels of the roulette simulator and strategy simulator for their supported behavior. Neither a browser animation nor simulated practice chips provide evidence about a real casino's equipment or software.

Report the full result

State completed sessions and why runs ended. Show mean, median and relevant percentiles when available, and distinguish ending profit from peak-to-trough drawdown. Keep a losing result when it contradicts the hoped-for story. A displayed winning path demonstrates possibility; it does not establish positive expected value.

Use house edge as an analytical cross-check and bankroll limits to inspect finite stopping. Original studies should publish actual inputs, methods and collected results rather than treating a planned experiment as completed evidence.