Methodology
How every number on this site is produced, so that any of them can be reproduced.
All figures assume a fair European wheel: 37 equally likely pockets, independent spinsmathIndependent spinsEach spin has the same probabilities regardless of history. The basis for every calculation on this site.Read full →, payoutmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full → 36/n − 1, no la partageruleLa partageFrench rule: when zero hits, half of an even-money stake is returned. Halves the house edge on those bets to 1.35%.Read full → unless stated. Simulations use a seeded generator and state their seed and sample size.
Closed-form figures
ProbabilitymathProbabilityChance of an outcome, from 0 to 1 or 0% to 100%. One number: 1/37 = 2.70%.Read full → = numbers covered / 37. Expected valuemathExpected valueThe average result per bet over the long run. −1/37 of the stake for every standard European bet.Read full → = −stake/37. VariancemathVarianceA measure of how widely results spread around the expected value. High for straight up, low for even-money bets.Read full → per unitmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full → = p·W² + (1 − p) − EV². Streaks: (18/37)ᵏ. Risk of ruinmathRisk of ruinProbability of losing the whole bankroll before reaching a target or spin count.Read full →: gambler’s ruin formula with p = 18/37. Sample-size estimates: normal approximation to a one-proportion test at α = 0.05 one-sided and 80% power.
Simulations
Monte Carlo sessions use even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, pays 1:1.Read full → with win probability 18/37. Bets are capped at the table limittableTable limitMinimum and maximum bet allowed. The maximum is what stops doubling progressions.Read full → and the remaining bankrollmoneyBankrollThe total amount set aside for play. Bankroll management is deciding how much of it to risk per bet and per session.Read full →; a session ends at the spin count or at zero. ProgressionstrategyProgressionAny rule that changes the stake based on previous results. Negative progressions raise it after losses, positive after wins.Read full → rules are documented on each strategy page. Seeds are fixed so a given setting is reproducible across visits; the Session Simulator exposes its seed as a session number.
Statistical tests
Wheel-bias pages use Pearson’s chi-square goodness-of-fit with 36 degrees of freedomlabDegrees of freedomThe number of independent values in a statistic. For a chi-square test on 37 pockets it is 36, because the counts must add up to the total.Read full →. The p-valuelabp-valueThe probability of seeing a deviation at least as large as the one observed if the wheel were fair.Read full → comes from the regularized incomplete gamma function. SectorwheelSectorA contiguous arc of pockets on the wheel, as distinct from a group on the layout.Read full → tests report deviation in standard deviationsmathStandard deviationSquare root of variance; the typical distance of a result from the expected value.Read full → of a binomial with p = pocketsequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full →/37.
Rounding
Percentages are shown to two decimals, money to the cent, and cents are dropped on whole-dollar amounts. Intermediate calculations are not rounded.
Comic relief
Every number here can be run again and comes out the same.