Methodology
How dem dey produce every number for dis site, so anybody fit produce any of dem again.
All di figures assume fair European wheel: 37 pockets wey get di same chance, spins wey no dey depend on each odamathsIndependent spinsEach spin get di same probabilities no matter wetin happen before. Na di base for every calculation for dis site.Read di whole tin →, payoutmoniPayoutWetin bet wey win dey return, wey dem dey quote as “X to 1” on top di stake wey dem return.Read di whole tin → 36/n − 1, no la partageruleLa partageFrench rule: when zero come out, dem go return half of even-money stake. E dey cut di house edge for dose bets into half, to 1.35%.Read di whole tin → unless we tok am. Simulations dey use seeded generator and dem dey state dia seed and di size of di sample.
Figures wey get closed form
ProbabilitymathsProbabilityDi chance of one outcome, from 0 to 1 or from 0% to 100%. One number: 1/37 = 2.70%.Read di whole tin → = numbers wey e cover / 37. Expected valuemathsExpected valueDi average result for each bet for di long run. −1/37 of di stake for every standard European bet.Read di whole tin → = −stake/37. VariancemathsVarianceOne measure of how wide di results dey spread around di expected value. E high for straight up, e low for even-money bets.Read di whole tin → for each unitmoniUnitDi base stake wey system or player dey work with. Dem dey describe progressions in units so dat dem go fit work for any table.Read di whole tin → = p·W² + (1 − p) − EV². Streaks: (18/37)ᵏ. Risk of ruinmathsRisk of ruinDi probability sey you go lose di whole bankroll before you reach one target or one number of spins.Read di whole tin →: di formula of gambler ruin with p = 18/37. Estimates of sample size: normal approximation to one-proportion test for α = 0.05 one-sided and 80% power.
Simulations
Monte Carlo sessions dey use even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, e dey pay 1:1.Read di whole tin → wey get win probability of 18/37. Bets no dey pass di table limittableTable limitDi minimum and maximum bet wey dem allow. Na di maximum dey stop progressions wey dey double.Read di whole tin → and di bankrollmoniBankrollDi total moni wey you set aside for play. Bankroll management na to decide how much of am you go risk for each bet and for each session.Read di whole tin → wey remain; session dey end for di number of spins or for zero. ProgressionstrategyProgressionAny rule wey dey change di stake based on di results wey don pass. Negative progressions dey raise am afta losses, positive ones afta wins.Read di whole tin → rules dey written for each strategy page. Seeds dey fixed so di same setting go give di same result for every visit; di Simulator for Roulette Session dey show im seed as session number.
Statistical tests
Wheel-bias pages dey use di chi-square goodness-of-fit of Pearson with 36 degrees of freedomlabDegrees of freedomDi number of values wey no depend on each oda inside one statistic. For chi-square test on 37 pockets na 36, becos di counts must add up to di total.Read di whole tin →. Di p-valuelabp-valueDi probability to see deviation wey big reach di one wey you see or pass am, if di wheel dey fair.Read di whole tin → dey come from di regularized incomplete gamma function. SectorwheelSectorPockets wey follow each oda for one arc of di wheel, no be group for di layout.Read di whole tin → tests dey report deviation for standard deviationsmathsStandard deviationSquare root of variance; di normal distance between one result and di expected value.Read di whole tin → of binomial with p = pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin →/37.
How we dey round numbers
Percentages dey show with two decimals, moni reach di cent, and we dey drop di cents for amounts wey be whole dollars. We no dey round di calculations for middle.
Small laugh
Every number here, you fit run am again and e go come out di same.