Di chi-square test

Ow fi work it out

Di expected count fi evry pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting → a n/37. Fi each pocket, square di difference between observed an expected an divide by expected; add up di 37 piece. A fair wheel gi value roun 36 pon average (di degrees a freedomlabDegrees a freedomDi numba a independent value inna a statistic. Fi a chi-square test pon 37 pocket it a 36, cause di count dem haffi add up to di total.Read di whole ting →), wid a standard deviationmathsStandard deviationDi square root a variance; ow far a result usually deh fram di expected value.Read di whole ting → a bout 8.5. Ova 51.0 significant at di 5% level; ova 58.6 at 1%. Di Wheel Bias Analyzer work out di statistic an di exact p-valuelabp-valueDi probability fi see a deviation at leas as big as di one yuh see, if di wheel did fair.Read di whole ting → fram di regularized incomplete gamma function.

A example weh work out

1,000 spin. Thirty-six pocket land between 20 an 34 hit; pocket 8 have 41. Di expected a 27.03. Di pocket-8 piece alone a (41 − 27.03)²/27.03 = 7.2. Seh di odda 36 piece add up to 38 (normal). χ² = 45.2 pon 36 df, p ≈ 0.14. Nuh significant: a fair wheel do dis one time outta seven. Pocket 8 a one candidate, nuh a finding, an di ansa a anodda thousand spin.

Assumption

Independent spinmathsIndependent spinEvry spin have di same probability dem, nuh matta wah happen bifo (one spin nuh know bout di nex one). Di base fi evry calculation pon dis site.Read di whole ting →, an expected count a at least 5 fi evry pocket, an dat mean n ≥ 185 fi di test fi valid at all, an far more fi it fi useful. Fi mix spin fram different wheel break di fus assumption inna spirit (yuh a test a mixture, nuh one wheel). A dealer-signature effect woulda break it fi true, an it woulda push up χ² even if nuh pocket physically come up more.

Di dealer signature inna rouletteIndependent spin inna roulette

Pearson an Monte Carlo

Karl Pearson publish di test inna 1900, an one a im fus example weh im work out a did 26,306 Monte Carlo roulette spin weh people write dung. Im find seh dem too uneven fi be chance, an im declare seh “Monte Carlo roulette… is not a game of chance”. Later writer dem conclude seh di journalist dem weh write dung di spin fi a newspaper did mek up nuff a dem, an dat a one lesson by itself bout weh data come fram.

Roulette inna Monte Carlo

A real test: automatic wheel inna Las Vegas

Playa dem often suspec seh a automatic wheel steer di ballgearBallDi likkle ball weh di dealer fling roun di track di opposite way to di rotor. Modern ball mek outta ivorine or Teflon, 18–21 mm.Read di whole ting → weh fram big bet. A 2017 analysis put di suspicion to di test pon Interblock double-zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting → wheel widout dealer inna Las Vegas, bettin pon a arc a five numba weh deh side by side, di kind a bet a wheel clocker mek. Inna 299 spin di arc win 29 time gainst 39.3 expected, a shortfall weh a fair wheel gi bout 4% a di time. Di chi-square ova all 38 pocket a did 45.29 pon 37 degrees a freedom: p = 16.5%. A second sample a 1,204 spin pon tree wheel gi χ² = 34.79, p = 57%, an nuh arc a any size dem try did significant. Both sample togedda, 1,503 spin, gi χ² = 41.75, p = 27%. Di verdict: nuh evidence a steerin. Di fus sample alone did look suspicious; a di second one settle it.

Afta chi-square

Fi one pocket yuh suspec, a binomial test more powerful. Fi a arc yuh suspec, di sectorpon di wheelSectorA piece a di wheel weh di pocket dem follow one anodda roun di arc, nuh a group pon di betting layout.Read di whole ting → z-test pon di sector analysis page. Chi-square a di omnibus test: it tell yuh sumting off widout seh wah. Use it fus, den look.

Analysis a di sector dem

Formula

Question dem