Roulette Lab · Lab · Statistics · 7 min

Sample Size

Q: Kya koi shortcut hai?

Pockets ki jagah sectors test karna madad karta hai, kyunki physical defect aksar ek arc par asar daalta hai aur signal pockets mein jud jaata hai. Yeh order of magnitude nahi badalta.

Q: Kya main usi wheel ka alag-alag dinon ka data jod sakta hoon?

Haan, agar wheel head wahi hai aur uski servicing nahi hui. Yahi jaanna mushkil hissa hai.

Q: 80% power kyun?

Convention. Iska matlab hai ki bataye gaye size ka asli bias paanch mein chaar baar pakda jaayega.

Kitne spins ke baad kisi pattern ka koi matlab hota hai.

Chhota jawab

Kisi pocket ko 37 mein 1 ki jagah 30 mein 1 baar aate hue theek-thaak confidence se pakadne ke liye lagbhag 4,400 spins chahiye. 35 mein 1 wala pocket, jo sach mein paisa dila sakta hai, lagbhag 70,000 spins leta hai.

25 mein 1

~1,100 spins

30 mein 1

~4,400 spins

35 mein 1

~70,000 spins

noise

∝ 1/√n

Itne zyada kyun

Signal, yaani har hazaar spins mein kuch extra hits, √(n·p·(1−p)) ≈ √(n/37) ke binomial noise ke muqable chhota hai. Noise 1/√n ki tarah girta hai, isliye uncertainty aadhi karne mein chaar guna spins lagte hain. 1/30 wala pocketsaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → har hazaar mein 33 hits deta hai jabki expected 27 hain: chhe extra hits, aur standard deviationganitStandard deviationVariance ka square root; expected value se kisi result ki aam doori.Poora padhein → lagbhag paanch. Hazaar ka ek sample in dono ko bharose se alag nahi kar sakta.

Biased pocket pakadne ke liye zaroori spins (80% power, one-sided 5%)spins

20 mein 1

≈ 500

25 mein 1

≈ 1,100

30 mein 1

≈ 4,400

33 mein 1

≈ 10,000

35 mein 1

≈ 70,000

spins

035000≈ 70,000

Jo biases paisa dila sakte hain (1/35 ya usse behtar) unke liye das-hazaaron spins chahiye. Jo hazaar spins mein dikh jaate hain woh bahut bade hain aur maintenance ke baad bachenge nahi.

Formula

Ek pocket ke one-sided test ke liye, 5% level aur 80% power par, zaroori n lagbhag ((1.645·√(p₀(1−p₀)) + 0.84·√(p₁(1−p₁))) / (p₁ − p₀))² hai, jahan p₀ = 1/37 aur p₁ shak wala rate hai. Yeh pehle se chune gaye ek pocket ke liye sahi hai. Agar aap sabse garam pocket dhoondhne ke liye saare 37 pockets scan kar rahe hain, toh false-positive rate imaandaar rakhne ke liye lagbhag do se teen se guna kijiye.

Practical matlab

300 spins ke baad hot numbermythHot numberAisa number jo haal mein expected se zyada baar aaya hai. Fair wheel par yeh kuch predict nahi karta.Poora padhein → noise hai. 3,000 ke baad woh usi wheel se 3,000 aur collect karne ki wajah hai. 30,000 ke baad woh shayad aisa wheel hai jise physically measure karna worth hai. History mein har documented bias exploit das-hazaaron record kiye gaye spins par bana tha, aur har ek mein mahine lage.

record kiye gaye spinsaap imaandaari se kya keh sakte hain

< 500kisi bhi pocket ke baare mein kuch nahi

1,000chi-square test chal sakta hai; sirf bade defects pakadta hai

5,0001/30 wala pocket shayad dikh jaaye; 1/35 wala nahi

20,0001/33 wala pocket saaf dikhta hai; sectors map kiye ja sakte hain

70,000+faydemand 1/35 wala pocket confirm kiya ja sakta hai

koi bhi number, kai wheels ka data mila karkuch nahi; aap ek mixture test kar rahe hain

Data ki keemat

50 spins per ghante par, 10,000 spins matlab 200 ghante ki recording, ya kai hafton tak published histories copy karna, ek hi pehchaane gaye wheel headsaamanWheel headRotor ka doosra naam: numbers wala ghoomne wala hissa.Poora padhein → se, jise casino ne is beech na ghumaya ho na re-fret kiya ho. Statistics nahi, balki yahi wajah hai ki bias play khatam ho gaya: maintenance cycle data-collection cycle se chhota hai.

Published Spin History Kaise Padhein

Khud edge ke liye sample size

Yahi arithmetic batata hai ki player ko apne results mein house edgeganitHouse edgeHar stake ka woh hissa jo casino average mein rakh leta hai: European roulette mein 2.70%.Poora padhein → dekhne mein kitna time lagta hai: ek sigma ke liye lagbhag 1,400 even-money spins, aur edge ke bilkul saaf dikhne ke liye 10,000. Jo bhi kehta hai ki koi system isse kam spins mein kaam karta hai, woh noise report kar raha hai.

Formula

n ≈ ((1.645·√(p₀(1−p₀)) + 0.84·√(p₁(1−p₁))) / (p₁ − p₀))²

σ(count) = √(n·p·(1−p))

Sawaal

Kya koi shortcut hai?

Pockets ki jagah sectorswheelSectorWheel par pockets ka lagatar ek hissa (arc), layout ke kisi group se alag cheez.Poora padhein → test karna madad karta hai, kyunki physical defect aksar ek arc par asar daalta hai aur signal pockets mein jud jaata hai. Yeh order of magnitude nahi badalta.

Kya main usi wheel ka alag-alag dinon ka data jod sakta hoon?

Haan, agar wheel head wahi hai aur uski servicing nahi hui. Yahi jaanna mushkil hissa hai.

80% power kyun?

Convention. Iska matlab hai ki bataye gaye size ka asli bias paanch mein chaar baar pakda jaayega.

Thodi hansi

Noise 1/√n ki tarah girta hai. Sabr usse bhi tez.

Sources

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gambler’s ruin, chapter XIV.
Barnhart, R. T. Beating the Wheel. Lyle Stuart, 1983.

2026-09-28 ko review kiyamodel: European, single zero walamethodology ↗sources ↗