Statistical Significance
“Significant” ka matlab hai fair wheel ke tahat mushkil, “asli” nahi aur “munafe wala” nahi.
0.05 ki p-value ka matlab hai ki fair wheel itna tedha pattern bees mein ek baar dega. Agar aap bees wheels dekhenge, toh ek ittefaaq se paas ho jayega.
P-value kya hai
Agar wheel fair hota, toh dekhe gaye jitna ya usse bada deviation dikhne ki probabilityganitProbabilityKisi outcome ka chance, 0 se 1 tak ya 0% se 100% tak. Ek number: 1/37 = 2.70%.Poora padhein →. Yeh ek maan-yata ke tahat data ke baare mein bayaan hai, wheel ke baare mein nahi. 0.03 ki p-valuelabp-valueAgar wheel fair hota, to observed deviation jitna ya usse bada deviation dekhne ki probability.Poora padhein → kehti hai: fair wheel aisa 3% baar karta hai. Yeh nahi kehti: 97% chance hai ki wheel biased hai. Doosre bayaan ke liye yeh jaanna padega ki biased wheelslabBiased wheelAisa wheel jiske physical defects kuch pockets ko 1/37 se zyada likely bana dete hain. Bahut kam milta hai, aur hazaron record kiye gaye spins se hi pakda ja sakta hai.Poora padhein → shuru se kitne aam hain, aur modern casino mein woh bahut kam hain, jisse akele significant nateeje ka khoj ki jagah tukka hona kahin zyada sambhav hai.
Multiple comparisons
Fair wheel par aap jo bhi test chalate hain uske 5% level par paas hone ka 5% chance hai. Bees wheels test kijiye aur ek paas ho jayega. Ek wheel ko bees time windows mein test kijiye aur ek paas ho jayega. Ek sample ko 37 pocketsaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → groupings, chhe sectorwheelSectorWheel par pockets ka lagatar ek hissa (arc), layout ke kisi group se alag cheez.Poora padhein → groupings aur teen color groupings ke saath test kijiye aur kuch na kuch paas ho jayega. Ilaaj yeh hai ki data dekhne se pehle test tay kijiye, use ek baar chalaiye, aur naye data par pushti kijiye. Jo scanning ek “biased” wheel dhoondhti hai, aksar wahi nateeja paida karti hai.
Significance banaam size
Bahut bada sample ek maamooli bias ko bhi significant bana sakta hai. 1/37 ki jagah 1/36.5 par lagne wala pocket asli kharabi hai jo kuch million spins mein significance tak pahunchegi aur phir bhi 35 to 1 payoutpaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → par paisa haaregi. Player ke liye effect size maayne rakhta hai: kya koi pocket 1/36 ya behtar par lagta hai, aur kitna? Chi-square aapko wheel ke baare mein batata hai; sirf hit rate bet ke baare mein batata hai.
Power
Doosri galti hai maujood bias ko chook jana. 1,000 spins ke saath 1/30 par pocket (bahut bada bias) 5% level par sirf lagbhag aadhi baar pakda jata hai. Ise sample size theek karta hai, hoshiyaari nahi. Sample size page numbers deta hai.
Ek practical standard
Bias ka daava dilchasp hone ke liye: pehle se chuna gaya test, 0.05 ki jagah p < 0.01, milte-julte size ke independent sample par replication, aur replication ke baad favoured pockets par 1/34 ya behtar ka anumaanit hit rate. Game ke itihaas mein yeh standard gine-chune baar poora hua hai aur, jahan tak public records dikhate hain, kisi modern maintained wheel par kabhi nahi.
Sawaal
1920s ki parampara. Ismein kuch khaas nahi; jab aap bahut saare wheels scan kar rahe hon toh 0.01 zyada samajhdaar had hai.
Shayad woh uniform nateeje nahi de raha. Yeh dealer ka asar, recording ki galti ya data-entry ki problem ho sakti hai. Dohraiye.
Nahi. Yeh batata hai ki distribution gadbad hai. Kahan, yeh sector analysis aur effect size batate hain.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
Ek reported double-zerowheelZeroAkela green pocket jise koi even-money, dozen ya column bet cover nahi karta; house edge ka source. Doosre naam: single zero, 0.Poora padhein → wheel par pehla dozenbetDozen1–12, 13–24 ya 25–36, payout 2:1.Poora padhein → 3,000 spins mein 742 baar aaya. Yeh average se kitne standard deviationsganitStandard deviationVariance ka square root; expected value se kisi result ki aam doori.Poora padhein → neeche hai, aur fair wheel aisa kitni baar karega?
Solution dikhaiye
Jawab Lagbhag 8.1 standard deviations kam. Fair wheel aisa lagbhag 3 × 10¹⁵ koshishon mein ek baar karega, yaani kabhi nahi. Sawaal ke saath chhapa jawab 11.75 kehta hai; humein 8.07 milta hai.
Pehle dozen mein 38 mein se 12 pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → hain. 3,000 spins mein iska average 3,000 × 12/38 = 947.4 hits hai, spread √(3,000 × 12/38 × 26/38) = 25.5 ke saath.
742 average se 205.4 neeche hai: 205.4/25.5 = 8.07 spreads.
Fair wheel lagbhag 740 koshishon mein ek baar teen spreads kam padta hai; aath spreads kam, lagbhag 3 × 10¹⁵ mein ek baar (bell curve, ek taraf). Is baat ko dhyaan mein rakhne se ki padhne wale ne teen dozens mein se sabse bura dekha, kuch zaroori nahi badalta. Aisa result batata hai ki wheel, ya ginti, galat hai. Single-zero wheel par yahi ginti 9.0 spreads kam hoti (average 973.0, spread 25.6).
Thodi hansi
Bees mein ek fair wheel “significant” hota hai. Number ka yahi matlab hai.
Sources
- Pearson, K. “On the criterion that a given system of deviations from the probable…”
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, roulette questions.