Sawaal: Zero Aane Mein Kitna Time
Zero average mein 37 mein ek spin par aata hai. Asal mein kitna intezaar karna padta hai, aur even-money bettor par iska kya asar hota hai?
Zero ka intezaar geometric hai: mean 37 spins, median 25, aur bees mein ek intezaar 110 spins se lamba hota hai. 200-spin session mein even-money bettor 5.4 zeros ki ummeed karta hai aur 1 se 10 tak kuch bhi dekh sakta hai.
Sawaal
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 → ki har spin par probabilityganitProbabilityKisi outcome ka chance, 0 se 1 tak ya 0% se 100% tak. Ek number: 1/37 = 2.70%.Poora padhein → 1/37 hai. (a) Agle 37 spins mein koi zero na aane ki probability kya hai? (b) Median intezaar kitna hai? (c) 200-spin even-money session mein player ko kitne zeros ki ummeed karni chahiye, aur range kya hai?
Hal
(a) (36/37)³⁷ = 36.3%. Ek-tihaai se zyada baar 37 spins bina kisi zero ke guzar jaate hain, yeh wahi arithmetic hai jisse 37 spins mein straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → par kam se kam ek hit sirf 63.7% hai. (b) Intezaar W geometric hai; p(W > k) = (36/37)ᵏ; median woh k hai jahan yeh 0.5 ko paar karta hai, yaani k ≈ 25. Aadhe intezaar 25 spins ya usse chhote hain aur aadhe lambe; 37 ka mean lambi tail ki wajah se upar khinchta hai. (c) 200 spins mein zeros binomial hain, mean 200/37 = 5.4 aur standard deviationganitStandard deviationVariance ka square root; expected value se kisi result ki aam doori.Poora padhein → √(200 × (1/37) × (36/37)) ≈ 2.3. 95% range lagbhag 1 se 10 hai.
Even-money bettor ko zero kitna padta hai
Har zero ek stake ka nuksaan hai, aur redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → par zeros hi poora edge hain: 37 average spins mein 18 jeet aur 18 haar barabar ho jaati hain, aur ek zero −1/37 hai. $10 par 200-spin session mein expected 5.4 zeros $54 ke padte hain, jo bilkul 200 × $10 / 37 hai. 2 zeros wale session mein $34 ka achha luck raha; 9 zeros wale session mein $36 ka bura luck, aur woh rigged lagega. La partageniyamLa partageFrench rule: zero aane par even-money stake ka aadha wapas milta hai. In bets par house edge aadha hokar 1.35% ho jaata hai.Poora padhein → table par har zero aadhe stake ka padta hai aur aankde aadhe ho jaate hain.
La Partage Roulette RuleKya Online Roulette Rigged Hai? Myth
Agla sawaal
Lagatar do zeros ki probability kya hai? (1/37)² = 1/1,369. 20 tables wale casino mein 50 spins ek ghanta par, yaani har 1.4 ghante mein kahin na kahin lagbhag ek baar lagatar do zeros. Jo players yeh dekhte hain woh maan lete hain ki wheel kharab hai; arithmetic kehta hai ki bas Tuesday hai.
Khud try kijiye
Session Simulator har session ke zeros ginta hai. 100 spins kuch sau baar chalaaiye aur ginti ka plot banaaiye: upar wala histogram apni lambi right tail ke saath dikhega. Kahaaniyaan usi tail se aati hain.
Formula
Sawaal
Fair wheel par nahi. Biased wheellabBiased 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 → par koi bhi pocketsaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → ho sakta hai, aur pata lagaane mein hazaron spins lagenge.
Yeh bhi baaki sab ki tarah 2.70% ki bet hai. Yeh session ka roop badalti hai (zero jeet ban jaata hai), keemat nahi.
Kyunki intezaar ka distribution tircha hai: bahut saare chhote intezaar, kuch bahut lambe.
Thodi hansi
Mean 37, median 25, aur ek lambi tail jahan kisse rehte hain.
Sources
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.