Roulette Probability
Roulette ki har probability pockets ki ginti ko 37 se bhaag dena hai.
p = cover kiye gaye numbers / 37. Ek number: 2.70%. Atharah: 48.65%. Kisi khaas sequence ka chance single-spin probabilities ko guna karke nikalta hai.
Ek spin
37 pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → mein se har ek ka chance barabar hai, isliye ek spin par roulette mein jeetne ka chance bas ginti ka mamla hai. Chaar numbers par bet 4/37 baar jeetta hai, lagbhag 10.8%. Single-spin probabilityganitProbabilityKisi outcome ka chance, 0 se 1 tak ya 0% se 100% tak. Ek number: 1/37 = 2.70%.Poora padhein → mein isse zyada kuch nahi hai, isi liye poora game ek napkin par analyze ho sakta hai.
Kai spins
Spins independent hain, isliye sequence ki probabilities guna hoti hain. Lagatar do redsbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein →: (18/37)² = 23.7%. Red phir 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 →: (18/37)(1/37) = 1.3%. Lagatar do baar satrah: (1/37)² = 0.073%, lagbhag 1,369 mein ek. Khaas sequence ke liye order matter karta hai, ginti ke liye nahi: “red phir blackbetBlack18 black numbers par even-money bet. French mein: noir.Poora padhein →” 25.0% hai, lekin “do spins mein ek red aur ek black, kisi bhi order mein” 50.0% hai.
Kam se kam ek baar
Complement use kijiye. 37 spins mein straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → par ek bhi hit na hone ka chance (36/37)³⁷ = 36.3% hai, isliye kam se kam ek hit ka chance 63.7% hai, woh “pakka” nahi jo kai players 1 in 37 ke 37 chances se maan lete hain. Yahi calculation batati hai ki 37 spins mein kisi number ke ek baar bhi na aane ka chance lagbhag 3 mein 1 hai, isi liye results board par hamesha kuch “cold” numbers dikhte hain.
Expected intezaar
Average mein ek straight-up number har 37 spins mein ek baar aata hai, lekin intezaar bahut alag-alag hota hai: median intezaar lagbhag 25 spins hai (aadhe samay woh pehle aata hai) aur bees mein se ek intezaar 110 spins se lamba hota hai. Geometric process ke waiting times long-tailed hote hain, aur jo player “jaanta” hai ki 60 spins ke baad number due hai, woh aisi cheez bata raha hai jo paanch mein ek baar hoti hai.
Aam galtiyan
Aise events ki probabilities jodna jo dono ho sakte hain (red ya odd 36/37 nahi; 26/37 hai, kyunki das numbers dono hain). Ek hi spin ke events ke liye guna karna (ek spin par red aur odd 10/37 hai, 18/37 × 18/37 nahi). Pichhle spins ko us sequence ka hissa maanna jis par aap ab bet kar rahe hain: das reds ke baad gyaarahven ka chance 18/37 hai, (18/37)¹¹ nahi.
Roulette mein odds kya hain, aur yeh probability se kaise alag hain?
Casinos payoutspaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → ko odds ke roop mein batate hain. Ek single number 1/37 probability se jeetta hai, isliye roulette mein ek number par jeetne ke odds 36 to 1 against hain. 35 to 1 ka payout isliye ek unitpaisaUnitBase stake jismein koi system ya player kaam karta hai. Progressions units mein batayi jaati hain taaki kisi bhi table par laagu hon.Poora padhein → kam hai, aur yahi apne asli roop mein house edgeganitHouse edgeHar stake ka woh hissa jo casino average mein rakh leta hai: European roulette mein 2.70%.Poora padhein → hai. Badalne ka tareeka: odds against = (1 − p)/p; probability = 1/(odds + 1).
Formula
Sawaal
(1/37)² = 1/1369 ≈ 0.073%.
36/37 = 97.3%. Baaki zero hai.
Saare 37 ka chance 1/37 hai. Satrah sabse zyada bet kiya jaane wala number hai, jo logon ke baare mein ek fact hai.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
Aap spin ke baad spin redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → par bet lagate hain. Iska chance kya hai ki aapki paanchvi jeet theek aathve spin par aaye? Aur ki pehle aath spins mein aapki paanch jeet ho?
Solution dikhaiye
Jawab Spin aath par paanchvi jeet ke liye 12.9%, lagbhag 8 mein 1. Tab tak paanch jeet ke liye 33.4%.
Spin aath par paanchvi jeet ka matlab do cheezein hain: spin aath jeetta hai, aur pehle saat spins mein theek chaar jeet aur teen haar hain, kisi bhi kram mein. Saat spins mein chaar jeet rakhne ke 35 tareeke hain.
Isliye chance 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9% hai.
Spin aath tak paanch jeet ke liye, spins paanch, chhe aur saat par paanchvi jeet ke liye usi tarah ka term jodiye: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%. Statisticians ise negative binomial distribution kehte hain: tay sankhya ki safaltaon mein kitni koshishein lagti hain. Taylor (2021) American wheel par yahi sawaal hal karte hain, 12.2%.
Thodi hansi
Pockets giniye. 37 se bhaag dijiye. Sequence ke liye guna kijiye. Ho gaya.
Sources
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.