Roulette Computers
Computer ball ka timing kaise karta hai, pehle computer kisne banaye, aur use kitna accurate hona padta hai.
Roulette computer spin ke pehle kuch seconds mein ball aur rotor ka timing leta hai aur batata hai ki ball wheel ke kis hisse mein girni chahiye. Edward Thorp aur Claude Shannon ne pehla computer 1961 mein banaya, aur Eudaemons ne 1976 se digital computer banaye. Is tareeke ke liye zaroori hai ki ball launch hone ke baad bhi bets li jayein: aaj live studios launch par hi betting band kar dete hain, aur Nevada mein 1985 se aise devices par ban hai.
Pehla roulette computer system kaise bana
Yeh idea Edward Thorp ko 1955 ke spring mein aaya, jab woh UCLA mein physics ke graduate student the: jo wheel itna achha bana ho ki usme bias na ho, use ballsaamanBallChhoti ball jo rotor ki ulti disha mein track par chhodi jaati hai. Aaj ki balls ivorine ya Teflon ki hoti hain, 18–21 mm.Poora padhein → ko utne hi predictable tareeke se ghumana chahiye jaise koi planet ghoomta hai. Unhone ek sasta half-size wheel film kiya, frame mein stopwatch ke saath, aur paya ki woh predict karne ke liye bahut irregular tha; December 1958 mein Nevada ki trip ne dikhaya ki casino ke wheels smoothly chalte hain. Phir blackjack ne unka dhyan le liya. November 1960 mein, MIT mein, unhone Claude Shannon se kaha ki unka card-counting paper National Academy of Sciences ko bhej dein; meeting ke end mein Shannon ne poocha ki woh aur kis cheez par kaam kar rahe hain, aur roulette project Shannon ke basement mein shift ho gaya. Unhone Reno se $1,500 mein ek regulation wheel khareeda, use slate ki ek purani billiard table par rakha, aur ball ka timing ek strobe light aur second ke sauve hisse tak padhi jaane wali clock ke saath liya. Practice ke saath unke timing errors lagbhag 0.03 se ghatkar 0.01 second par aa gaye. June 1961 tak computer mein baarah transistors the aur woh cigarette ke packet jitna bada tha: joote mein ek switch, jo pair ke angoothe se chalta tha, rotorsaamanRotorWheel ka ghoomne wala hissa jismein pockets hote hain.Poora padhein → aur ball ka timing leta tha, aur ek kaan mein ek tone wheel ke aath sectorswheelSectorWheel par pockets ka lagatar ek hissa (arc), layout ke kisi group se alag cheez.Poora padhein → mein se ek ka naam batata tha. Us garmi mein Las Vegas mein Shannon wheel ke paas timing lete aur kisi bhi system player ki tarah numbers likhte, jabki Thorp table ke doosre kone par dimes ki bet lagate. Predictions sahi nikle, lekin earpiece tak jaane wale baal jaise patle taar baar-baar toot jaate, aur ek baar Thorp ke bagal wali ek mahila unke kaan se bahar jhaankte speaker ko dar se ghoorti reh gayi. Unhone kabhi serious bet nahi lagayi. Thorp ne roulette computer system ka elaan 1966 mein kiya aur details 1979 aur 1984 mein publish kiye.
Pehle digital computers
Thorp aur Shannon ki machine analog thi: uska circuit hi uska program tha, aur tareeka badalne ka matlab tha use dobara wire karna. Microprocessor ne yeh limit hata di. Caltech ke student Alan Lewis 1972 mein camera case mein ghar par bana ek digital computer lekar Las Vegas ke Circus Circus gaye, tables ke upar ki balcony se wheels ka timing liya aur neeche ek partner ko radio se predictions bheje. Computer chala, lekin paisa nahi bana; baad mein unhe pata chala ki unhone wheel ka tilt chhod diya tha. 1976 se Santa Cruz ke physics students ke ek group, Eudaemons, ne yeh kaam poori tarah kiya. Unhone ek casino wheel khareeda, ball, rotor, tilt aur bounce ko measure kiya, aur paanch settings wali equations likhin jinhe player har wheel ke liye bet lagane se pehle lagbhag bees minute tak pair ke angoothe se switches dabakar adjust karta tha. Unka computer spin ke kuch seconds baad aath sectors mein se ek ka naam batata tha. January 1978 mein ek asli table par isne ek edge diya jise unhone 25% aanka; body par bandha aur baad mein jooton mein fit kiya gaya hardware physics se kahin zyada baar fail hua (dekhiye The Eudaemons).
Late bets kyun mayne rakhti thi
Casino ball launch hone ke baad bets lena band karke prediction ko poori tarah rok sakta hai. Thorp ne paya ki lagbhag koi casino aisa nahi karta tha: Reno, Las Vegas, London, Monte Carlo, Nice, Venice aur Puerto Rico mein aam tareeka yeh tha ki ball girne se ek-do chakkar pehle “no more betsprakriyaNo more betsDealer ki call (ya screen par prompt) jo betting band karti hai. Ab chips na rakhe, na khiskaye, na hataye ja sakte hain.Poora padhein →” bola jaata tha. Tab se har prediction scheme ko yahi window chahiye thi, Eudaemons se lekar Ritz team ki racetracktableRacetrackLive aur electronic layouts par oval patti jo numbers ko wheel ke kram mein dikhati hai, neighbors aur sector bets ek tap mein lagane ke liye.Poora padhein → par late calls tak. Nevada ne May 1985 mein prediction devices ko gair-kanooni kar diya, aur aaj live studios launch par hi betting band kar dete hain.
Casinos ne kaise jawab diya
Jin saalon mein launch ke baad bhi bets li jaati thi, casinos shak wale players se dealer ke zariye ladte the. 1966 mein Nice mein Norman Leigh ke system players aur baad ki prediction teams ke kisse batate hain: har spin par naya croupierlogCroupierRoulette table ka dealer.Poora padhein →, badli hui ball, chhote ya tez spins, casino ke apne logon se bhari table, aur aakhir mein band table. Yeh kahaniyan players ki taraf se aati hain aur inhe check karna mushkil hai (Goldman, 2007). Phir bhi yeh tareeke samajh mein aate hain: chhota ya tez spin ball ko kisi pocketsaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → par nishana nahi laga sakta, lekin woh us timing ko zaroor bigaad deta hai jise predictor measure karta hai.
Prediction kitna achha hona chahiye
Thorp (1984) ne hisaab lagaya ki prediction ki keemat kya hai jab uska error bell curve ko follow karta hai: ek typical spin mein predicted pocket σ pockets idhar ya udhar hota hai. Sirf predicted number par bet lagaiye, ya us par aur har taraf ke do neighborsbetNeighborsWheel par ek number aur uske dono taraf ke do-do pockets, paanch straight-up chips.Poora padhein → par, aur edge sirf σ par nirbhar karta hai. Perfect prediction har straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → jeetega. σ = 10 pockets par, jo accuracy Thorp aur Shannon ne haasil ki, straight-up lagbhag +44% deta hai, yahi figure Thorp unke device ke liye dete hain; unka 1998 ka account ise wheel ke sabse favoured aathve hisse par rakhta hai. Error badhne ke saath edge tezi se girta hai aur European wheel par lagbhag 17 pockets aur American wheel par 16 par khatam ho jaata hai, jab prediction lagbhag aadhe wheel se chook jaata hai. Thorp ka apna error budget dikhata hai ki yeh limit paas kyun hai: rotor aur ball ke timing se 1.4 aur 5.5 pockets ke alag errors, deflectorssaamanDeflectorApron par lage metal ke rukawat jaise tukde jo girti hui ball ko idhar-udhar bikher dete hain. Doosre naam: canoe, diamond, pin.Poora padhein → par se ball girne se 7 aur pockets mein bounce se 6, milkar lagbhag 10.8 bante hain.
Sawaal
Nahi. Wahan koi ball hai hi nahi. Number animation se pehle software chun leta hai.
Woh timing ke aage kamzor hongi, isiliye koi bhi table is tarah nahi chalayi jaati.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
NeighborsbetNeighborsWheel par ek number aur uske dono taraf ke do-do pockets, paanch straight-up chips.Poora padhein → call ek number par aur wheel par uske dono taraf ke do-do pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → par ek-ek chippaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → lagata hai: paanch chips. Break even ke liye prediction ko kitni baar in paanch pockets mein girna chahiye, aur agar woh paanch mein ek baar sahi ho to kya kamata hai?
Solution dikhaiye
Jawab Yeh 36 mein 5, 13.9% par break even hota hai, jabki akeli kismat se 13.5%. Paanch mein ek baar sahi hone par yeh lagaye se 44% zyada lautata hai.
Agar call hit hota hai, ek chip 35 to 1 jeetti hai aur apni jeet ke saath wapas aati hai, 36 chips, aur baaki chaar haar jaati hain. Isliye ek hit 5 lagane par 36 lautata hai, aur call break even hota hai agar 36 mein 5 baar hit kare, 13.9%. Kismat se yeh 37 mein 5 baar hit karta hai, 13.5%. Yahi chhota antar, aadhe percentage point se bhi kam, poore 2.70% ka srot hai.
Paanch mein ek hit par har 5 lagane par 0.2 × 36 = 7.2 chips wapas aati hain, +44%. Chaar mein ek par, +80%.
Isiliye accuracy mein chhota sudhaar itna keemti hai, aur isiliye casinos high stakes par call betstableCall betHaath se lagane ke bajaye dealer ko bola gaya bet, aam taur par voisins ya tiers jaisa wheel-sector bet. Doosra naam: “announced bet”.Poora padhein → jaldi band kar dete hain: yahi chhota antar house ka poora margin hai. Kaha jaata hai ki 2004 ke Ritz players ne isi tarah bet lagaya.
Thorp ne apne prediction mein chaar independent errors gine, pockets mein: rotorsaamanRotorWheel ka ghoomne wala hissa jismein pockets hote hain.Poora padhein → ki timing se 1.4, ballsaamanBallChhoti ball jo rotor ki ulti disha mein track par chhodi jaati hai. Aaj ki balls ivorine ya Teflon ki hoti hain, 18–21 mm.Poora padhein → ki timing se 5.5, deflectorssaamanDeflectorApron par lage metal ke rukawat jaise tukde jo girti hui ball ko idhar-udhar bikher dete hain. Doosre naam: canoe, diamond, pin.Poora padhein → par ball ke girne se 7 aur pockets mein uchhal se 6. Total kitna bada hai, aur dono timing errors kitna jodte hain?
Solution dikhaiye
Jawab Kul lagbhag 10.8 pockets. Timing errors ke bina yeh 9.2 hota, isliye dono timings sirf 1.6 jodti hain.
Independent errors seedhe nahi judte; unke squares judte hain. Total ka typical size squares ke jod ka square root hai: 1.4² + 5.5² + 7² + 6² = 1.96 + 30.25 + 49 + 36 = 117.2, aur √117.2 ≈ 10.8.
Dono timing errors ke bina: √(49 + 36) = √85 ≈ 9.2.
10.8 pockets ka total is page ki table ki 17-pocket limit ke andar hai aur ek number par lagbhag +34% ke barabar hai. Thorp ne jo sabak nikala: jab deflectors par girna sabse bada error ho, to behtar timing se kam hi milta hai.
Thodi hansi
Physics kaam karti hai. Betting window band ho chuki hai.
Sources
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”
- Bass, T. A. The Eudaemonic Pie.
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Goldman, N. Great Gambling Scams.
- Nevada Revised Statutes, chapter 465.