Kwamfutocin roulette
Yadda kwamfuta ke auna lokacin ƙwallo, waɗanda suka gina na farko, da irin daidaiton da dole ta kasance da shi.

Kwamfutar roulette tana auna lokacin ƙwallo da na rotor a daƙiƙoƙin farko na juyi, sannan ta faɗi ɓangaren dabaran da ya kamata ƙwallon ya faɗa. Edward Thorp da Claude Shannon sun gina ta farko a 1961, Eudaemons kuma sun gina na dijital tun daga 1976. Hanyar tana buƙatar a karɓi cace-cace bayan sakin ƙwallo: a yau studiyo kai tsaye suna rufe caca a lokacin sakin ƙwallo, kuma Nevada ta haramta irin waɗannan na'urori tun 1985.
Yadda aka gina tsarin kwamfutar roulette na farko
Ra'ayin ya zo wa Edward Thorp a lokacin bazara na 1955, lokacin da yake ɗalibin digiri na gaba a fannin fiziks a UCLA: dabaran da aka ƙera sosai har ba zai karkata ba ya kamata ya kewaya da ƙwallokayan aikiƘwalloƘaramin ƙwallon da ake jefawa a hanyarsa a akasin juyawar rotor. Ƙwallayen zamani na ivorine ko Teflon ne, 18–21 mm.Karanta gaba ɗaya → cikin tsari kamar duniyar sama. Ya ɗauki bidiyon wani dabaran mai arha mai rabin girma tare da agogon awon lokaci a cikin hoton, ya gano cewa ba shi da tsari sosai har ba za a iya hasashe ba, kuma tafiya zuwa Nevada a watan Disamba 1958 ta nuna masa cewa dabaran gidajen caca suna juyawa cikin santsi. Sai blackjack ya ɗauke hankalinsa. A watan Nuwamba 1960, a MIT, ya roƙi Claude Shannon ya aika takardarsa ta ƙirga katuna zuwa National Academy of Sciences; a ƙarshen ganawar Shannon ya tambaye shi me kuma yake aiki a kai, kuma aikin roulette ya koma ɗakin ƙarƙashin ƙasa na gidan Shannon. Sun sayi dabaran na ƙa'ida daga Reno a kan $1,500, suka ɗora shi a kan tsohon teburin billiard na dutse, suka auna lokacin ƙwallo da hasken strobe da agogon da ake karantawa har zuwa ɗaya bisa ɗari na daƙiƙa. Da yin aiki, kuskuren aunawarsu ya ragu daga kusan 0.03 zuwa 0.01 na daƙiƙa. Zuwa watan Yuni 1961, kwamfutar tana da transistors goma sha biyu kuma girmanta kamar fakitin taba sigari: makunni a cikin takalmi, wanda ake dannawa da babban yatsan ƙafa, yana auna lokacin rotorkayan aikiRotorƁangaren dabaran da ke juyawa wanda ke ɗauke da ramuka.Karanta gaba ɗaya → da na ƙwallo, kuma sauti a kunne ɗaya yana faɗin ɗaya daga cikin sassadabaranSasheRamuka da ke bin juna a jere a kan dabaran kamar baka, sabanin ƙungiyar lambobi a kan teburin caca.Karanta gaba ɗaya → takwas na dabaran. A Las Vegas a lokacin zafin wannan shekarar, Shannon yana auna lokaci a gefen dabaran yana rubuta lambobi kamar kowane ɗan wasa mai tsari, yayin da Thorp ke caca da sulallan dime a ɗaya ƙarshen teburin. Hasashen ya yi daidai, amma siraran wayoyi zuwa abin kunne suna ta tsinkewa, kuma wani lokaci wata mace a gefen Thorp ta zura ido cikin firgici ga lasifikar da ke fitowa daga kunnensa. Ba su taɓa yin caca da gaske ba. Thorp ya sanar da tsarin kwamfutar roulette a 1966 kuma ya wallafa cikakkun bayanai a 1979 da 1984.

Kwamfutoci na dijital na farko
Na'urar Thorp da Shannon ta analog ce: da'irarta ita ce shirinta, kuma canza hanyar yana nufin sake haɗa wayoyinta. Microprocessor ya kawar da wannan iyaka. Alan Lewis, ɗalibi a Caltech, ya kai kwamfutar dijital da ya gina a gida a cikin akwatin kyamara zuwa Circus Circus a Las Vegas a 1972, yana auna lokacin dabarai daga baranda da ke saman teburori kuma yana aika hasashe ta rediyo ga abokin aikinsa a ƙasa. Ta yi aiki, amma ba ta kawo kuɗi ba; daga baya ya gane cewa bai saka karkatar dabaran a lissafinsa ba. Daga 1976, wata ƙungiyar ɗaliban fiziks a Santa Cruz, Eudaemons, sun yi aikin sosai. Sun sayi dabaran gidan caca, sun auna ƙwallo, rotor, karkata da tsalle, kuma sun rubuta lissafi mai saituna biyar da ɗan wasa ke daidaitawa ga kowane dabaran ta hanyar danna makunnan ƙafa na kusan minti ashirin kafin caca. Kwamfutarsu tana faɗin ɗaya daga cikin sassa takwas bayan ɗan daƙiƙoƙi cikin juyi. A tebur na gaske a watan Janairu 1978, ta ba da fifiko da suka ƙiyasta a 25%; kayan aikin, da aka ɗaure a jiki daga baya kuma aka gina su cikin takalma, sun gaza fiye da kimiyyar motsin nesa ba kusa ba (duba The Eudaemons).

Me ya sa cace-cace a makare suke da muhimmanci
Gidan caca zai iya dakatar da hasashe gaba ɗaya ta hanyar ƙin karɓar caca da zarar an saki ƙwallo. Thorp ya gano cewa kusan babu wanda ke yin hakan: a Reno, Las Vegas, London, Monte Carlo, Nice, Venice da Puerto Rico, al'adar da aka saba ita ce a faɗi “babu sauran cacatsarin aikiAn rufe cacaKiran croupier (ko saƙon da ke kan allo) da ke rufe yin caca. Ba za a ƙara ajiyewa, motsawa ko ɗauke tsabobin caca ba.Karanta gaba ɗaya →” zagaye ɗaya ko biyu kafin ƙwallo ya faɗi. Wannan taga ita ce abin da kowane shirin hasashe tun daga lokacin ya buƙata, daga Eudaemons zuwa kiran makare na ƙungiyar Ritz a kan racetrackteburRacetrackZirin mai siffar ƙwai a kan teburan caca na kai tsaye da na lantarki da ke nuna lambobi bisa jerinsu a kan dabaran, ana amfani da shi don ajiye cacar maƙwabta da ta sashe da taɓawa ɗaya.Karanta gaba ɗaya →. Nevada ta haramta na'urorin hasashe a watan Mayu 1985, kuma a yau studiyo kai tsaye suna rufe caca a lokacin sakin ƙwallo.
Yadda gidajen caca suka mayar da martani
A shekarun da ake karɓar cace-cace bayan sakin ƙwallo, gidajen caca sun yaƙi ʼyan wasan da ake zargi ta hanyar croupier. Labarun ʼyan wasan tsarin Norman Leigh a Nice a 1966 da na ƙungiyoyin hasashe na baya sun bayyana sabon croupiermutaneCroupierMai gudanar da wasa a teburin roulette.Karanta gaba ɗaya → a kowane juyi, canza ƙwallo, juye-juye gajeru ko masu sauri, tebur cike da mutanen gidan caca kansa, kuma a ƙarshe rufe tebur. Waɗannan labarai sun fito ne daga ɓangaren ʼyan wasan kuma suna da wuyar tantancewa (Goldman, 2007). Duk da haka dabarun suna da ma'ana: juyi gajere ko mai sauri ba zai iya kai ƙwallo zuwa wani ramikayan aikiRamiƊaya daga cikin ɗakuna 37 masu lamba a kan rotor. Ana kuma kiransa: slot, cup.Karanta gaba ɗaya → na musamman ba, amma yana ɓata lokacin da mai hasashe ke aunawa.

Daidaiton da hasashe ke buƙata
Thorp (1984) ya lissafa ƙimar hasashe idan kuskurensa yana bin lanƙwan ƙararrawa: a juyi na yau da kullum ramin da aka yi hasashe yana kaucewa da ramuka σ ta wannan gefe ko wancan. Idan aka yi caca kan lambar da aka yi hasashe ita kaɗai, ko ita da maƙwabtacacaMaƙwabta (neighbors)Lamba da ramuka biyu a kowane gefensa a kan dabaran, tsabobin caca biyar na straight up.Karanta gaba ɗaya → biyu a kowane gefe, fifikon ya dogara ne ga σ kawai. Hasashe cikakke zai ci kowace straight up (cacar lamba ɗaya)cacaStraight upLamba ɗaya tak, biya 35:1.Karanta gaba ɗaya →. A σ = ramuka 10, daidaiton da Thorp da Shannon suka kai, straight up yana dawowa da kusan +44%, adadin da Thorp ya bayar ga na'urarsu; bayaninsa na 1998 ya sanya shi a kan kashi ɗaya bisa takwas na dabaran da aka fi fifitawa. Fifikon yana faɗuwa da sauri yayin da kuskure ke ƙaruwa, kuma yana ƙarewa a kusan ramuka 17 a kan dabaran Turai da 16 a kan na Amurka, lokacin da hasashe ke kaucewa da kusan rabin dabaran. Kasafin kuskuren Thorp na kansa yana nuna dalilin da ya sa wannan iyaka ke kusa: kurakurai daban-daban na ramuka 1.4 da 5.5 daga auna lokacin rotor da na ƙwallo, 7 daga faɗuwar ƙwallo a kan deflectorskayan aikiMai karkatarwa (deflector)Ɗaya daga cikin shingayen ƙarfe da ke kan apron waɗanda ke warwatsa ƙwallon da ke faɗuwa. Ana kuma kiransa: canoe, diamond, pin.Karanta gaba ɗaya → da 6 daga tsalle a cikin ramuka suna haɗuwa zuwa kusan 10.8.
Tambayoyi
A'a. Babu ƙwallo. Manhaja ce ke zaɓar lambar kafin motsin hoto.
Za a iya cin moriyarsu ta hanyar auna lokaci, shi ya sa babu wanda ake gudanarwa haka.
Nishaɗi da lissafi
Ku fara gwada waɗannan da kanku. Kowace mafita a naɗe take; ku buɗe ta idan kun shirya.
Cacar maƙwabtacacaMaƙwabta (neighbors)Lamba da ramuka biyu a kowane gefensa a kan dabaran, tsabobin caca biyar na straight up.Karanta gaba ɗaya → tana sa tsabar cacakuɗiTsabar cacaAlamar da ke wakiltar ƙayyadadden adadin kuɗi, wadda ake ajiyewa a kan teburin caca don yin caca. Ana kuma kiranta: check.Karanta gaba ɗaya → ɗaya a kan lamba da kuma a kan ramukakayan aikiRamiƊaya daga cikin ɗakuna 37 masu lamba a kan rotor. Ana kuma kiransa: slot, cup.Karanta gaba ɗaya → biyu a kowane gefensa a dabaran: tsabobin caca biyar. Sau nawa dole hasashe ya faɗa cikin waɗannan ramuka biyar don ya zama ba riba ba asara, kuma me yake samarwa idan ya yi daidai sau ɗaya cikin biyar?
Nuna mafita
Amsa Ba riba ba asara a 5 cikin 36, 13.9%, idan aka kwatanta da 13.5% ta hanyar sa'a kaɗai. Idan ya yi daidai sau ɗaya cikin biyar, yana mayar da 44% fiye da abin da aka sa.
Idan cacar ta ci, tsabar caca ɗaya tana cin 35 zuwa 1 kuma tana dawowa da ribarta, tsabobin caca 36, sauran huɗu kuma ana rasa su. Don haka nasara tana mayar da 36 a kan 5 da aka sa, kuma cacar ba riba ba asara ce idan ta ci sau 5 cikin 36, 13.9%. Ta hanyar sa'a tana cin sau 5 cikin 37, 13.5%. Wannan ƙaramar tazara, ƙasa da rabin kashi ɗaya, ita ce inda dukkan 2.70% ke fitowa.
A nasara ɗaya cikin biyar, 0.2 × 36 = tsabobin caca 7.2 suna dawowa a kan kowace 5 da aka sa, +44%. A ɗaya cikin huɗu, +80%.
Shi ya sa ƙaramin ƙarin daidaito yake da daraja sosai, kuma shi ya sa gidajen caca ke rufe cace-cacen bakiteburCacar baki (call bet)Cacar da ake faɗa wa croupier da baki maimakon a ajiye ta da hannu, galibi cacar sashen dabaran kamar voisins ko tiers. Ana kuma kiranta “cacar da aka faɗa”.Karanta gaba ɗaya → da wuri a manyan kuɗin caca: wannan ƙaramar tazara ita ce dukkan ribar gidan caca. An ruwaito cewa ʼyan wasan Ritz na 2004 sun yi caca ta wannan hanya.
Thorp ya lissafa kurakurai huɗu masu zaman kansu a cikin hasashensa, a ƙirgen ramuka: 1.4 daga auna lokacin rotorkayan aikiRotorƁangaren dabaran da ke juyawa wanda ke ɗauke da ramuka.Karanta gaba ɗaya →, 5.5 daga auna lokacin ƙwallokayan aikiƘwalloƘaramin ƙwallon da ake jefawa a hanyarsa a akasin juyawar rotor. Ƙwallayen zamani na ivorine ko Teflon ne, 18–21 mm.Karanta gaba ɗaya →, 7 daga faɗuwar ƙwallon a kan deflectorskayan aikiMai karkatarwa (deflector)Ɗaya daga cikin shingayen ƙarfe da ke kan apron waɗanda ke warwatsa ƙwallon da ke faɗuwa. Ana kuma kiransa: canoe, diamond, pin.Karanta gaba ɗaya → (masu karkatarwa), 6 kuma daga tsallen da ke cikin ramukan. Yaya girman jimillar, kuma nawa kurakuran auna lokaci biyu ke ƙarawa?
Nuna mafita
Amsa Kusan ramuka 10.8 gabaɗaya. Ba tare da kurakuran auna lokaci ba zai zama 9.2, don haka auna lokaci biyun suna ƙara 1.6 kawai.
Kurakurai masu zaman kansu ba sa haɗuwa kai tsaye; muraba'insu ne ke haɗuwa. Girman jimillar da aka saba shi ne tushen muraba'i na jimillar muraba'ai: 1.4² + 5.5² + 7² + 6² = 1.96 + 30.25 + 49 + 36 = 117.2, kuma √117.2 ≈ 10.8.
Ba tare da kurakuran auna lokaci biyu ba: √(49 + 36) = √85 ≈ 9.2.
Jimillar ramuka 10.8 tana cikin iyakar ramuka 17 a teburin da ke wannan shafi kuma tana da darajar kusan +34% a kan lamba ɗaya. Darasin da Thorp ya koya: da zarar faɗuwar a kan masu karkatarwa ta zama kuskure mafi girma, ingantaccen auna lokaci ba ya kawo abu mai yawa.
Ɗan barkwanci

Kimiyyar motsi tana aiki. Lokacin yin caca ya rufe.
Majiyoyi
- 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.