Kompyuta za Roulette
Engeri kompyuta gy'epimamu ekiseera ky'akapiira, abaasooka okuzizimba, n'obutuufu bwe zeetaaga okuba nabwo.

Kompyuta ya roulette epima ekiseera ky'akapiira ne rotor mu sikonda ezisooka ez'okwetooloola era n'eyogera ekitundu kya nnamuziga akapiira we kasaanidde okugwa. Edward Thorp ne Claude Shannon be baazimba esooka mu 1961, ate aba Eudaemons ne bazimba eza digito okuva mu 1976. Enkola eno yeetaaga zzaala okukkirizibwa ng'akapiira kamaze okusuulibwa: situdiyo ez'obutereevu kati ziggala zzaala ng'akapiira kasuulibwa, era Nevada ewera ebyuma ng'ebyo okuva mu 1985.
Engeri enkola ya kompyuta ya roulette esooka gye yazimbibwamu
Endowooza yajjira Edward Thorp mu biseera by'omusana ebya 1955, bwe yali omuyizi wa fizikisi ow'oku ddaala erya waggulu e UCLA: nnamuziga ekoleddwa obulungi ennyo ku buteeba na kusosola esaanidde okwetoolooza akapiiraebikozesebwaAkapiiraAkapiira akatono akakasukibwa mu lugudo nga kadduka mu ludda olukontana n'olwa rotor. Obupiira obw'omulembe bwa ivorine oba Teflon, mm 18–21.Soma byonna → mu ngeri esobola okulagulwa nga pulaneti. Yakwata vidiyo ya nnamuziga ey'ebbeeyi entono ey'obunene bw'ekitundu ng'essaawa epima ekiseera eri mu kifaananyi, n'azuula nti tekyalina nteekateeka ya kulagulwa, era olugendo lwe e Nevada mu Desemba 1958 lwamulaga nti nnamuziga za kaasino zaatambula bulungi. Blackjack olwo n'ebuutikira. Mu Novemba 1960, e MIT, yasaba Claude Shannon okuweereza ekiwandiiko kye ku kubala kaadi eri National Academy of Sciences; ku nkomerero y'olukiiko Shannon yamubuuza kiki ekirala ky'akolako, era pulojekiti ya roulette n'egenda mu kisenge kya wansi ekya Shannon. Baagula nnamuziga ey'omutindo gwa kaasino okuva e Reno ku $1,500, ne bagiteeka ku mmeeza enkadde eya biliyaadi ey'ejjinja, ne bapima ekiseera ky'akapiira nga bakozesa ekitangaala ekimyansa n'essaawa esomebwa okutuuka ku kitundu kimu eky'ekikumi ekya sikonda. Nga bamaze okwegezaamu, ensobi zaabwe mu kupima ekiseera zakka okuva ku nga 0.03 okutuuka ku sikonda 0.01. Mu Juuni 1961 kompyuta yalina transistor kkumi na bbiri era yali ya bunene bwa paketi ya sigala: swiiki mu ngatto, ekozesebwa n'ekigere ekinene, yapima ekiseera kya rotorebikozesebwaRotorEkitundu kya nnamuziga ekyetooloola ekirimu ebinnya.Soma byonna → n'eky'akapiira, era eddoboozi mu kutu kumu lyayogera ekimu ku bitundu bya nnamuzigannamuzigaEkitundu kya nnamuzigaEkitundu ky'ebinnya ebigoberegana ku nnamuziga, nga kyawukana ku kibinja ku mmeeza ya zzaala.Soma byonna → omunaana. E Las Vegas mu biseera eby'omusana ebyo Shannon yapima ekiseera ku nnamuziga era n'awandiika ennamba ng'omuzannyi yenna akozesa enkola, ate Thorp n'asiba zzaala za ssente entono ku nkomerero endala ey'emmeeza. Okulagula kwakola, naye waya ennyimpi ng'enviiri ezigenda ku kyuma eky'omu kutu zaakutukanga, era omulundi gumu omukazi eyali kumpi ne Thorp yatunuulira mu kutya sipiika eyali efuluma mu kutu kwe. Tebaasiba zzaala za maanyi n'akatono. Thorp yalangirira enkola ya kompyuta ya roulette mu 1966 era n'afulumya ebikwatako mu 1979 ne 1984.

Kompyuta za digito ezaasooka
Ekyuma kya Thorp ne Shannon kyali kya analog: olukusa lwakyo olw'amasannyalaze lwe lwali pulogulaamu yaakyo, era okukyusa enkola kyategeeza okuddamu okuyunga waya. Microprocessor yaggyawo ekkomo eryo. Alan Lewis, omuyizi e Caltech, yatwala kompyuta ya digito gye yazimba yekka mu nsawo ya kkamera e Circus Circus mu Las Vegas mu 1972, n'apima ekiseera kya nnamuziga ng'ali ku kayumba aka waggulu w'emmeeza era n'aweereza okulagula ku leediyo eri munne eyali wansi. Yakola, naye teyaleeta ssente; oluvannyuma yategeera nti yali yeerabidde okukyama kwa nnamuziga. Okuva mu 1976 ekibinja ky'abayizi ba fizikisi e Santa Cruz, aba Eudaemons, baakola omulimu guno mu bujjuvu. Baagula nnamuziga ya kaasino, ne bapima akapiira, rotor, okukyama n'okubuuka, era ne bawandiika ensengekera ezirina ensengeka ttaano omuzannyi ze yatereezanga ku buli nnamuziga ng'anyiga swiiki ez'ebigere okumala eddakiika nga abiri nga tannasiba zzaala. Kompyuta yaabwe yayogeranga ekimu ku bitundu omunaana nga sikonda ntono zimaze okuyita mu kwetooloola. Ku mmeeza eya nnamaddala mu Janwaliyo 1978 yawa enkizo gye baateeka ku 25%; ebyuma, ebyasibibwanga ku mubiri ate oluvannyuma ne bizimbibwa mu ngatto, byalemanga emirundi mingi nnyo okusinga fizikisi (laba “Aba Eudaemons”).

Lwaki zzaala ez'oluvannyuma zaali nkulu
Kaasino esobola okukomya ddala okulagula ng'egaana zzaala ng'akapiira kamaze okusuulibwa. Thorp yazuula nti kumpi tewali yakikolanga: e Reno, Las Vegas, London, Monte Carlo, Nice, Venice ne Puerto Rico empisa eya bulijjo yali kwogera nti “tewakyali zzaalaenkolaTewakyali zzaalaEkigambo kya croupier (oba obubaka ku ssirini) ekiggalawo okusiba zzaala. Cipu tezikyasobola kuteekebwa, kujjululwa oba kuggibwawo.Soma byonna →” ng'akapiira kasigazza okwetooloola okumu oba okubiri nga tekannagwa. Ekiseera ekyo kye buli nteekateeka y'okulagula okuva olwo ky'ebadde yeetaaga, okuva ku ba Eudaemons okutuuka ku zzaala ez'oluvannyuma ez'ekibinja kya Ritz ku racetrackemmeezaRacetrackOlukoloboze olwekulungirivu ku mmeeza za zzaala ez'obutereevu n'ez'ebyuma ebikozesa amasannyalaze, olulaga ennamba nga bwe ziddiriŋŋana ku nnamuziga, olukozesebwa okusiba zzaala ku binnya ebiriraanye n'ez'ebitundu bya nnamuziga nga onyiga omulundi gumu.Soma byonna →. Nevada yawera ebyuma ebiragula mu Maayi 1985, era situdiyo ez'obutereevu kati ziggala zzaala ng'akapiira kasuulibwa.
Engeri kaasino gye zeerwanako
Mu myaka zzaala we zaali zikyakkirizibwa ng'akapiira kamaze okusuulibwa, kaasino zaalwanyisanga abazannyi abateeberezebwa nga ziyita mu croupier. Ennyinnyonnyola z'abazannyi ba Norman Leigh abaakozesa enkola e Nice mu 1966 n'ez'ebibinja by'okulagula eby'oluvannyuma zoogera ku croupierabantuCroupierOmuddukanya w'emmeeza ya roulette.Soma byonna → omuggya buli kwetooloola, akapiira akakyusiddwa, okwetooloola okufunzibwa oba okw'amangu, emmeeza ejjudde abantu ba kaasino bennyini, era ku nkomerero emmeeza eggaddwa. Engero zino zivudde ku ludda lw'abazannyi era nzibu okukakasa (Goldman, 2007). Naye enkola ezo zirina amakulu: okwetooloola okumpi oba okw'amangu tekusobola kulunngamya kapiira eri kinnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna →, naye kutabula ekiseera ekyuma ekiragula kye kipima.

Obulungi okulagula bwe kulina okuba nabwo
Thorp (1984) yabala omugaso gw'okulagula ng'ensobi yaakwo egoberera ekipande eky'ekifaananyi ky'ekide: mu kwetooloola okwa bulijjo ekinnya ekiraguddwa kiba kyewunzise ebinnya σ ku ludda olumu oba olulala. Siba zzaala ku nnamba eraguddwa yokka, oba ku yo ne ebinnya ebiriraanyezzaalaEbinnya ebiriraanyeEnnamba emu n'ebinnya bibiri ku buli ludda lwayo ku nnamuziga, cipu ttaano eza straight up.Soma byonna → bibiri ku buli ludda, era enkizo esinziira ku σ yokka. Okulagula okutuukiridde kwandiwangudde buli straight upzzaalaStraight upEnnamba emu yokka, esasula 35:1.Soma byonna →. Ku σ = ebinnya 10, obutuufu Thorp ne Shannon bwe baatuukako, straight up ekomyawo nga +44%, omuwendo Thorp gw'awa ku kyuma kyabwe; ennyinnyonnyola ye eya 1998 egiteeka ku kitundu kimu ku munaana ekya nnamuziga ekisinga okusosolwa. Enkizo ekka mangu ng'ensobi yeeyongera era eggwaawo ku binnya nga 17 ku nnamuziga wa Bulaaya ne 16 ku wa Amerika, okulagula bwe kusubwa kumpi ekitundu kya nnamuziga. Embalirira y'ensobi eya Thorp yennyini eraga lwaki ekkomo eryo liri kumpi: ensobi ez'enjawulo eza binnya 1.4 ne 5.5 okuva mu kupima ekiseera kya rotor n'eky'akapiira, 7 okuva mu kugwa kw'akapiira nga kayita ku biziyiza akapiiraebikozesebwaEkiziyiza akapiiraKimu ku biziyiza eby'ekyuma ku apron ebisaasaanya akapiira nga kakka. Era biyitibwa: canoe, diamond, pin.Soma byonna → ne 6 okuva mu kubuuka mu binnya zigattika ne ziba nga 10.8.
Ebibuuzo
Nedda. Tewali kapiira. Ennamba erondebwa pulogulaamu nga ekifaananyi ekitambula tekinnatandika.
Zandiyinzizza okuwangulwa olw'okupima ekiseera, era eyo y'ensonga lwaki tewali n'emu ekolebwa bw'etyo.
Okwesanyusa n'Okubala
Gezaako bino ggwe kennyini okusooka. Buli kugonjoola kuzingiddwa; kuggulewo ng'oli mwetegefu.
Okulangirira kw'ebinnya ebiriraanyezzaalaEbinnya ebiriraanyeEnnamba emu n'ebinnya bibiri ku buli ludda lwayo ku nnamuziga, cipu ttaano eza straight up.Soma byonna → kuteeka cipussenteCipuAkabonero akakiikirira omuwendo ogutakyuka, akateekebwa ku mmeeza ya zzaala okusiba zzaala. Era kayitibwa: check.Soma byonna → emu ku nnamba ne ku binnyaebikozesebwaEkinnyaKimu ku bisenge 37 ebiriko ennamba ku rotor. Era biyitibwa: slot, cup.Soma byonna → bibiri ku buli ludda lwayo ku nnamuziga: cipu ttaano. Okulagula kulina okugwa mu binnya ebyo ebitaano emirundi emeka okwenkanankana, era kufuna ki bwe kuba okutuufu omulundi gumu ku etaano?
Laga okugonjoola
Eky'okuddamu Kwenkanankana ku 5 ku 36, 13.9%, so ng'olw'omukisa gwokka buli 13.5%. Bwe kuba okutuufu omulundi gumu ku etaano, kuzzaayo 44% okusinga kye kusiba.
Okulangirira bwe kujja, cipu emu ewangula 35 ku 1 era ekomawo n'amagoba gaayo, cipu 36, ate endala ennya zifiirwa. Kale okujja kuzzaayo 36 ku 5 ezisibiddwa, era okulangirira kwenkanankana bwe kujja emirundi 5 ku 36, 13.9%. Olw'omukisa kujja emirundi 5 ku 37, 13.5%. Enjawulo eyo entono, wansi w'ekitundu kya ppaasenti emu, y'evaamu 2.70% yonna.
Ku kujja kumu ku etaano, cipu 0.2 × 36 = 7.2 zikomawo ku buli 5 ezisibiddwa, +44%. Ku kumu ku ena, +80%.
Y'ensonga lwaki okulongooka okutono mu butuufu kugasa nnyo, era lwaki kaasino ziggalawo zzaala ez'okulangiriraemmeezaCall betZzaala gy'olangirira eri croupier mu kifo ky'okugiteeka n'omukono, emirundi mingi zzaala ku kitundu kya nnamuziga nga voisins oba tiers. Era eyitibwa “zzaala ey'okulangirira”.Soma byonna → mangu ku ssente za zzaala ennyingi: enjawulo eyo entono ge magoba gonna aga kaasino. Abazannyi ba Ritz aba 2004 kigambibwa nti baasiba mu ngeri eno.
Thorp yawandiika ensobi nnya ezeetongodde mu kulagula kwe, mu binnya: 1.4 okuva mu kupima ebiseera bya rotorebikozesebwaRotorEkitundu kya nnamuziga ekyetooloola ekirimu ebinnya.Soma byonna →, 5.5 okuva mu kupima ebiseera by'akapiiraebikozesebwaAkapiiraAkapiira akatono akakasukibwa mu lugudo nga kadduka mu ludda olukontana n'olwa rotor. Obupiira obw'omulembe bwa ivorine oba Teflon, mm 18–21.Soma byonna →, 7 okuva mu kugwa kw'akapiira nga kayita ku biziyiza akapiiraebikozesebwaEkiziyiza akapiiraKimu ku biziyiza eby'ekyuma ku apron ebisaasaanya akapiira nga kakka. Era biyitibwa: canoe, diamond, pin.Soma byonna → ne 6 okuva mu kubuuka mu binnya. Omugatte gwenkana wa, era ensobi ebbiri ez'okupima ebiseera zongerako kyenkana wa?
Laga okugonjoola
Eky'okuddamu Nga ebinnya 10.8 byonna awamu. Awatali nsobi za kupima biseera gwandibadde 9.2, kale okupima ebiseera okubiri kwongerako 1.6 zokka.
Ensobi ezeetongodde tezigattibwa butereevu; square zaazo ze zigattibwa. Obunene obwa bulijjo obw'omugatte ye square root y'omugatte gwa square: 1.4² + 5.5² + 7² + 6² = 1.96 + 30.25 + 49 + 36 = 117.2, ne √117.2 ≈ 10.8.
Awatali nsobi bbiri ez'okupima ebiseera: √(49 + 36) = √85 ≈ 9.2.
Omugatte gw'ebinnya 10.8 guli munda w'ekkomo ly'ebinnya 17 mu kipande ku lupapula luno era gugasa nga +34% ku nnamba emu. Ekyokuyiga Thorp kye yaggyamu: okugwa nga kayita ku biziyiza akapiira bwe kuba ensobi esinga obunene, okupima ebiseera obulungi okusingawo kugula kitono.
Eky'okusesa

Fizikisi ekola. Ekiseera ky'okusiba zzaala kyaggalwa.
Ensibuko
- 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, essuula 465.