Ama-Eudaemons
Abafundi be-physics, isondo lekhasino elathengwa ngemali esandleni, kanye nekhompyutha encane ngokwanele ukuthi igqokwe uye nayo etafuleni.
Kusukela ngo-1976 kuya ku-1981 iqembu labafundi be-physics e-Santa Cruz lakha amakhompyutha edijithali ayebala isikhathi sebhola nesondo elijikelezayo futhi asho isigaba sesondo ngenkathi ukubheja kusavulekile. Ukuhlola kwabo kwathembisa inzuzo yomdlali engu-44% kanti iseshini yokuqala ende yanikeza cishe u-25%. Imishini yayilokhu yehluleka, inguqulo eyayakhiwe ngaphakathi esicathulweni yehlulwa umsindo kagesi ngo-1981, futhi bawina izinkulungwane ezimbalwa zamadola.
Umqondo endaweni yokuphuza e-Las Vegas, 1975
Ehlobo lika-1975 u-Norman Packard, umfundi we-physics, wachitha izinyanga ezimbili ebala amakhadi ku-blackjack e-Las Vegas nomngane wakhe, u-Jack Biles, futhi bacishe nje balingana. Ngesiphuzo sokugcina u-Biles wathi angabheja ukuthi i-roulette ingehlulwa nge-physics, futhi u-Packard wakhumbula umugqa oyimfihlakalo encwadini ka-Edward Thorp ethi Beat the Dealer mayelana nendlela ye-roulette. Laba bobabili baboleka isiqophi somsindo, bema eceleni kwamasondo emakhasino amaningana futhi bathepha imakrofoni njalo uma ibholaokokusebenzaIbholaIbhola elincane eliphonswa emzileni libheke ngakolunye uhlangothi lwe-rotor. Amabhola esimanje enziwa nge-ivorine noma nge-Teflon, angu-18–21 mm.Funda konke → lidlula endaweni engashintshi. Lapho kudwetshwe ephepheni lamagrafu, ukuthepha kwakhombisa ibhola lihamba kancane futhi liwa ngendlela ehlelekile. Umngane ka-Packard wesikole, u-Doyne Farmer, umfundi weziqu eziphakeme e-University of California, Santa Cruz, wathi kuwukuchitha isikhathi kwaze kwaba yilapho ezenzela izibalo yena: umuntu okwazi ukubala isikhathi sebhola cishe kuze kufike engxenyeni eyodwa kweziyishumi yomzuzwana kufanele, ephepheni, akwazi ukusho ukuthi lizowela kuphi phakathi kwezinombolo ezimbalwa.
Isondo elabhorethri ye-physics
Entwasahlobo ka-1976 u-Farmer no-Dan Browne bakhokha u-$1,500 ngemali esandleni ngesondo lekhasino elalungisiwe endaweni yokusebenzela e-Reno, bethi lingelomcimbi wenhlangano yabafundi. Izinyanga eziningi babelithwala ebusuku beliyisa elabhorethri yokufundisa yasenyuvesi futhi balilinganisa ngezinzwa ze-infrared, iwashi likagesi abazakhela lona kanye nekhamera eyayiqaliswa ngumsindo webhola lishaya insimbi. Lokho abakuthola kusewuhlu olufushane oluhle lwezinto ezibalulekile ekujikelezeni. Umoya yiwona owenza ukuthi ibhola lihambe kancane kakhulu, ngaphezu komzila. Isondo elingalingani kahle ngisho nangengxenye eyodwa kweziyishumi ye-intshi lishintsha indawo lapho ibhola lishiya khona umzila, futhi esondweni elitshekile ibhola livame ukuphuma ohlangothini oluphakeme, okwenza ukubikezela kube lula. Amabhola ayahlukahluka: ibhola le-Teflon lalihamba kancane ngokushesha okuphindwe kabili kunelenziwe ngenhlanganisela yebhola le-billiard. Futhi uma ibhola selishiye umzila lisaqhubeka ligxuma, ngokwesilinganiso lingadluli ingxenye eyodwa kwezine kuya kweyodwa kwezintathu yokuzungeza. Lokho kugxuma kwakuwumbuzo wonke umqondo owawuncike kuwo, futhi kwakungabanzi ngokwanele ukuthi kucime ukubikezela. Ekupheleni kwehlobo babeka inzuzo yomdlali engaba khona ku-44%, inombolo eyayinikezwe ngu-Thorp ngedivayisi yakhe.
Inkampani nophaya
Lo msebenzi bawubiza ngokuthi yi-Eudaemonic Enterprises, kusukela egameni lesiGreki elisho injabulo yempilo ephilwa ngokuhlakanipha. Wonke umuntu owayesebenza kuwo kwakumele akhokhelwe ngemali eyayizowinwa esikhathini esizayo ngokulingana namahora ayewafakile: ucezu lwalokho ababekubiza ngokuthi yi-Eudaemonic Pie. Imali ewinile yayihloselwe ukukhokhela umphakathi wabangane abenza isayensi ngemigomo yabo.
Ikhompyutha ngaphansi kwekhwapha, 1976–1978
Umshini wokuqala wasuka kukhompyutha eyayihlanganiswa ngokwakho eyafika ngeposi ngoSeptemba 1976 ngo-$250, eyakhiwe ngephrosesa ye-6502 nayo eyayisetshenziswa ngamakhompyutha e-Apple. U-Farmer, owayengakaze ahlele ikhompyutha ngaphambili, wafaka kuyo izibalo zebhola ne-rotorokokusebenzaI-rotorIngxenye yesondo ejikelezayo ephethe amagodi.Funda konke →. Inguqulo yasekhasino yayigqokwa iboshelwe emzimbeni, ngaphansi kwekhwapha noma, kwabesifazane, ebhodisini. Umdlali osesondweni wayecindezela izinkinobho ngezinzwane ezinkulu: uzwane olulodwa lwalumaka iqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → bese lumaka ibhola njalo uma lidlula endaweni engashintshi, olunye lwaludlulisa uhlelo phakathi kwezilungiselelo zalo. Ukulungisa uhlelo ukuze lufanele isondo elithile kwakuthatha cishe imizuzu engamashumi amabili yokucindezela ngokuthula. Bese, imizuzwana embalwa ekujikelezeni ngakunye, ikhompyutha yayisho esinye sezigabaisondoIsigabaIngxenye eqhubekayo yamagodi alandelanayo esondweni, ehlukile eqenjini lezinombolo ethebuleni lokubheja.Funda konke → eziyisishiyagalombili zesondo, noma ikhombise ukuthi “ungabheji”, ngokudlidliza izinto ezincane eziqhuqhuzayo esikhumbeni. Umdlali wesibili owayemi kude kancane ngakolunye uhlangothi lwetafula, oxhunywe ngesignali yomsakazo ebuthakathaka, wayezwa ukudlidliza okufanayo futhi embozela izinombolo ezintathu noma ezine zaleso sigaba, ngezinye izikhathi efaka inombolo engumakhelwane wayo esondweni ukuze iphethini kube nzima ukuyifunda.
Uhambo lokuqala, oluya e-Lake Tahoe nase-Reno ngoDisemba 1977, lwaluwukwehluleka kwemishini okude okukodwa. Emasontweni ambalwa kamuva, e-Golden Gate emaphakathi nedolobha lase-Las Vegas, u-Farmer wadlala yedwa amahora amane nengxenye ngamasenti ayishumi ithokheniimaliIthokheniUphawu olumele inani elinqunyiwe, olubekwa ethebuleni lokubheja ukuze ubheje. Kubuye kuthiwe: check.Funda konke → ngalinye. Inzuzo yayincane, kodwa ekujikelezeni okungamakhulu amaningana yena no-Browne babeka inzuzo yomdlali, ngokuqaphela, ku-25%.
Ihlobo lika-1978
Ngalelo hlobo iqembu ladlala ngokushintshana amasonto amaningi, emaphakathi nedolobha nase-Strip, amaseshini amabili ngosuku futhi lingaphindi ikhasino efanayo ngobusuku obulandelanayo. Babegcina ibhuku lokubhala ngekhasino ngalinye: amasondo alo nokuthi ayetshekile kangakanani, abasebenzi balo, ukushintshana kwabasebenzi. Amasondo ase-Las Vegas atholakala etshekile ngendlela eyabasiza, futhi imidlalo yasebusuku kakhulu ihamba kancane, yilokho ikhompyutha eyakudingayo, ngoba i-rotor ehamba kancane nebhola elisheshayo kushiya isikhathi esengeziwe sokulinganisa nokubheja. Kwaba khona ubusuku obuhle. E-Circus Circus ukushintshwa kwe-croupierabantuI-croupierUmsebenzi ophethe itafula le-roulette.Funda konke → ngehora lesibili ekuseni kwaguqula iseshini ehlulwayo yaba ngamakhulu amaningana amadola ngamasenti angu-25 ithokheni ngalinye. Futhi kwakukhona uchungechunge oluqhubekayo lokwehluleka: izintambo ezixegayo, ukuxhumana ngomsakazo okwakushintsha ngokwezinga lokushisa, ukushaqeka ngugesi ezintanjeni ze-antenna ezazithungelwe emahembeni abo. Ngobunye ubusuku izinto eziqhuqhuzayo zabambeka, izintambo zashisa ngokweqile, futhi u-Ingrid Hoermann waqhubeka edlala naphezu kokusha kunokuba ashiye itafula ayewina kulo. Abasebenzi bekhasino babona ukuwina kodwa abazange bayibone indlela; kwake kwathi i-croupier, ecasulwe yinqwaba yamathokheni eyayikhula, yabamba isondo elalijikeleza yalisonta ngamandla.
Ezinyangeni eziyishumi nantathu benza uhambo oluyisishiyagalombili oluya e-Nevada futhi, bebheja ikakhulukazi amasenti ayishumi namakota, bawina izinkulungwane ezimbalwa zamadola. Iseshini e-California Club ngoDisemba 1978 yaletha okungaphezu kuka-$1,000 emahoreni amathathu futhi yabaqinisekisa ukuthi le ndlela ifanelwe yimishini engcono.
U-Packard no-Biles babala isikhathi samabhola e-roulette ngesiqophi somsindo e-Las Vegas.
Isondo lekhasino elathengwa e-Reno; ihlobo lokulinganisa; ikhompyutha yokuqala yokuhlanganisa.
Uhambo lokuqala lwasekhasino, e-Lake Tahoe nase-Reno. Imishini iyehluleka.
I-Golden Gate, e-Las Vegas: amahora amane nengxenye ngamanani amasenti ayishumi, inzuzo yomdlali ibekwa ku-25%.
Amasonto okudlala e-Las Vegas nekhompyutha igqokwe emzimbeni.
I-California Club: okungaphezu kuka-$1,000 emahoreni amathathu.
Ikhompyutha yakhiwa kabusha ukuze ingene ngaphakathi esicathulweni.
E-Las Vegas: umsindo kagesi ugubuzela ukuxhumana ngomsakazo. Iphrojekthi iyama.
I-Nevada yenza amadivayisi okubikezela angabi semthethweni. Kushicilelwa incwadi ethi The Eudaemonic Pie.
Ikhompyutha esicathulweni, 1980–1981
Ukuze basuse izintambo emizimbeni yabo banquma ukufaka konke ezicathulweni. U-Mark Truitt, owayesanda kuthola iziqu ze-physics futhi owayephume engxoxweni yomsebenzi we-radar yezempi, wachitha unyaka nengxenye kulokhu. Umqondo owenza ukuthi kungene wavela kuchwepheshe wasenyuvesi: cisha ikhompyutha phakathi kokubikezela, futhi idinga amabhethri ambalwa kakhulu. U-Truitt wafaka ama-chip emabhodini amabili esekethe azizenzela wona, wabeka elinye phezu kwelinye wagcwalisa isikhala ngengcina eqinile, okwenza ibhulokhi elingaba ngama-intshi amabili ngamane nobukhulu obuyingxenye ye-intshi, elingahanjwa phezu kwalo. Amabhethri, i-antenna kanye nezimbili kwezintathu izinto ezidlidlizayo kwafakwa esithendeni. Izinto ezintathu ezidlidlizayo ngamazinga amathathu ejubane zanikeza izimpawu eziyisishiyagalolunye: izigaba eziyisishiyagalombili kanye no-“ungabheji”. Umlungisi wezicathulo wagubha izicathulo ezijwayelekile zesikhumba futhi akazange abuze lutho.
NgoNovemba 1981 u-Farmer nombhali u-Thomas Bass bathatha izicathulo kanye no-$2,500 baya e-Las Vegas. Etafuleni lokuqala ukubikezela kokuqala kwaphumelela, kwase kuthi izinto ezidlidlizayo zaqala ukudlidliza ngokungahleliwe. Amakhasino agcwele umsindo kagesi, ovela kumakhamera okuqapha, ezimpawini ze-neon nasemishinini ye-slot, futhi wagubuzela ukuxhumana okubuthakathaka ngomsakazo phakathi kwezicathulo; umabonakude ekamelweni le-motel wenza into efanayo. Izinsuku zokulungisa ngabantu abane azikwazanga ukukulungisa, futhi iphrojekthi yama lapho. Imishini yafakwa esiphathweni egumbini elingaphansi komhlaba e-Santa Cruz.
Okushiwo u-44%
Esondweni laseMelika i-straight upukubhejaI-straight upInombolo eyodwa, kukhokha u-35:1.Funda konke → iwina kanye ekujikelezeni okungu-38 ngokwesilinganiso futhi ikhokha u-35 ku-1, okubiza umdlali u-5.26%. Inzuzo yomdlali engu-44% yinani lokho kubheja okufanayo uma kuwina kanye ekujikelezeni okungu-25: amathokheni angu-36 ayabuya kuwo wonke amathokheni angu-25 abhejiwe. Ngakho ikhompyutha yayingadingi ukwazi inombolo. Kwakumele yenze izinombolo eyazikhethayo ziphume kaningi cishe ngokuphindwe kanye nengxenye kunalokho okuvunyelwa yithuba.
Kungani inzuzo enkulu yayisazwakala njengokugembula
Inzuzo ku-35 ku-1 ikhokha kancane futhi ngokungalingani. Omunye wabeluleki beqembu waxwayisa ukuthi umdlali obheja u-$100 enombolweni ngayinye angalahlekelwa u-$10,000 noma u-$20,000 ngaphambi kokuba inzuzo ibonakale, futhi izibalo ziyavumelana: ngenzuzo yomdlali engu-44% ezinombolweni ezizodwa, umdlali usengemuva ngemuva kokujikeleza okungu-100 cishe kanye kwezine. Yingakho ama-Eudaemons aqala ngamasenti ayishumi futhi akha imali yawo yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke → ngemali ewinile, futhi yingakho u-Alan Lewis, owajoyina ngo-1978, wachitha isikhathi sakhe ecabanga ukuthi kufanele kubhejwe malini. Kamuva u-Farmer wacabanga ukuthi babeqaphe ngokweqile. Amanani amancane abagcina bephephile, kodwa futhi asho ukuthi iminyaka yomsebenzi yaletha okuncane kakhulu.
Lokho okwakubiza nalokho okwakukhokha
Cishe u-$15,000 wasetshenziswa ezingxenyeni, emathuluzini nasemiholweni ka-Truitt, iningi layo livela ku-Farmer naku-Letty Belin, ummeli owashada naye kamuva. U-Farmer wabalelwa amahora angu-3,500 omsebenzi, u-Truitt angu-3,000 kanti u-Packard angu-2,000. Ngakolunye uhlangothi kukhona izinkulungwane ezimbalwa zamadola ezawinwa ngamanani amancane. Ngo-1983 u-Farmer wakhangisa kumagazini wokugembula efuna abatshalizimali, echaza i-prototype enenzuzo yomdlali efakazelwe ekhasino engu-20 kuya ku-40%. Ngenkathi ama-Eudaemons edlala, ukusesha kuka-Belin emthethweni wase-Nevada akuzange kuthole lutho olwenqabela ukubikezela umdlalo; ngoMeyi 1985 lesi sifundazwe senza ukusebenzisa idivayisi ngaleyo njongo kube yicala. Okwahlala kwakuyisayensi. Ukwakha amakhompyutha kwaqeqesha u-Farmer, u-Packard nabangane babo ukuze bafunde i-chaos, lapho baduma khona.
Ukufunda incwadi namuhla
U-Thomas Bass, owabheja ohambweni lokugcina, waxoxa le ndaba encwadini ethi The Eudaemonic Pie (1985), eyakhiwe ezingxoxweni ezinde neqembu, futhi iwumthombo waleli khasi. Umlando wayo omfushane we-roulette awuthembeki kangako njengendaba yayo yephrojekthi. Iphinda indaba yabamabhalane abayisithupha abaqashwa ngu-Jagger, esuka encwadini yango-1901 ingadluli lapho (bheka i-“Joseph Jagger: Isu le-roulette e-Monte Carlo”), futhi ibeka ukuhlolwa kuka-Thorp no-Shannon ekhasino ngo-1962, kanti izindaba zika-Thorp uqobo zithi kwakungehlobo lika-1961.
Imibuzo
Cha. Awina izinkulungwane ezimbalwa zamadola ngamanani amasenti ayishumi namakota, futhi asebenzisa cishe u-$15,000 kanye nezinkulungwane eziningi zamahora.
Ngenkathi bedlala, i-Nevada yayingenawo umthetho owenqabela ukubikezela umdlalo ngedivayisi. Isinawo kusukela ngo-1985, futhi iningi lezindawo ezinamakhasino manje linawo.
Cha lapho ukubheja kuvalwa khona ngenkathi ibhola lijikijelwa, njengoba kwenzeka ezitudiyo ezibukhoma, futhi ukuphatha idivayisi enjalo ungene nayo ekhasino kuyicala ezindaweni eziningi zomthetho.
Ubumnandi bezibalo
Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.
Ama-Eudaemons ayebona ukuthi ikhompyutha yawo yayinikeza u-44% ku-straight upukubhejaI-straight upInombolo eyodwa, kukhokha u-35:1.Funda konke → esondweni laseMelika, lapho lokho kubheja kukhokha 35 ku-1. Inombolo ekhethiwe kumele iwine kangaki ukuze lokho kube yiqiniso? Futhi ukubikezela bekuzodingeka kukhiphe angaki kumagodiokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → angu-38, uma ibholaokokusebenzaIbholaIbhola elincane eliphonswa emzileni libheke ngakolunye uhlangothi lwe-rotor. Amabhola esimanje enziwa nge-ivorine noma nge-Teflon, angu-18–21 mm.Funda konke → belinamathuba alinganayo okuwela kunoma yiliphi kulawo asele?
Bonisa isixazululo
Impendulo Kanye ekujikelezeni okungu-25. Lokho kufana nokukhipha amagodi angu-13 kushiywe angu-25.
IthokheniimaliIthokheniUphawu olumele inani elinqunyiwe, olubekwa ethebuleni lokubheja ukuze ubheje. Kubuye kuthiwe: check.Funda konke → ewinayo ibuya namanye angu-35: amathokheni angu-36. Uma inombolo iwina kanye ekujikelezeni okungu-n, amathokheni angu-n abhejiwe abuyisa angu-36, ngakho ukubheja kunenani lika-36/n − 1.
Kwenze kube ngu-0.44: 36/n = 1.44, ngakho n = 25. Ngaphandle kokubikezela u-n ungu-38 futhi ukubheja kunenani lika-36/38 − 1 = −5.26%.
Manje cabanga ukuthi ukubikezela kukhipha amagodi angu-k futhi ibhola linamathuba alinganayo okuwela kulelo nalelo kwangu-38 − k asele. Ithokheni kwelinye lawo iwina kanye ekujikelezeni okungu-38 − k. Ukuze kube ngu-44% sidinga u-38 − k = 25, ngakho k = 13: ngaphezudlwana kwengxenye yesithathu yesondo.
Encwadini u-Farmer ucashunwa ethi u-40% uvela ekukhipheni amagodi ayisishiyagalombili. Kule modeli elula amagodi ayisishiyagalombili anikeza u-36/30 − 1 = 20%, ngakho isimo sangempela kumele ukuthi sasingalingani: amanye amagodi asele ayenamathuba amakhulu kakhulu kunamanye.
amagodi akhishiweamagodi aseleinani le-straight up038−5.26%2360%830+20%1325+44%1919+89%Cabanga ukuthi inombolo yakho iwina ngempela kanye ekujikelezeni okungu-25 ngo-35 ku-1, inzuzo yomdlali engu-44%. Ubheja ithokheni eyodwa ekujikelezeni ngakunye. Ayini amathuba okuthi ube semuva ngemuva kokujikeleza okungu-100? Ngemuva kokungu-500?
Bonisa isixazululo
Impendulo Cishe u-23% ngemuva kokujikeleza okungu-100 futhi kusengu-6% ngemuva kokungu-500.
Ngemuva kokujikeleza okungu-100 usubheje amathokheni angu-100, futhi ukuwina ngakunye kubuyisa angu-36. Ukuwina okubili kubuyisa angu-72, ukulahlekelwa okungu-28; okuthathu kubuyisa angu-108, inzuzo engu-8. Ngakho usemuva uma uwina kabili noma ngaphansi.
Amathuba okungawini nakanye ekujikelezeni okungu-100 angu-(24/25)¹⁰⁰ = 1.7%. Ukuwina okukodwa ncamashi: 100 × (1/25) × (24/25)⁹⁹ = 7.0%. Okubili ncamashi: 4,950 × (1/25)² × (24/25)⁹⁸ = 14.5%. Konke ndawonye 23.2%.
Ngemuva kokujikeleza okungu-500 udinga ukuwina okungu-14 ukuze ube phambili (14 × 36 = 504), kanti isilinganiso singu-20. Amathuba okuwina okungu-13 noma ngaphansi acishe abe ngu-6.2%.
Lolu wuhlangothi olunye lokubheja okunamathuba amancane. Inzuzo inkulu, futhi cishe ochungechungeni olulodwa kwezine lokujikeleza okungu-100 ayibonakali. Umdlali ongazi ngokuqinisekile ukuthi inzuzo ikhona akakwazi ukuhlukanisa inhlanhla embi nekhompyutha ephukile, futhi yileso simo ama-Eudaemons ayevame ukuba kuso.
ukujikelezaukuwina okudingekayo ukuze ube phambiliamathuba okuba semuva50240.1%100323.2%200618.6%500146.2%Incwadi ithi ngenzuzo engu-44%, u-$100 obhejwa izikhathi ezingu-50 ngehora kufanele ulethe u-$2,200 ngehora. Kuhlole. Bese ubala ukuthi inzuzo efanayo yayiletha malini ngamanani iqembu elalibheja ngawo ngempela: i-dime (amasenti ayishumi) ekujikelezeni ngakunye.
Bonisa isixazululo
Impendulo U-$2,200 ulungile ku-$100 ekujikelezeni ngakunye. Nge-dime ekujikelezeni ngakunye kungu-$2.20 ngehora.
Inzuzo iyingxenye yakho konke okubhejwayo. Ngo-$100 ekujikelezeni ngakunye nokujikeleza okungu-50 ngehora, kubhejwa u-$5,000, futhi u-44% walokho ungu-$2,200.
Ngamasenti angu-10 ekujikelezeni ngakunye, kubhejwa u-$5 ngehora, futhi u-44% ka-$5 ungu-$2.20. Ngisho kumbozwa izinombolo ezine nge-dime ngayinye, kungu-$8.80 ngehora kubantu ababili.
Iqembu lalibheja kancane ngoba lalakha imali yokubhejaimaliImali yokubhejaInani lonke lemali ebekelwe ukudlala. Ukuphatha imali yokubheja kusho ukunquma ukuthi ingakanani yayo ozoyibeka engcupheni ekubhejeni ngakunye nasesheshini ngayinye.Funda konke → lingenalutho, futhi ngoba, njengoba iphazili engenhla ibonisa, inzuzo engu-44% ngo-35 ku-1 ingahlulwa amahora amaningi. Intengo yalokho kuqapha kwakuwukuthi indlela yayingasebenza kahle ngokuphelele kodwa ikhokhe kancane kunomsebenzi.
Okokuhlekisa
I-physics yasebenza. I-neon yawina.
Imithombo
- Bass, T. A. The Eudaemonic Pie.
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. “The invention of the first wearable computer.”
- Nevada Revised Statutes, chapter 465.