Di Eudaemons
Fizyiks studɛnt dɛn, kasino wil we dɛn bay wit kesh, ɛn kɔmpyuta we smɔl te yu kin wɛr am go na di tebul.

Frɔm 1976 te to 1981, wan grup fɔ fizyiks studɛnt na Santa Cruz mek dijital kɔmpyuta dɛn we de tɛm di bɔl ɛn di rotɔ, ɛn we de nem wan sɛkta pan di wil we di bɛt stil opin. Dɛn tɛst dɛn bin sho advantej fɔ 44%, ɛn di fɔs lɔng sɛshɔn gi bɔt 25%. Di mashin dɛn bin de spɔyl ɔltɛm, nɔys frɔm ilɛktrik bit di wan we dɛn bil insay shu na 1981, ɛn dɛn win sɔm tawzin dɔla nɔmɔ.
Wan tin we kam na at na Las Vegas ba, 1975
Na di samatɛm fɔ 1975, Norman Packard, we bin na fizyiks studɛnt, spɛn tu mɔnt de kɔnt kad na blakjak na Las Vegas wit in padi Jack Biles, ɛn i jɔs nɔ win nɔ lɔs. We dɛn de drink di las drink, Biles se i go bɛt se pɔsin kin bit rulɛt wit fizyiks, ɛn Packard mɛmba wan lay na Edward Thorp in buk Beat the Dealer we de tɔk smɔl bɔt wan we fɔ bit rulɛt. Di tu dɛn lɛnt tep rɛkɔda, tinap nia wil dɛn na sɔm kasino ɛn nak di maykrofon ɛni tɛm we di bɔlikwipmɛntBɔlDi smɔl bɔl we dɛn trowe na di rod agens di rotɔ. Di nyu bɔl dɛn na ivorine ɔ Teflon, 18–21 mm.Rid ɔl → pas wan say we nɔ de muf. We dɛn drɔ am pan graf pepa, di nak dɛn sho se di bɔl de slo ɛn fɔdɔm wan stedi we. Packard in skul padi Doyne Farmer, we bin de du ay stɔdi na di University of California, Santa Cruz, se na tɛm wes, te i du di kɔnt insɛf: pɔsin we kin tɛm di bɔl to bɔt wan tɛnt pat fɔ wan sɛkɔn fɔ ebul, pan pepa, fɔ tɔk usay i go lan, nia sɔm nɔmba.
Wan wil na di fizyiks lab
Na di ɔntɛm fɔ 1976, Farmer ɛn Dan Browne pe $1,500 kesh fɔ wan kasino wil we dɛn dɔn fiks bak, na wan wokshɔp na Reno; dɛn se na fɔ fraternity pati. Fɔ mɔnt dɛn, dɛn kin tot am na nɛt go na di yunivasiti in lab ɛn mɛzhɔ am wit infrarɛd sɛnsa, ilɛktrik klɔk we dɛn mek dɛnsɛf, ɛn kamera we de snap we di bɔl nak mɛtal. Wetin dɛn fɛn stil na fayn shɔt lis fɔ wetin impɔtant na spin. Na di briz de slo di bɔl pas, pas di bɔl rod. Wil we nɔ lɛvul, ilɛk na wan tɛnt pat fɔ inch nɔmɔ, de chenj usay di bɔl de lɛf di rod, ɛn pan wil we tilt, di bɔl kin kɔmɔt na di ay say, ɛn dat de mek di prɛdikshɔn izi. Bɔl dɛn nɔ de di sem: wan Teflon bɔl slo tu tɛm fast pas wan we dɛn mek lɛk biliad bɔl. Ɛn we di bɔl dɔn lɛf di rod, i stil de jomp, pan avrej nɔ mɔ pas wan kwata to wan tɔd fɔ di rawnd. Na da jomp de na di kwɛstyɔn we di wan plan ol pan, ɛn i nɔ big te i pwɛl di prɛdikshɔn. Bay di ɛnd fɔ di samatɛm, dɛn se di advantej we fit de na 44%, di sem nɔmba we Thorp bin gi fɔ in yon mashin.

Di kɔmpini ɛn di pay
Dɛn kɔl di biznɛs Eudaemonic Enterprises, frɔm wan Grik wɔd fɔ di gladi we pɔsin kin gɛt we i de liv wit sɛns. Ɛnibɔdi we wok pan am fɔ gɛt pe frɔm di win mɔni we go kam, akɔdin to ɔmɔs awa i wok: wan pis pan wetin dɛn kɔl di Eudaemonic Pie. Di win mɔni fɔ pe fɔ wan kɔmyuniti fɔ padi dɛn we de du sayns di we aw dɛn want.
Kɔmpyuta ɔnda di an, 1976–1978
Di fɔs mashin gro frɔm wan kit kɔmpyuta we kam bay pos na Sɛptɛmba 1976 fɔ $250, we dɛn bil pan di 6502 prɔsɛsa we Apple in kɔmpyuta dɛn bak bin de yuz. Farmer, we nɔ bin ɛva program bifo, rayt di ikwɛshɔn dɛn fɔ di bɔl ɛn di rotɔikwipmɛntRotɔDi pat fɔ di wil we de tɔn ɛn we kɛr di pɔkit dɛn.Rid ɔl → insay am. Di wan fɔ kasino, dɛn tay am pan dɛn bɔdi, ɔnda di an ɔ, fɔ di uman dɛn, insay bra. Di pleya na di wil kin klik swich wit in big tɔ dɛn: wan tɔ mak di zirowilZiroDi wan grin pɔkit we nɔ ivin-mɔni, dɔzin ɔ kɔlɔm bɛt nɔ kɔba; na usay di kasino advantej kɔmɔt. Dɛn kin kɔl am bak: wan ziro, 0.Rid ɔl → ɛn dɔn di bɔl ɛni tɛm we dɛn pas wan say we nɔ de muf, di ɔda tɔ chenj di program frɔm wan sɛtin to ɔda wan. Fɔ fit di program to wan wil tek bɔt twɛnti minit fɔ klik saful saful. Dɔn, sɔm sɛkɔn afta ɛni spin bigin, di kɔmpyuta nem wan pan et sɛktawilSɛktaPɔkit dɛn we de fala wan ɔda na wan pat fɔ di wil, nɔto grup na di bɛt tebul.Rid ɔl → na di wil, ɔ i sho “nɔ bɛt”, bay we smɔl tin dɛn de vayb pan di skin. Wan sɛkɔn pleya we de fa dɔŋ di tebul, we konɛkt wit wan wik redio signal, fil di sem vayb ɛn i kɔba tri ɔ fɔ nɔmba na da sɛkta de; sɔntɛm i chenj wan nɔmba fɔ di wan we de nia am pan di wil so dat pipul nɔ go izi fɔ si di patɛn.
Di fɔs trip, to Lake Tahoe ɛn Reno na Disɛmba 1977, na wan lɔng tɛm we di mashin dɛn nɔ wok. Sɔm wik leta, na di Golden Gate na dawntawn Las Vegas, Farmer ple in wan fɔ fɔ awa ɛn af, tɛn sɛnt fɔ wan chipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl →. Di prɔfit smɔl, bɔt pan sɔm ɔndrɛd spin, in ɛn Browne se di advantej, wit kia, na 25%.

Di samatɛm fɔ 1978
Da samatɛm de, di grup ple wan afta di ɔda fɔ wik dɛn, dawntawn ɛn na di Strip, tu sɛshɔn ɛni de, ɛn dɛn nɔ ɛva go na di sem kasino tu nɛt wan afta di ɔda. Dɛn gɛt nɔtbuk fɔ ɛni kasino: di wil dɛn ɛn ɔmɔs dɛn nɔ lɛvul, di wokman dɛn, wetɛm dɛn de chenj shift. Las Vegas wil dɛn bin tilt fayn fɔ dɛn, ɛn di gem dɛn na lɛt nɛt bin slo, ɛn na dat di kɔmpyuta nid, bikɔs slo rotɔ ɛn fast bɔl de gi mɔ tɛm fɔ mɛzhɔ ɛn fɔ bɛt. Gud nɛt dɛn bin de. Na Circus Circus, we dɛn chenj di dilapipulDila (krupiyɛ)Di dila na di rulɛt tebul.Rid ɔl → tu o’klɔk na mɔnin, wan sɛshɔn we bin de lɔs tɔn to sɔm ɔndrɛd dɔla, 25 sɛnt fɔ wan chip. Ɛn prɔblɛm dɛn bin de kam stedi: waya we lus, redio konɛkshɔn we de chenj wit di wɛda, ilɛktrik shɔk frɔm di antɛna waya dɛn we dɛn sɔw insay dɛn shɛt. Wan nɛt di vayb tin dɛn jam, di waya dɛn ɔt tumɔs, ɛn Ingrid Hoermann kɔntinyu fɔ ple ilɛk i de bɔn am, pas fɔ lɛf wan tebul we i de win. Di kasino wokman dɛn notis di win bɔt dɛn nɔ ɛva notis aw dɛn du am; wan tɛm, wan dila we vɛks bikɔs di chip dɛn de bil ɔp, ol di wil we de tɔn ɛn twis am.
Pan tatin mɔnt, dɛn mek et trip to Nevada ɛn, we dɛn bin de bɛt mɔs tɛm tɛn sɛnt ɛn kwata, dɛn win sɔm tawzin dɔla. Wan sɛshɔn na di California Club na Disɛmba 1978 gi mɔ pas $1,000 pan tri awa ɛn i mek dɛn biliv se di we aw dɛn de du am fit fɔ gɛt bɛtɛ mashin.
Packard ɛn Biles de tɛm rulɛt bɔl wit tep rɛkɔda na Las Vegas.
Dɛn bay kasino wil na Reno; wan samatɛm fɔ mɛzhɔ; di fɔs kit kɔmpyuta.
Di fɔs kasino trip, Lake Tahoe ɛn Reno. Di mashin dɛn nɔ wok.
Golden Gate, Las Vegas: fɔ awa ɛn af wit tɛn sɛnt bɛt, advantej na 25%.
Wik dɛn fɔ ple na Las Vegas wit di kɔmpyuta pan di bɔdi.
California Club: mɔ pas $1,000 pan tri awa.
Dɛn bil di kɔmpyuta bak fɔ fit insay shu.
Las Vegas: ilɛktrik nɔys kɔba di redio konɛkshɔn. Di projɛkt stɔp.
Nevada mek mashin fɔ si bifo agens di lɔ. The Eudaemonic Pie kɔmɔt.
Di kɔmpyuta insay shu, 1980–1981
Fɔ pul di waya dɛn kɔmɔt pan dɛn bɔdi, dɛn disayd fɔ put ɔltin insay shu. Mark Truitt, wan nyu fizyiks gradyuet we bin dɔn waka kɔmɔt na wan intavyu fɔ wok pan sojaman rada, spɛn wan ia ɛn af pan am. Di aydia we mek am fit kam frɔm wan tɛknishian na di yunivasiti: ɔf di kɔmpyuta bitwin prɛdikshɔn, ɛn i go nid bɛtri smɔl pas bifo. Truitt put di chip dɛn pan tu sakit bɔd we i mek insɛf, i tɔn wan ɔp pan di ɔda wan ɛn fil di spes wit at wakis; dat mek wan blɔk bɔt tu inch bay fɔ, ɛn af inch tik, we pɔsin kin waka pan. Bɛtri, antɛna ɛn tu pan di tri vayb tin go insay di il. Tri vayb tin wit tri spid gi nayn signal: et sɛkta ɛn “nɔ bɛt”. Wan shumeka dig insay ɔdinari lɛda shu ɛn i nɔ aks ɛni kwɛstyɔn.
Na Novɛmba 1981, Farmer ɛn di rayta Thomas Bass kɛr di shu dɛn ɛn $2,500 go Las Vegas. Na di fɔs tebul, di fɔs prɛdikshɔn rayt, ɛn dɔn di vayb tin dɛn bigin fɔ vayb ɛni kayn we. Kasino dɛn ful wit ilɛktrik nɔys, frɔm sikyuriti kamera, niɔn bɔd ɛn slɔt mashin, ɛn i kɔba di wik redio konɛkshɔn bitwin di shu dɛn; wan tivi na di motɛl rum du di sem tin. Fɔ pipul fiks am fɔ dez, bɔt i nɔ wɛl, ɛn di projɛkt stɔp de. Di mashin dɛn go insay wan trɔnk na wan ɔnda-grɔn rum na Santa Cruz.

Wetin 44% min
Pan Amɛrikan wil, bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → de win wan tɛm pan 38 spin pan avrej ɛn i de pe 35 to 1, ɛn dat de kɔst di pleya 5.26%. Advantej fɔ 44% na di valyu fɔ di sem bɛt we i win wan tɛm pan 25 spin: 36 chip kam bak fɔ ɛni 25 we yu bɛt. So di kɔmpyuta nɔ bin nid fɔ no di nɔmba. I bin nid fɔ mek di nɔmba dɛn we i pik kam bɔt wan ɛn af tɛm mɔ pas wetin chans de alaw.
Wetin mek big advantej stil fil lɛk gambul
Advantej pan 35 to 1 de pe slo ɛn i nɔ de stedi. Wan pan di grup in advayza dɛn wɔn se pleya we de bɛt $100 pan wan nɔmba kin dɔn lɔs $10,000 ɔ $20,000 bifo di advantej sho, ɛn di kɔnt gri: wit advantej fɔ 44% pan wan wan nɔmba, pleya stil de biɛn afta 100 spin nia wan tɛm pan fɔ. Na dat mek di Eudaemon dɛn bigin wit tɛn sɛnt ɛn bil dɛn gambul mɔnimɔniGambul mɔniƆl di mɔni we yu dɔn put asay fɔ ple. Fɔ manej yu gambul mɔni min fɔ disayd ɔmɔs pan am yu go risk fɔ ɛni bɛt ɛn fɔ ɛni sɛshɔn.Rid ɔl → frɔm di win mɔni, ɛn na dat mek Alan Lewis, we jɔyn dɛn na 1978, spɛn in tɛm pan ɔmɔs fɔ bɛt. Leta Farmer tink se dɛn bin fred tumɔs. Smɔl bɛt kip dɛn sef, bɔt i bak min se ia dɛn fɔ wok gi dɛn smɔl mɔni nɔmɔ.
Wetin i kɔst ɛn wetin i pe
Bɔt $15,000 go pan pat dɛn, tul dɛn ɛn Truitt in pe, mɔs pan am frɔm Farmer ɛn frɔm Letty Belin, wan lɔya we leta mared am. Dɛn se Farmer wok 3,500 awa, Truitt 3,000 ɛn Packard 2,000. Agens dat, sɔm tawzin dɔla nɔmɔ dɛn win wit smɔl bɛt. Na 1983 Farmer put advatismɛnt na wan gambul magazin fɔ invɛsta dɛn, ɛn i tɔk bɔt wan prototayp we gɛt kasino advantej we dɛn dɔn pruv, 20 to 40%. Di tɛm we di Eudaemon dɛn bin de ple, Belin bin dɔn luk Nevada lɔ ɛn i nɔ fɛn natin we tɔk se pɔsin nɔ fɔ prɛdikt gem; na Me 1985 di stet mek am kraym fɔ yuz mashin fɔ dat. Wetin las na di sayns. Fɔ bil di kɔmpyuta dɛn tren Farmer, Packard ɛn dɛn padi dɛn fɔ stɔdi kayɔs, ɛn na de dɛn mek dɛn nem.
Fɔ rid di buk tide
Thomas Bass, we put di bɛt dɛn na di las trip, tɛl di stori na The Eudaemonic Pie (1985), we i bil pan lɔng intavyu wit di grup, ɛn na di sɔs fɔ dis pej. Di shɔt istri fɔ rulɛt we de insay nɔ sef lɛk aw i tɔk bɔt di projɛkt. I tɔk bak di stori bɔt di siks klak dɛn we Jagger ayad, we kɔmɔt na wan buk frɔm 1901 ɛn nɔ go bifo dat (luk Joseph Jagger), ɛn i put Thorp ɛn Shannon in kasino tɛst na 1962, usay Thorp in yon stori dɛn se na di samatɛm fɔ 1961.
Kwɛstyɔn dɛn
Nɔ. Dɛn win sɔm tawzin dɔla wit tɛn sɛnt ɛn kwata bɛt, ɛn dɛn spɛn bɔt $15,000 ɛn bɔku bɔku tawzin awa.
Di tɛm we dɛn bin de ple, Nevada nɔ bin gɛt lɔ agens fɔ prɛdikt gem wit mashin. I gɛt wan frɔm 1985, ɛn naw mɔs ples dɛn we gɛt kasino gɛt am.
Nɔ usay di bɛt de klos we dɛn trowe di bɔl, lɛk aw i de na layv studio dɛn, ɛn fɔ kɛr da kayn mashin go insay kasino na kraym na mɔs ples dɛn.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Di Eudaemons bin kɔnt se dɛn kɔmpyuta valyu 44% pan bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → pan Amɛrikan wil, usay di bɛt de pe 35 to 1. Ɔmɔs tɛm di nɔmba we dɛn pik fɔ win mek dat tru? Ɛn ɔmɔs pan di 38 pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → prɛdikshɔn fɔ pul kɔmɔt, if di bɔlikwipmɛntBɔlDi smɔl bɔl we dɛn trowe na di rod agens di rotɔ. Di nyu bɔl dɛn na ivorine ɔ Teflon, 18–21 mm.Rid ɔl → gɛt di sem chans fɔ fɔdɔm insay ɛni wan pan di wan dɛn we lɛf?
Sho di ansa
Ansa Wan tɛm insay 25 spin. Dat na di sem tin lɛk fɔ pul 13 pɔkit ɛn lɛf 25.
ChipmɔniChipTokɛn we min wan sɛt mɔni; yu put am na di bɛt tebul fɔ mek bɛt. Dɛn kin kɔl am bak: check.Rid ɔl → we win de kam bak wit 35 mɔ: 36 chip. If di nɔmba win wan tɛm insay n spin, n chip we yu bɛt de briŋ 36 bak, so di bɛt valyu 36/n − 1.
Mek dat bi 0.44: 36/n = 1.44, so n = 25. If prɛdikshɔn nɔ de, n na 38 ɛn di bɛt valyu 36/38 − 1 = −5.26%.
Naw pik se prɛdikshɔn pul k pɔkit ɛn di bɔl gɛt di sem chans fɔ fɔdɔm insay ɛni wan pan di ɔda 38 − k. Chip pan wan pan dɛn de win wan tɛm insay 38 − k spin. Fɔ 44% wi nid 38 − k = 25, so k = 13: smɔl mɔ pas wan tɔd pan di wil.
Insay di buk, dɛn se Farmer tɔk se 40% kɔmɔt frɔm we yu pul et pɔkit. Pan dis izi mɔdɛl et de gi 36/30 − 1 = 20%, so di rial pikchɔ fɔ bin nɔ ivin: sɔm pan di pɔkit dɛn we lɛf bin gɛt fa mɔ chans pas di ɔda wan dɛn.
pɔkit we dɛn pulpɔkit we lɛfbɛt pan wan nɔmba valyu038−5.26%2360%830+20%1325+44%1919+89%Pik se yu nɔmba rial rial de win wan tɛm insay 25 spin bay 35 to 1, advantej fɔ 44%. Yu de bɛt wan chip ɛni spin. Wetin na di chans se yu go de dɔŋ afta 100 spin? Afta 500?
Sho di ansa
Ansa Lɛk 23% afta 100 spin ɛn stil lɛk 6% afta 500.
Afta 100 spin yu dɔn bɛt 100 chip, ɛn ɛni win de briŋ 36 bak. Tu win de briŋ 72, lɔs fɔ 28; tri de briŋ 108, prɔfit fɔ 8. So yu de dɔŋ if yu win tu tɛm ɔ lɛs.
Di chans fɔ nɔ win atɔl insay 100 spin na (24/25)¹⁰⁰ = 1.7%. Wan win rayt rayt: 100 × (1/25) × (24/25)⁹⁹ = 7.0%. Tu rayt rayt: 4,950 × (1/25)² × (24/25)⁹⁸ = 14.5%. Togɛda 23.2%.
Afta 500 spin yu nid 14 win fɔ de ɔp (14 × 36 = 504), ɛn di avrej na 20. Di chans fɔ 13 ɔ lɛs na lɛk 6.2%.
Dis na di ɔda say fɔ bɛt we at fɔ win. Di advantej big, ɛn lɛk wan sɛshɔn fɔ 100 spin insay fɔ i nɔ de sho. Pleya we nɔ no fɔ shɔ se di advantej de nɔ go ebul fɔ si di difrɛns bitwin bad strik ɛn kɔmpyuta we pwɛl, ɛn na usay di Eudaemons bin de bɔku tɛm.
spinwin we yu nid fɔ de ɔpchans fɔ de dɔŋ50240.1%100323.2%200618.6%500146.2%Di buk se wit 44% advantej, $100 we yu bɛt 50 tɛm pan awa fɔ gi $2,200 pan awa. Chɛk am. Dɔn kɔnt wetin di sem advantej bin gi bay di bɛt we di grup bin rial rial de ple: wan daym ɛni spin.
Sho di ansa
Ansa $2,200 rayt fɔ $100 ɛni spin. Bay wan daym ɛni spin na $2.20 pan awa.
Advantej na pat pan ɔl di mɔni we yu bɛt. Bay $100 ɛni spin ɛn 50 spin pan awa, yu de bɛt $5,000, ɛn 44% pan dat na $2,200.
Bay 10 sɛnt ɛni spin, yu de bɛt $5 insay wan awa, ɛn 44% pan $5 na $2.20. Ilɛk dɛn kɔba fɔ nɔmba wit wan daym ɛni wan, na $8.80 pan awa fɔ tu pɔsin.
Di grup bin de ple smɔl bikɔs dɛn bin de bil gambul mɔnimɔniGambul mɔniƆl di mɔni we yu dɔn put asay fɔ ple. Fɔ manej yu gambul mɔni min fɔ disayd ɔmɔs pan am yu go risk fɔ ɛni bɛt ɛn fɔ ɛni sɛshɔn.Rid ɔl → frɔm natin ɛn bikɔs, lɛk aw di pazul ɔp sho, 44% advantej bay 35 to 1 kin lɔs fɔ awa ɛn awa. Di prays fɔ da kia na se di mɛtɔd kin de wok fayn fayn ɛn stil pe lɛs pas wok.
Smɔl jok fɔ ɛz di maynd

Di fizyiks wok. Di niɔn win.
Usay wi gɛt am frɔm
- 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.