The Eudaemons
Physics ke students, cash mein khareeda gaya ek casino wheel, aur itna chhota computer ki table par pehen kar le jaaya ja sake.
1976 se 1981 tak Santa Cruz mein physics students ke ek group ne digital computers banaye jo ball aur rotor ka time naapte the aur bets khule rehte hue hi wheel ka ek sector bata dete the. Unke tests ne 44% advantage ka vaada kiya aur pehle lambe session mein lagbhag 25% mila. Hardware baar-baar fail hota raha, joote mein bana version 1981 mein electrical noise se haar gaya, aur unhone kuch hazaar dollar jeete.
Las Vegas ke ek bar mein ek andaza, 1975
1975 ki garmiyon mein physics student Norman Packard ne apne dost Jack Biles ke saath Las Vegas mein do mahine blackjack par cards count kiye aur mushkil se break even kiya. Aakhri drink par Biles ne kaha ki woh shart laga sakta hai ki roulette ko physics se haraya ja sakta hai, aur Packard ko Edward Thorp ki Beat the Dealer ki ek rahasyamay line yaad aayi jo roulette ke ek method ke baare mein thi. Dono ne ek tape recorder udhaar liya, kai casinos mein wheels ke paas khade hue aur har baar 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 → ke ek fixed point se guzarne par microphone thapthapaya. Graph paper par plot karne par thapon ne dikhaya ki ball ek niyamit tareeke se dheemi hoti aur girti hai. Packard ke school ke dost Doyne Farmer, jo University of California, Santa Cruz mein graduate student the, ne ise samay ki barbaadi kaha, jab tak unhone khud hisaab nahi lagaya: jo insaan ball ka time ek second ke dasve hisse tak naap sake, use kaagaz par yeh bata paana chahiye ki woh kuch numbers ke andar kahan giregi.
Physics laboratory mein ek wheel
1976 ke spring mein Farmer aur Dan Browne ne Reno ki ek workshop mein ek reconditioned casino wheel ke liye $1,500 cash diye, yeh kehkar ki yeh ek fraternity party ke liye hai. Mahinon tak woh ise raat mein university ki teaching laboratory le jaate aur infrared sensors, ghar ki bani electronic ghadi aur metal par ball ke takrane ki awaaz se chalne wale camera se naapte. Unhone jo paaya woh aaj bhi ek achhi chhoti list hai ki spin mein kya maayne rakhta hai. Zyada-tar dheema hawa karti hai, track se zyada. Inch ke dasve hisse jitna bhi tedha wheel badal deta hai ki ball track kahan chhodti hai, aur jhuke hue wheel par ball oonchi taraf se utarti hai, jisse prediction aasaan hota hai. Balls alag hoti hain: Teflon ki ball billiard-ball composite wali se do guna tezi se dheemi hui. Aur track chhodne ke baad bhi ball uchhalti hai, average mein chakkar ke ek-chauthai se ek-tihaai se zyada nahi. Poori yojana isi uchhal ke sawaal par tiki thi, aur woh itni chaudi nahi thi ki prediction ko mita de. Garmiyon ke ant tak unhone sambhavit advantage 44% aanka, wahi figure jo Thorp ne apne device ke liye diya tha.
Company aur pie
Unhone is venture ka naam Eudaemonic Enterprises rakha, ek Greek shabd se jiska matlab hai tark se jiye gaye jeevan ki khushi. Ismein kaam karne wale har insaan ko future jeet mein se lagaye gaye ghanton ke hisaab se paisa milna tha: jise woh Eudaemonic Pie kehte the uska ek tukda. Jeet ka maqsad doston ki ek community ka kharcha uthana tha jo apni sharton par science kare.
Baanh ke neeche computer, 1976–1978
Pehli machine ek kit computer se bani jo September 1976 mein $250 mein mail se aaya, 6502 processor par bana jo Apple ke computers mein bhi tha. Farmer, jinhone pehle kabhi programming nahi ki thi, ne usmein ball aur rotorsaamanRotorWheel ka ghoomne wala hissa jismein pockets hote hain.Poora padhein → ke equations likhe. Casino version shareer par baandh kar pehna jaata, baanh ke neeche ya, auraton ke liye, bra mein. Wheel par baitha player pair ke angoothon se switches dabata: ek angootha zerowheelZeroAkela green pocket jise koi even-money, dozen ya column bet cover nahi karta; house edge ka source. Doosre naam: single zero, 0.Poora padhein → aur phir ball ko har baar fixed point se guzarne par mark karta, doosra program ki settings badalta. Program ko ek khaas wheel ke hisaab se set karne mein lagbhag bees minute ki chupchaap clicking lagti. Phir har spin ke kuch second baad computer wheel ke aath sectorswheelSectorWheel par pockets ka lagatar ek hissa (arc), layout ke kisi group se alag cheez.Poora padhein → mein se ek bataata, ya “no bet” ka signal deta, twacha par chhote plungers ki bhanbhanahat se. Table par thoda door baitha doosra player, ek kamzor radio signal se juda, wahi bhanbhanahat mehsoos karta aur us sector ke teen-chaar numbers cover karta, kabhi wheel par bagal wala number bhi daal deta taaki pattern padhna mushkil ho.
Pehli trip, December 1977 mein Lake Tahoe aur Reno ki, ek lambi equipment failure thi. Kuch hafton baad downtown Las Vegas ke Golden Gate mein Farmer ne das cent ki chippaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → par akele saadhe chaar ghante khela. Munafa chhota tha, lekin kai sau spins par unhone aur Browne ne edge, saavdhani se, 25% aanka.
1978 ki garmiyan
Us garmi group ne hafton tak shifts mein khela, downtown aur Strip par, din mein do sessions aur lagatar do raaton mein kabhi ek hi casino nahi. Har casino ki ek notebook rakhi: uske wheels aur woh kitne tedhe the, uska staff, uski shift badalne ka samay. Las Vegas ke wheels mehrbaani se jhuke hue nikle aur der raat ke games dheeme, jo computer ko chahiye tha, kyunki dheema rotor aur tez ball naapne aur bet lagane ka zyada samay dete hain. Achhi raatein bhi thi. Circus Circus mein raat do baje croupierlogCroupierRoulette table ka dealer.Poora padhein → badalne se ek haarta hua session 25 cent ki chip par kai sau dollar mein badal gaya. Aur failures ki ek lagatar line thi: dheele taar, temperature ke saath bhatakte radio links, shirts mein sile antenna taaron se bijli ke jhatke. Ek raat plungers atak gaye, wiring garam ho gayi, aur Ingrid Hoermann jeetti hui table chhodne ke bajaye jalne ke bawajood khelti rahi. Casino staff ne jeet notice ki, method kabhi nahi; ek baar chips ke badhte dher se pareshaan ek croupier ne ghoomta wheel pakad kar jhatke se ghuma diya.
Terah mahinon mein unhone Nevada ki aath trips ki aur, zyada-tar dimes aur quarters lagakar, kuch hazaar dollar jeete. December 1978 mein California Club ke ek session ne teen ghante mein $1,000 se zyada diye aur unhe yakeen dilaya ki method behtar hardware ka haqdaar hai.
Packard aur Biles Las Vegas mein tape recorder se roulette balls ka time naapte hain.
Reno mein casino wheel khareeda; garmiyon bhar naap-tol; pehla kit computer.
Pehli casino trip, Lake Tahoe aur Reno. Equipment fail hota hai.
Golden Gate, Las Vegas: dime stakes par saadhe chaar ghante, edge 25% aanka gaya.
Shareer par pehne computer ke saath Las Vegas mein hafton ka khel.
California Club: teen ghante mein $1,000 se zyada.
Computer ko joote ke andar fit karne ke liye dobara banaya jaata hai.
Las Vegas: electrical noise radio link ko dabaa deta hai. Project ruk jaata hai.
Nevada prediction devices par ban lagata hai. The Eudaemonic Pie publish hoti hai.
Joote mein computer, 1980–1981
Taaron ko shareer se hataane ke liye unhone sab kuch jooton mein daalne ka faisla kiya. Mark Truitt, ek naye physics graduate jo military radar ke kaam ka job interview beech mein chhod kar chale aaye the, ne ispar dedh saal lagaya. Jis idea se yeh fit hua woh university ke ek technician se aaya: predictions ke beech computer band kar do, toh bahut kam batteries chahiye. Truitt ne chips ko do circuit boards par lagaya jo unhone khud etch kiye, ek ko doosre ke upar ulta rakha aur beech ki jagah sakht wax se bhar di, jisse lagbhag do inch by chaar inch aur aadha inch mota block bana jispar chala ja sakta tha. Batteries, antenna aur teen mein se do buzzers heel mein gaye. Teen speed par teen buzzers se nau signals milte: aath sectors aur “no bet”. Ek mochi ne aam leather ke jooton ko andar se khokhla kiya aur koi sawaal nahi poocha.
November 1981 mein Farmer aur lekhak Thomas Bass joote aur $2,500 lekar Las Vegas gaye. Pehli table par pehla prediction laga, aur phir buzzers random bajne lage. Casinos electrical noise se bhare hote hain, surveillance cameras, neon signs aur slot machines se, aur isne jooton ke beech ke kamzor radio link ko dabaa diya; motel room mein ek television ne bhi yahi kiya. Chaar logon ki dino ki marammat bhi ise theek nahi kar payi, aur project wahin ruk gaya. Equipment Santa Cruz ke ek basement mein ek trunk mein chala gaya.
44% ka matlab kya hai
American wheel par ek straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → average mein 38 spins mein ek baar jeetta hai aur 35 to 1 deta hai, jiski player ko 5.26% keemat padti hai. 44% advantage us bet ki value hai jab woh 25 spins mein ek baar jeete: har 25 lagayi chips par 36 wapas aati hain. Isliye computer ko kabhi number jaanna nahi tha. Use bas apne chune numbers ko chance ki ijazat se lagbhag dedh guna zyada baar laana tha.
Bada edge bhi gambling jaisa kyun laga
35 to 1 par edge dheere aur asamaan dhang se paisa deta hai. Group ke ek salahkaar ne chetaya ki har number par $100 lagane wala player advantage dikhne se pehle $10,000 ya $20,000 neeche ho sakta hai, aur hisaab bhi yahi kehta hai: single numbers par 44% edge ke saath bhi player 100 spins ke baad lagbhag chaar mein ek baar peeche hota hai. Isiliye Eudaemons ne dimes se shuruaat ki aur jeet se apna bankrollpaisaBankrollKhelne ke liye alag rakhi gayi kul raqam. Bankroll management ka matlab hai tay karna ki har bet aur har session mein iska kitna hissa risk karna hai.Poora padhein → banaya, aur isiliye 1978 mein jude Alan Lewis ne apna samay is par lagaya ki kitna bet karna hai. Farmer ne baad mein socha ki woh zaroorat se zyada saavdhaan the. Chhote stakes ne unhe surakshit rakha, aur iska matlab yeh bhi tha ki saalon ki mehnat se bahut kam kamaai hui.
Kitna laga aur kitna mila
Lagbhag $15,000 parts, tools aur Truitt ki tankhwah mein gaye, zyada-tar Farmer se aur Letty Belin se, ek lawyer jinse baad mein Farmer ne shaadi ki. Farmer ke naam 3,500 ghante ka kaam darj hua, Truitt ke 3,000 aur Packard ke 2,000. Iske saamne chhote stakes par jeete kuch hazaar dollar hain. 1983 mein Farmer ne ek gambling magazine mein investors ke liye ad diya, ek prototype ka varnan karte hue jiska casino advantage 20 se 40% saabit tha. Jab Eudaemons khelte the, tab Belin ki Nevada law ki khoj mein aisa kuch nahi mila tha jo game predict karne se rokta ho; May 1985 mein state ne iske liye device use karna apraadh bana diya. Jo bacha woh science thi. Computers banane se Farmer, Packard aur unke doston ko chaos ke adhyayan ki training mili, aur wahin unhone apna naam banaya.
Aaj kitaab padhna
Thomas Bass, jinhone aakhri trip par bets lagaye, ne yeh kahani The Eudaemonic Pie (1985) mein batayi, group ke saath lambe interviews par aadharit, aur yahi is page ka source hai. Iska roulette ka chhota itihaas project ke bayaan jitna bharosemand nahi. Yeh Jagger ke chhe kiraye ke clerks wali kahani dohrata hai, jo 1901 ki ek kitaab tak jaati hai aur usse aage nahi (dekhiye Joseph Jagger), aur Thorp aur Shannon ka casino test 1962 mein rakhta hai, jabki Thorp ke apne bayaan 1961 ki garmi kehte hain.
Sawaal
Nahi. Unhone dime aur quarter stakes par kuch hazaar dollar jeete, aur lagbhag $15,000 aur hazaaron ghante kharch kiye.
Jab woh khelte the, Nevada mein device se game predict karne ke khilaaf koi law nahi tha. 1985 se hai, aur ab casinos wali zyada-tar jagahon par hai.
Wahan nahi jahan ball chalte hi betting band ho jaati hai, jaise live studios mein, aur aisa device casino mein le jaana zyada-tar jurisdictions mein apraadh hai.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
Eudaemons ka andaaza tha ki American wheel par, jahan bet 35 to 1 deti hai, unka computer straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → par 44% ka tha. Iske sach hone ke liye chuna gaya number kitni baar jeetna chahiye? Aur agar 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 → baaki mein se kisi mein bhi barabar chance se gire, to prediction ko 38 pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → mein se kitne khaarij karne honge?
Solution dikhaiye
Jawab 25 spins mein ek baar. Yeh 13 pockets khaarij karke 25 chhodne ke barabar hai.
Jeetne wali chippaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → 35 aur ke saath wapas aati hai: 36 chips. Agar number n spins mein ek baar jeete, to n chips lagane par 36 wapas aati hain, isliye bet ki keemat 36/n − 1 hai.
Ise 0.44 rakhiye: 36/n = 1.44, isliye n = 25. Bina prediction ke n 38 hai aur bet ki keemat 36/38 − 1 = −5.26% hai.
Ab maan lijiye prediction k pockets khaarij karta hai aur ball baaki 38 − k mein se har ek mein barabar chance se girti hai. Unmein se ek par chip 38 − k spins mein ek baar jeetti hai. 44% ke liye 38 − k = 25 chahiye, isliye k = 13: wheel ke ek-tihaai se thoda zyada.
Kitaab mein Farmer ko yeh kehte quote kiya gaya hai ki 40% aath pockets khaarij karne se aata hai. Is saral model par aath se 36/30 − 1 = 20% milta hai, isliye asli tasveer asmaan rahi hogi: baaki pockets mein se kuch doosron se kahin zyada sambhav.
khaarij pocketsbache pocketsstraight-up ki keemat038−5.26%2360%830+20%1325+44%1919+89%Maan lijiye aapka number sach mein 35 to 1 par 25 spins mein ek baar jeetta hai, 44% edge. Aap har spin ek chip lagate hain. 100 spins ke baad aapke peeche hone ka chance kitna hai? 500 ke baad?
Solution dikhaiye
Jawab 100 spins ke baad lagbhag 23% aur 500 ke baad bhi lagbhag 6%.
100 spins ke baad aapne 100 chips lagayi hain, aur har jeet 36 lautati hai. Do jeet 72 laati hain, 28 ka nuksaan; teen 108 laati hain, 8 ka faayda. Isliye do ya kam jeet par aap peeche hain.
100 spins mein koi jeet na hone ka chance (24/25)¹⁰⁰ = 1.7% hai. Theek ek jeet: 100 × (1/25) × (24/25)⁹⁹ = 7.0%. Theek do: 4,950 × (1/25)² × (24/25)⁹⁸ = 14.5%. Milakar 23.2%.
500 spins ke baad aage hone ke liye 14 jeet chahiye (14 × 36 = 504), aur average 20 hai. 13 ya kam ka chance lagbhag 6.2% hai.
Yeh lambe odds wali bet ka doosra pehlu hai. Edge bada hai, aur 100 spins ki lagbhag chaar mein ek series mein yeh dikhta nahi. Jis khiladi ko pakka pata nahi ki edge hai, woh buri series aur toote computer mein fark nahi kar sakta, aur Eudaemons aksar isi haalat mein the.
spinsaage hone ke liye zaroori jeetpeeche hone ka chance50240.1%100323.2%200618.6%500146.2%Kitaab kehti hai ki 44% edge ke saath, ghante mein 50 baar $100 lagane se ghante mein $2,200 kamane chahiye. Ise check kijiye. Phir hisaab lagaiye ki group ne jin stakes par asal mein khela, ek spin par ek dime, us par wahi edge kitna kamata tha.
Solution dikhaiye
Jawab $100 per spin ke liye $2,200 sahi hai. Ek dime per spin par yeh ghante mein $2.20 hai.
Edge lagayi gayi har cheez ka ek hissa hai. $100 per spin aur ghante mein 50 spins par $5,000 lagta hai, aur uska 44% $2,200 hai.
10 cents per spin par ghante mein $5 lagta hai, aur $5 ka 44% $2.20 hai. Chaar numbers ko ek-ek dime se cover karke bhi do logon ke liye ghante mein $8.80 hai.
Group ne kam stakes par khela kyunki woh shunya se bankrollpaisaBankrollKhelne ke liye alag rakhi gayi kul raqam. Bankroll management ka matlab hai tay karna ki har bet aur har session mein iska kitna hissa risk karna hai.Poora padhein → bana rahe the aur kyunki, jaisa upar ki paheli dikhati hai, 35 to 1 par 44% edge ghanton tak haar sakta hai. Is saavdhaani ki keemat yeh thi ki tareeka bilkul theek kaam karte hue bhi ek naukri se kam de sakta tha.
Thodi hansi
Physics ne kaam kiya. Neon jeet gaya.
Sources
- 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.