Taariika e Pinal · Taariika · Yimɓe · hojomaaji 10

Eudaemons ɓen

Almuɓɓe fiisik, taarorde kasino soodaande e kaalis jungo, e ordinateer tokooso no haanirta ɓornireede haa taabal.

Jaabawol rabbiɗngol

Gila 1976 haa 1981, goomu almuɓɓe fiisik e Santa Cruz mahii ordinateeruuji dijital ɗi etotonooɗi waktu bal e rotoor, ina innda geɗal taarorde tuma nde pariiji ina ngonnoo e udditii. Ƴeewndooji maɓɓe fodii ɓural 44%, tee jonnde juutnde adannde addii hedde 25%. Kuutorɗe ɗee ina kaɓɓannoo sahaa kala, mbaydi mahaandi e nder pade foolaa bayle elektirik e 1981, tee ɓe ndañii ujunaaji dolaar seeɗa.

duuɓi
1976–1981
dabare
etude waktu bal e rotoor
ɓural
44% e ƴeewndooji · ≈ 25% e taabal
dañi
ujunaaji dolaar seeɗa

Miijo e bar Las Vegas, 1975

E ceeɗu 1975, Norman Packard, almuudo fiisik, waɗi lebbi ɗiɗi ina limoo kartaaje e blackjack e Las Vegas e sehil mum Jack Biles, tee ɓe fotdi tan seeɗa. E njaram sakkitoram Biles wiyi o waɗay pari wonde ruleet ina waawi foolireede fiisik, tee Packard siftori konngol suuɗngol e Beat the Dealer Edward Thorp e dow dabare ruleet. Ɓe ɗiɗo njoññii masiŋ winndoowo hito, ndarii sara taarorɗe e kasinooji ɗuuɗɗi, ina piya mikoro oo kala nde balkuutorɗeBalBal tokoosal werlaangal e laawol ngol e laawol rotoor ngol. Balli jamaanu hannde ko ivorine walla Teflon, 18–21 mm.Tar fof → oo rewi nokku tabitiingo. Winndaaɗe e kaayit kaareeji, piyeeji ɗii kollii bal oo ina leeltoo, ina yana e laawol fotngol. Sehil duɗal Packard Doyne Farmer, almuudo ɓurɗo toownude e University of California, Santa Cruz, wiyi ɗum ko majjinde waktu haa nde o waɗi hiisa oo e hoore mum: neɗɗo waawɗo etude waktu bal haa hedde segonde gootel e nder sappo ina foti, e kaayit, waawde wiyde ɗo o joofata e nder limooje seeɗa.

Taarorde e laboratuwaar fiisik

E fuɗɗoode hitaande 1976 Farmer e Dan Browne njoɓii $1 500 kaalis jungo ngam taarorde kasino moƴƴitinaande e kuuɓtorde e Reno, ɓe mbiyi ko ngam kawgel almuɓɓe. E nder lebbi ɗuuɗɗi ɓe ina ndoggoo nde jemma haa laboratuwaar jannginirde jaaɓi-haaɓe ndee, ina ƴeewta nde e kapteeruuji infaraas, montoor elektoronik peewnaaɗo e galle, e kamera fuɗɗortooɗo e hito bal fiyoowo njamndi. Ko ɓe njiyi ina woni haa jooni doggol rabbiɗngol moƴƴol e ko teddi e taarol. Henndu ko ɓuri leeltinde bal, ɓuri laawol. Taarorde ɓeŋŋiinde hay seeɗa, hono inch gootel e nder sappo, ina wayla ɗo bal yaltata e laawol, tee e taarorde ɓeŋŋiinde bal ina heewi yaltude e baŋnge toowngo, ɗum ina newna anndude adii. Balli ina ceertii: bal Teflon ina leeltoo laabi ɗiɗi ɓuri bal mahaaɗo e ko bal biyaar mahetee. Tee so bal oo yaltii laawol, ina diwa haa jooni, e hakkundeere ko ɓurataa nayaɓal haa tataɓal taarorde. Ngol diwgol ko naamne ngol peeje ɗee fof njoggii, tee ngol yaajaani ngam momtude anndude adii. E gasol ceeɗu, ɓe ndokki ɓural waawngal 44%, limoore nde Thorp hokkunoo kuutorgal mum.

E taarorde laboratuwaar ɓeŋŋiinde, bal leeltotooɗo ina yalta laawol e baŋnge toowngo.

Fiisik Taarorde Ruleet

Sosiyetee e tarte

Ɓe noddiri golle ɗee Eudaemonic Enterprises, gila e konngol Gerek firtoowol weltaare nguurndam mo hakkille ardii. Kala gollirɗo e mum foti yoɓeede e dañal garoowo, e hiisa waktuuji ɗi o golli: feccere e ko ɓe noddiri Eudaemonic Pie. Dañal ngal ina faandaa yoɓde renndo sehilaaɓe waɗooɓe ganndal no ɓe njiɗiri.

Ordinateer haɓɓaaɗo e ɓalli, 1976–1978

Masiŋ adanɗo ummii e ordinateer peewnetee mo ari e poste e Septaambar 1976 e $250, mahaaɗo e porosesoor 6502 mo ordinateeruuji Apple kuutortonoo kadi. Farmer, mo winndaano porogaraam abada, winndi e mum ekkaasiyoŋaaji bal e rotoorkuutorɗeRotoorGeɗal taarorde taarotooɗo, roondiiɗo cuuɗi ɗii.Tar fof →. Mbaydi kasino ina ɓornoo haɓɓaaɗo e ɓalli, les kaɓɓal walla, wonande rewɓe, e nder sumpu. Fijoowo e taarorde ina ñukka butonji e fedeeji koyɗe mawɗe: fedeende wootere ina maandina seerotaarordeSeeroSuudu haako wootere nde hay pari njoɓdi fotndi, sappo e ɗiɗi walla kolon kuuɓataa; ko ɗum woni iwdi ɓural kasino. Ina noddee kadi: seero gooto, 0.Tar fof → refti bal kala nde rewi nokku tabitiingo, goɗɗo ina dirtina porogaraam hakkunde teelte mum. Feewnude porogaraam e taarorde wootere ina jogii hedde hojomaaji noogaas ñukkagol deeƴngol. Refti, segonde seeɗa caggal fuɗɗoode kala taarol, ordinateer ina innda gootal e geɗe taarordetaarordeGeɗal taarordeCeeɓnde cuuɗi takkondirɗi e taarorde, ceertunde e mooftere e tapi.Tar fof → jeetati, walla ina holla “pari alaa”, e dillaangol pistonji tokooseeji e laral. Fijoowo ɗiɗaɓo ɓadiiɗo seeɗa e taabal, jokkondirɗo e radio famɗuɗo, ina nana dillaangol ngol tigi tee ina huuɓa limooje tati walla nay e oon geɗal, sahaaji ina wayla limoore e limoore nde sara mum e taarorde ngam ndonu ngu ɓura saɗtude jaŋngeede.

Ɗanngol adanngol, haa Lake Tahoe e Reno e Desaambar 1977, ko kaɓɓannde kuutorɗe juutnde wootere. Yontereeji seeɗa ɓaawo ɗuum, e Golden Gate e Downtown Las Vegas, Farmer fijii kanko tan waktuuji nay e feccere e santiimuuji sappo e kala jetoŋkaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof →. Dañal ngal ina tokoosi, kono e nder teemedde taarle ɗuuɗɗe kanko e Browne ndokki ɓural ngal, e reentaare, 25%.

Butoŋ fedeende koyngal ina etoo waktu bal; ordinateer haɓɓaaɗo e ɓalli ina dilla ngam hollude geɗal.

Taarorɗe Ruleet Las Vegas

Ceeɗu 1978

E oon ceeɗu goomu ngu fijii e lomtondiral yontereeji ɗuuɗɗi, e Downtown e Strip, jonɗe ɗiɗi ñalnde kala tee alaa kasino gooto e jemmaaji jokkondirɗi. Ɓe njogii kaye e kala kasino: taarorɗe mum e no ɗe ɓeŋŋori, golliiɓe mum, waylooji lomtondiral mum. Taarorɗe Las Vegas pellitii wonde ko ɓeŋŋiiɗe no ordinateer yiɗi, tee fijooji jemma jaawaani, ɗum ko ko ordinateer oo hatojinoo, sabu rotoor leeltuɗo e bal jaawɗo ina accita waktu ɓurɗo ngam etude e waɗde pari. Jemmaaji moƴƴi ina ngonnoo. E Circus Circus waylugol kurupiyeyimɓeKurupiyeKurupiye ko gollotooɗo e taabal ruleet.Tar fof → e waktu ɗiɗi jamma waylii jonnde majjere wonti teemedde dolaar ɗuuɗɗe e santiim 25 e kala jetoŋ. Tee kaɓɓanɗe ina njokkondironoo: gaañe nawɗe, jokkondire radio ɗe wulngol waylata, fiyaneede elektirik e gaañe antenn ɗemmbaaɗe e nder simisaaji maɓɓe. Jemma gooto pistonji ɗi nanngondirii, gaañe ɗe ngulii, tee Ingrid Hoermann jokki fijde e duppeede ɓuri accude taabal dañal. Golliiɓe kasino tinndii dañal ngal, kono tinndaani dabare ndee abada; laawol gootol kurupiye, mo jetoŋji ɓeydotooɗi ɓernini, nanngi taarorde ndee ina taara, taarnii nde e doole.

E nder lebbi sappo e tati ɓe mbaɗii ɗanɗe jeetati haa Nevada tee, ina mbaɗa pariiji ko ɓuri heewde e santiimuuji sappo e noogaas e joy, ɓe ndañii ujunaaji dolaar seeɗa. Jonnde e California Club e Desaambar 1978 addii ko ɓuri $1 000 e nder waktuuji tati, tee ɗum hoolnii ɓe wonde dabare ndee haani kuutorɗe ɓurɗe moƴƴude.

Golle ɗee, hitaande e hitaande
1975

Packard e Biles ina etoo waktu balli ruleet e masiŋ winndoowo hito e Las Vegas.

1976

Taarorde kasino soodaande e Reno; ceeɗu etooɗe; ordinateer peewnetee adanɗo.

Des 1977

Ɗanngol kasino adanngol, Lake Tahoe e Reno. Kuutorɗe ɗee ina kaɓɓana.

Saa 1978

Golden Gate, Las Vegas: waktuuji nay e feccere e pariiji santiimuuji sappo, ɓural ngal ina hiisaa 25%.

ceeɗu 1978

Yontereeji fijo e Las Vegas e ordinateer ɓornaaɗo e ɓalli.

Des 1978

California Club: ko ɓuri $1 000 e nder waktuuji tati.

1980–81

Ordinateer oo ina mahtee ngam naatde e nder pade.

Now 1981

Las Vegas: bayle elektirik ina ŋabba jokkondiral radio. Golle ɗee ina ndarta.

1985

Nevada ina haɗa kuutorɗe anndude adii. The Eudaemonic Pie ina yaltinee.

Ordinateer e nder pade, 1980–1981

Ngam ittude gaañe ɗee e ɓalli maɓɓe ɓe ñaawi wattude fof e nder pade. Mark Truitt, gannduɗo fiisik kesɗo mo yalti e naamnaal golle radar konu, waɗi hitaande e feccere e ɗum. Miijo ngo waɗi ɗum ina naata ummii ko e karallo jaaɓi-haaɓe: ñif ordinateer hakkunde annditagol adii e annditagol goɗngol, tee ina hatojinoo bateriiji seeɗa no feewi. Truitt watti cipuuji ɗin e alluuje elektoronik ɗiɗi ɗe o waɗi e hoore mum, o waylii gooto e dow goɗɗo, o hebbini hakkunde maɓɓe e cire tiiɗnde, ɗum waɗi bloc hedde inch ɗiɗi e inch nay e ɓuttol feccere inch, mo waawi yaheede e dow mum. Bateriiji, antenn e dilloyɗe ɗiɗi e nder tati ɗin naatii e teŋngal. Dilloyɗe tati e jaawe tati ndokki maandeeji jeenay: geɗe jeetati e “pari alaa”. Sakke wujji pade laral ɗe ngoowaa, naamnaani hay huunde.

E Nowaambar 1981 Farmer e winndoowo Thomas Bass nawi pade ɗee e $2 500 haa Las Vegas. E taabal adanngal, annditagol adanngol hawri, refti dilloyɗe ɗe puɗɗii dillude e sahaa. Kasinooji ina keɓɓi bayle elektirik, gila e kameraaji ƴeewtagol, maandeeji neon e masiŋaaji fijo, tee ɗum ŋabbi jokkondiral radio famɗungal hakkunde pade ɗee; telewisiyoŋ e suudu motel waɗi ɗum tigi. Balɗe moƴƴitinde yimɓe nay cellinaani ɗum, tee golle ɗee ndarii ɗoon. Kuutorɗe ɗee naatii e nder kees e nder suudu les leydi e Santa Cruz.

Bayle masiŋaaji fijo, neon e kameraaji ŋabbi jokkondiral radio famɗungal pade ɗee.

Ko 44% firti

E taarorde Amerik, pari limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → ina daña laawol gootol e nder taarle 38 e hakkundeere, ina yoɓa 35 e 1, ɗum ina coggana fijoowo 5,26%. Ɓural 44% ko njaru pari ngoo tigi so ina daña laawol gootol e nder taarle 25: jetoŋji 36 ina ruttoo e kala 25 pariyaaɗi. Ɗum waɗi ordinateer oo hatojinaano anndude limoore ndee. Ina foti tan waɗde limooje ɗe suɓi ina njalta hedde laabi gooto e feccere ɓuri ko sahaa accata.

limoore suɓaande ina daña laawol gootol e ndernjaru pari limoore wootere
taarle 38 (alaa annditagol adii)−5,26%
taarle 360%
taarle 30+20%
taarle 25+44%
taarle 19+89%
Taarorde Amerik, 35 e 1. Njaru ndu ko 36 seƴaa e limoore taarle, ittaa 1.

Taarorde e Sariyaaji Ruleet Amerik

Ko waɗi ɓural mawngal ina yiyee hono fijo kaalis haa jooni

Ɓural e 35 e 1 ina yoɓa leeltii, e ko fotaani. Gooto e wasiyankooɓe goomu ngu reentini wonde fijoowo waɗoowo pari $100 e kala limoore ina waawi majjinde $10 000 walla $20 000 hade ɓural ngal feeñde, tee hiisa ina jaɓi ɗum: e ɓural 44% e limooje gootooje, fijoowo ina majjii haa jooni caggal taarle 100 hedde laawol gootol e nder nay. Ko ɗum waɗi Eudaemons fuɗɗii e santiimuuji sappo, mahi kaalis parikaalisKaalis pariKaalis fof ko seŋaa ngam fijde. Toppitagol kaalis pari ko ñaawde ko foti waɗeede e kala pari e kala jonnde.Tar fof → maɓɓe e dañal, e ko waɗi Alan Lewis, mo naati e maɓɓe e 1978, waɗi waktu mum e no foti waɗde pari. Farmer sikki ɓaawo ɗuum wonde ɓe ɓurnoo reentaade. Pariiji tokooseeji ina reenno ɓe, tee kadi ɗi firti wonde golle duuɓi ɗuuɗɗi ndañaani ko ɓuri seeɗa.

Ko ɗum coggi e ko ɗum yoɓi

Hedde $15 000 naatii e geɗe, kuutorɗe e njoɓdi Truitt, ko ɓuri heewde e mum ummii ko e Farmer e Letty Belin, awokaa mo resi mo ɓaawo ɗuum. Farmer hokkaa waktuuji golle 3 500, Truitt 3 000 e Packard 2 000. E yeeso ɗuum ina ngoni ujunaaji dolaar seeɗa ɗi ɓe ndañi e pariiji tokooseeji. E 1983 Farmer anndini e jaaynde fijo kaalis ina ɗaɓɓa jowtooɓe, ina sifa porototip jogiiɗo ɓural kasino tabitinaangal 20 haa 40%. Tuma nde Eudaemons ina pijnoo, ɗaɓɓitagol Belin e sariya Nevada heɓaani hay huunde haɗoore anndude fijo adii; e Mee 1985 leydi ndii waɗii kuutoraade kuutorgal ngam ɗum bonannde. Ko heddii ko ganndal. Mahgol ordinateeruuji ɗii ekkitinii Farmer, Packard e sehilaaɓe maɓɓe ngam jaŋde jiiɓru, ɗo ɓe lollinirii inɗe maɓɓe.

Jaŋngude deftere ndee hannde

Thomas Bass, mo waɗi pariiji ɗin e ɗanngol sakkitorngol, taalii taariindi ndi e The Eudaemonic Pie (1985), mahaande e yeewtere juutɗe e goomu ngu, tee ko ndi woni ɗaɓɓitirde ndee hello. Taariika ruleet rabbiɗɗo mum hoolnaaka hono taariindi golle ɗee. Ina ruttita taalol kalfaaɓe jeegom ɓe Jagger nawli, ngol ummii ko e deftere 1901 tan (ƴeew Joseph Jagger), tee ina watta ƴeewndo kasino Thorp e Shannon e 1962, kono taariiɗi Thorp e hoore mum ina mbiya ceeɗu 1961.

Naamne

Eudaemons ngonti alɗuɓe?

Alaa. Ɓe ndañii ujunaaji dolaar seeɗa e pariiji santiimuuji sappo e noogaas e joy, ɓe njoɓii hedde $15 000 e ujunaaji waktuuji ɗuuɗɗi.

Ɗum ina laawɗinoo?

Tuma nde ɓe pijnoo, Nevada alaa sariya haɗoowo anndude fijo adii e kuutorgal. Ina jogii sariya gila 1985, tee nokkuuji ɓurɗi heewde ɗi kasinooji ngoni ina njogii jooni.

Ɗum ina gollay hannde?

Wonaa ɗo pariiji uddotoo tuma nde bal werlaa, hono no waɗata e studiooji live, tee naatnude kuutorgal hono ngal e kasino ko bonannde e ɓurɗe heewde e leyɗe.

Weltaare e Matematik

Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.

  1. Eudaemons ɓee limtii wonde ordinateer maɓɓe ina foti 44% e limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → e taarorde Amerik, ɗo pari ngal yoɓata 35 e 1. Limoore suɓaande ndee ina foti daña laabi njelu ngam ɗum wonde goonga? CuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → njelu e nder 38 ɗee hiinnirgal ina foti ittude, so balkuutorɗeBalBal tokoosal werlaangal e laawol ngol e laawol rotoor ngol. Balli jamaanu hannde ko ivorine walla Teflon, 18–21 mm.Tar fof → ngal ina waawi yanude e kala e ɗe heddii e porobabilite gootal?

    Hollu jaabawol ngol

    Jaabawol Laabi gooto e nder taarle 25. Ɗum ina fotndi e ittude cuuɗi 13 accude 25.

    JetoŋkaalisJetoŋMaande hollirde kaalis tabitiiɗo, waɗetee e tapi ngam waɗde pari. Ina wiyee kadi: check.Tar fof → dañuɗo ina ruttoo e 35 goɗɗo: jetoŋji 36. So limoore ndee ina daña laabi gooto e nder taarle n, jetoŋji n pariyaaɗi ina ngaddi 36, ɗum waɗi pari ngal ina foti 36/n − 1.

    Fotndin ɗum e 0,44: 36/n = 1,44, ɗum waɗi n = 25. So hiinnirgal alaa n ko 38, pari ngal ina foti 36/38 − 1 = −5,26%.

    Jooni miijo hiinnirgal ina itta cuuɗi k, bal ngal ina waawi yanude e kala e 38 − k goɗɗi ɗii e porobabilite gootal. Jetoŋ e gootel e majji ina daña laabi gooto e nder taarle 38 − k. Ngam 44% ina foti 38 − k = 25, ɗum waɗi k = 13: ko ɓuri tataɓal taarorde ndee seeɗa.

    E deftere ndee Farmer ina wiyee wiyii 40% ina iwi e ittude cuuɗi jeetati. E mbaadi weeɓndi ndii jeetati ina addi 36/30 − 1 = 20%, ɗum waɗi natal goonga ngal ina foti wonde ko fotaani: won cuuɗi heddiiɗi ina ɓuri goɗɗi porobabilite no feewi.

    cuuɗi ittaaɗicuuɗi heddiiɗinjaru pari limoore wootere
    038−5,26%
    2360%
    830+20%
    1325+44%
    1919+89%
  2. Miijo limoore maa ina daña tigi laabi gooto e nder taarle 25 e 35 e 1, ɓural 44%. A waɗa pari jetoŋ gooto e kala taarol. Hol porobabilite maa wonde e majjere caggal taarle 100? Caggal 500?

    Hollu jaabawol ngol

    Jaabawol Hono 23% caggal taarle 100, hono 6% kadi caggal 500.

    Caggal taarle 100 a pariyii jetoŋji 100, kala dañal ina rutta 36. Dañe ɗiɗi ina ngaddi 72, majjere 28; tati ina ngaddi 108, dañal 8. Ɗum waɗi a woni e majjere so a dañii laabi ɗiɗi walla ko ɓuri famɗude.

    Porobabilite alaa dañal e taarle 100 ko (24/25)¹⁰⁰ = 1,7%. Dañal gootal tigi: 100 × (1/25) × (24/25)⁹⁹ = 7,0%. Ɗiɗi tigi: 4 950 × (1/25)² × (24/25)⁹⁸ = 14,5%. Kawral 23,2%.

    Caggal taarle 500 ina foti ma dañe 14 ngam wonde e dañal (14 × 36 = 504), hakkundeere ndee ko 20. Porobabilite 13 walla ko ɓuri famɗude ko hono 6,2%.

    Ɗum ko ɓerde goɗnde pari kot juutɗo. Ɓural ngal ina mawni, kono e hono jokkondiral gootal taarle 100 e nder nay ngal feeñataa. Fijoowo mo anndaa tigi wonde ɓural ngal ina woodi waawataa senndude jokkondiral bonngal e ordinateer bonɗo, ɗum ko nokku ka Eudaemons ɓee ngonnoo heen sahaa heewɗo.

    taarledañe ɗe poti ngam wonde e dañalporobabilite wonde e majjere
    50240,1%
    100323,2%
    200618,6%
    500146,2%
  3. Deftere ndee ina wiya e ɓural 44%, $100 pariyaaɗo laabi 50 e kala waktu ina foti addude $2 200 e kala waktu. Ƴeewto ɗum. Ndeen limtu ko ɓural gootal ngal addinoo e pariiji ɗi mooftal ngal fijunoo tigi: dim gooto e kala taarol.

    Hollu jaabawol ngol

    Jaabawol $2 200 ko goonga ngam $100 e kala taarol. E dim gooto e kala taarol ko $2,20 e kala waktu.

    Ɓural ko geɗal ko pariyaa fof. E $100 e kala taarol e taarle 50 e kala waktu, $5 000 ina pariyee, 44% mum ko $2 200.

    E santiim 10 e kala taarol, $5 ina pariyee e waktu, 44% $5 ko $2,20. Hay so limooje nay ina kuuɓee e dim e kala e majje, ko $8,80 e waktu ngam yimɓe ɗiɗo.

    Mooftal ngal fijii les sabu ina mahnoo kaalis parikaalisKaalis pariKaalis fof ko seŋaa ngam fijde. Toppitagol kaalis pari ko ñaawde ko foti waɗeede e kala pari e kala jonnde.Tar fof → iwde e meere, e sabu, hono no caɗeele dow ndee hollirta, ɓural 44% e 35 e 1 ina waawi majjude waktuuji keewɗi. Coggu reentaare ndee ko feere ndee ina waawnoo gollude no moƴƴi tigi tawa ina yoɓa ko ɓuri famɗude golle.

Ƴeewndo weltinoowo

Fiisik golliima. Neon dañii.

Fiisik golliima. Neon dañii.

Iwdi

  1. Bass, T. A. The Eudaemonic Pie. Houghton Mifflin, 1985.
  2. Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
  3. Thorp, E. O. “The invention of the first wearable computer.” Second International Symposium on Wearable Computers, IEEE, 1998.
  4. Nevada Revised Statutes, chapter 465. Kuulal 465.075, kuutoraade kuutorgal ngam anndude njeñtudi fijo adii (1985).
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