Mbiri ndi Chikhalidwe · Mbiri · Anthu · mphindi 10

The Eudaemons

Ophunzira a fiziki, gudumu la kasino logulidwa ndi ndalama za m’manja, ndi kompyuta yaing’ono yokwanira kuvala popita ku tebulo.

Yankho lalifupi

Kuyambira 1976 mpaka 1981 gulu la ophunzira a fiziki ku Santa Cruz linapanga makompyuta a digito amene ankawerengera nthawi ya mpira ndi ya rotor ndi kutchula gawo la gudumu pamene mabetcha anali akulandiridwabe. Mayeso awo analonjeza mwayi wa 44% ndipo gawo loyamba lalitali la masewera linapereka pafupifupi 25%. Zipangizo zinkangowonongeka, mtundu umene unaikidwa mu nsapato unagonjetsedwa ndi phokoso la magetsi mu 1981, ndipo anapambana madola zikwi zingapo.

zaka
1976–1981
njira
kuwerengera nthawi ya mpira ndi rotor
mwayi
44% m’mayeso · ≈ 25% pa tebulo
anapambana
madola zikwi zingapo

Maganizo mu bala ya ku Las Vegas, 1975

M’chilimwe cha 1975 Norman Packard, wophunzira fiziki, anakhala miyezi iwiri akuwerenga makadi pa blackjack ku Las Vegas ndi mnzake, Jack Biles, ndipo anangotsala pang’ono kufika pa ziro. Pa chakumwa chomaliza Biles ananena kuti angabetche kuti roulette ingagonjetsedwe ndi fiziki, ndipo Packard anakumbukira mzere wobisika m’buku la Edward Thorp Beat the Dealer wonena za njira ya roulette. Awiriwo anabwereka chojambulira mawu, anaima pafupi ndi magudumu m’makasino angapo ndi kugogoda pa maikolofoni nthawi iliyonse mpirazipangizoMpiraMpira waung’ono umene umaponyedwa mu njira motsutsana ndi rotor. Mipira yamakono ndi ya ivorine kapena Teflon, 18–21 mm.Werengani yonse → ukadutsa pa malo okhazikika. Atalembedwa pa pepala la graph, kugogodako kunasonyeza mpira ukuchepetsa liwiro ndi kugwa mwadongosolo. Mnzake wa kusukulu wa Packard, Doyne Farmer, wophunzira wa digiri yapamwamba ku University of California, Santa Cruz, anati kunali kutaya nthawi mpaka pamene anawerengera yekha: munthu amene angathe kuwerengera nthawi ya mpira mpaka pafupifupi gawo limodzi mwa khumi la sekondi ayenera, pa pepala, kunena kumene udzagwera mkati mwa manambala ochepa.

Gudumu mu labotale ya fiziki

M’nyengo ya masika ya 1976 Farmer ndi Dan Browne analipira $1,500 ndalama za m’manja pa gudumu la kasino lokonzedwanso ku malo ena okonzera zinthu ku Reno, ponena kuti linali la phwando la gulu la ophunzira. Kwa miyezi ankalinyamula usiku kupita nalo ku labotale yophunzitsira ya yunivesite ndi kuliyeza ndi masensa a infrared, wotchi yamagetsi yopangidwa kunyumba ndi kamera yoyatsidwa ndi phokoso la mpira ukugunda chitsulo. Zimene anapeza zidakali mndandanda wabwino wachidule wa zimene zili zofunika pa kuzungulira. Mpweya ndiwo umachepetsa liwiro kwambiri, kuposa njira ya mpira. Gudumu losakhala lofanana ndi pansi ndi pang’ono ngati gawo limodzi mwa khumi la inchi limasintha malo amene mpira umachokera pa njira, ndipo pa gudumu lopendekeka mpira umakonda kuchoka kumbali yokwera, zomwe zimapangitsa kulosera kukhala kosavuta. Mipira imasiyana: mpira wa Teflon unachepetsa liwiro kuwirikiza kawiri kuposa wa zinthu za mpira wa biliyadi. Ndipo mpira ukachoka pa njira umadumphadumphabe, pa avareji osaposa gawo limodzi mwa anayi mpaka limodzi mwa atatu la kuzungulira gudumu. Kudumpha kumeneko ndiko kunali funso limene dongosolo lonse linadalira, ndipo sikunali kwakukulu kokwanira kufafaniza kulosera. Pofika kumapeto kwa chilimwe anaika mwayi umene ungatheke pa 44%, nambala imene Thorp anapereka pa chipangizo chake.

Pa gudumu lopendekeka la labotale, mpira wochepetsa liwiro umachoka pa njira kumbali yokwera.

Fiziki ya Gudumu la Roulette

Kampani ndi keke

Anatcha bizinesiyo Eudaemonic Enterprises, kuchokera ku liwu la Chigiriki la chimwemwe cha moyo wotsogozedwa ndi nzeru. Aliyense amene anagwira ntchito pa iyo amayenera kulipidwa kuchokera ku phindu la m’tsogolo molingana ndi maola amene anaikamo: kagawo ka zimene ankatcha Eudaemonic Pie. Phindu limayenera kulipirira gulu la abwenzi ochita sayansi mwa njira yawoyawo.

Kompyuta pansi pa mkono, 1976–1978

Makina oyamba anachokera ku kompyuta ya zigawo zodzipangira yokha imene inafika kudzera pa positi mu Seputembala 1976 pa $250, yomangidwa pa purosesa ya 6502 imene makompyuta a Apple ankagwiritsanso ntchito. Farmer, amene anali asanalembepo pulogalamu, analembamo masamu a mpira ndi a rotorzipangizoRotorGawo lozungulira la gudumu limene limanyamula tibowo.Werengani yonse →. Mtundu wa ku kasino unkavalidwa womangiriridwa ku thupi, pansi pa mkono kapena, kwa akazi, mu bulaziya. Wosewera pa gudumu ankadina masiwichi ndi zala zazikulu za mapazi: chala chimodzi chinkasonyeza zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse → kenako mpira nthawi iliyonse zikadutsa pa malo okhazikika, china chinkasuntha pulogalamu pakati pa makonzedwe ake. Kukonza pulogalamu kuti igwirizane ndi gudumu linalake kunatenga pafupifupi mphindi makumi awiri za kudina mwakachetechete. Kenako, masekondi ochepa m’kuzungulira kulikonse, kompyuta inkatchula limodzi mwa magawogudumuGawoMndandanda wolumikizana wa tibowo pa gudumu, mosiyana ndi gulu pa dongosolo la mabetcha.Werengani yonse → asanu ndi atatu a gudumu, kapena kusonyeza “palibe betcha”, pogwedeza tizitsulo ting’onoting’ono pakhungu. Wosewera wachiwiri kutsogolo kwa tebulo, wolumikizidwa ndi chizindikiro cha wailesi chofooka, ankamva kugwedezeka komweko ndi kuphimba manambala atatu kapena anayi a gawo limenelo, nthawi zina kusinthanitsa ndi nambala yoyandikana nayo pa gudumu kuti njirayo ikhale yovuta kuzindikira.

Ulendo woyamba, ku Lake Tahoe ndi ku Reno mu Disembala 1977, unali kuwonongeka kwa zipangizo kwautali. Patapita masabata ochepa, ku Golden Gate m’tauni ya Las Vegas, Farmer anasewera yekha kwa maola anayi ndi theka pa masenti khumi pa chipindalamaChipiChizindikiro choimira ndalama yokhazikika, choikidwa pa dongosolo la mabetcha kuti mupange betcha. Chimatchedwanso: check.Werengani yonse →. Phindu linali laling’ono, koma pa kuzungulira mazana angapo iye ndi Browne anaika mwayi, mosamala, pa 25%.

Siwichi ya chala cha phazi inawerengera nthawi ya mpira; kompyuta yomangiriridwa ku thupi inagwedeza kusonyeza gawo.

Magudumu a Roulette a ku Las Vegas

Chilimwe cha 1978

Chilimwe chimenecho gululo linasewera mosinthana kwa masabata, m’tauni ndi pa Strip, magawo awiri patsiku ndipo osapita ku kasino imodzi usiku wotsatizana. Ankasunga kabuku pa kasino iliyonse: magudumu ake ndi mmene analiri osafanana ndi pansi, antchito ake, nthawi zosinthana ntchito. Magudumu a ku Las Vegas anapezeka kuti anali opendekeka mokomera ndipo masewera a usiku kwambiri anali ochedwa, zimene kompyuta inkafunikira, popeza rotor yochedwa ndi mpira wothamanga zimasiya nthawi yochuluka yoyeza ndi kubetcha. Panali mausiku abwino. Ku Circus Circus kusintha kwa croupieranthuCroupierDealer wa pa tebulo la roulette.Werengani yonse → nthawi ya ziwiri koloko usiku kunasandutsa gawo lotaya kukhala madola mazana angapo pa masenti 25 pa chipi. Ndipo panali kuwonongeka kosalekeza: mawaya omasuka, kulumikizana kwa wailesi kumene kunkasintha ndi kutentha, kugwidwa ndi magetsi kuchokera ku mawaya a antena osokedwa m’malaya awo. Usiku wina tizitsulo tinakakamira, mawaya anatentha kwambiri, ndipo Ingrid Hoermann anapitiriza kusewera ngakhale anapsa m’malo mochoka pa tebulo lopambana. Antchito a kasino anazindikira kupambanako koma osati njirayo; nthawi ina croupier, wokwiya ndi mulu wa machipi ukukula, anagwira gudumu likuzungulira ndi kulipotoza.

M’miyezi khumi ndi itatu anapita maulendo asanu ndi atatu ku Nevada ndipo, akubetcha makamaka masenti khumi ndi ma quarter, anapambana madola zikwi zingapo. Gawo ku California Club mu Disembala 1978 linabweretsa ndalama zoposa $1,000 m’maola atatu ndipo linawakhutiritsa kuti njirayo inayenera zipangizo zabwino.

Ntchitoyi, chaka ndi chaka
1975

Packard ndi Biles akuwerengera nthawi ya mipira ya roulette ndi chojambulira mawu ku Las Vegas.

1976

Gudumu la kasino logulidwa ku Reno; chilimwe cha miyeso; kompyuta yoyamba ya zigawo.

Dis 1977

Ulendo woyamba wa kasino, Lake Tahoe ndi Reno. Zipangizo zikuwonongeka.

Jan 1978

Golden Gate, Las Vegas: maola anayi ndi theka pa ndalama zobetcha za masenti khumi, mwayi unaikidwa pa 25%.

chilimwe 1978

Masabata a masewera ku Las Vegas ndi kompyuta itavalidwa pathupi.

Dis 1978

California Club: ndalama zoposa $1,000 m’maola atatu.

1980–81

Kompyuta ikupangidwanso kuti ilowe mu nsapato.

Nov 1981

Las Vegas: phokoso la magetsi likumiza kulumikizana kwa wailesi. Ntchitoyi ikuima.

1985

Nevada ikuletsa zipangizo zolosera. The Eudaemonic Pie ikufalitsidwa.

Kompyuta mu nsapato, 1980–1981

Kuti achotse mawaya m’matupi awo anaganiza zoika chilichonse mu nsapato. Mark Truitt, womaliza maphunziro a fiziki watsopano amene anachoka pa kuyankhulana kwa ntchito ya radar ya asilikali, anathera chaka chimodzi ndi theka pa ntchitoyi. Maganizo amene anapangitsa kuti zikwane anachokera kwa katswiri wa ku yunivesite: zimitsani kompyuta pakati pa maulosi, ndipo imafuna mabatire ochepa kwambiri. Truitt anaika ma chip pa ma bolodi awiri a ma circuit amene anawapanga yekha, anatembenuza limodzi pamwamba pa linzake ndi kudzaza mpata ndi phula lolimba, zimene zinapanga chidutswa cha pafupifupi mainchesi awiri kuchulukitsa anayi ndi kukhuthala kwa theka la inchi chimene chingapondedwe. Mabatire, antena ndi awiri mwa ma buzzer atatu analowa m’chidendene. Ma buzzer atatu pa maliwiro atatu anapereka zizindikiro zisanu ndi zinayi: magawo asanu ndi atatu ndi “palibe betcha”. Wosoka nsapato anabowola nsapato wamba za chikopa ndipo sanafunse mafunso.

Mu Novembala 1981 Farmer ndi wolemba Thomas Bass anatenga nsapatozo ndi $2,500 kupita ku Las Vegas. Pa tebulo loyamba kulosera koyamba kunagunda, kenako ma buzzer anayamba kulira mwachisawawa. Makasino ali odzaza ndi phokoso la magetsi, kuchokera ku makamera oyang’anira, zizindikiro za neon ndi makina a slot, ndipo linamiza kulumikizana kofooka kwa wailesi pakati pa nsapato; TV m’chipinda cha motelo inachitanso chimodzimodzi. Masiku a kukonza ndi anthu anayi sanachiritse vutoli, ndipo ntchitoyi inaimira pamenepo. Zipangizozo zinaikidwa m’bokosi m’chipinda chapansi ku Santa Cruz.

Phokoso la makina a slot, neon ndi makamera linamiza kulumikizana kofooka kwa wailesi kwa nsapato.

Tanthauzo la 44%

Pa gudumu la ku America straight upbetchaStraight upNambala imodzi, amalipira 35:1.Werengani yonse → imapambana kamodzi m’kuzungulira 38 pa avareji ndipo imalipira 35 ku 1, zimene zimawonongetsa wosewera 5.26%. Mwayi wa 44% ndiwo mtengo wa betcha lomwelo pamene limapambana kamodzi m’kuzungulira 25: machipi 36 amabwerera pa machipi 25 aliwonse obetchedwa. Choncho kompyuta sinafunikire kudziwa nambala. Inafunikira kupangitsa manambala amene inasankha kutuluka pafupifupi kamodzi ndi theka kawirikawiri kuposa mmene mwayi umalolera.

nambala yosankhidwa imapambana kamodzi m’mtengo wa straight up
kuzungulira 38 (palibe kulosera)−5.26%
kuzungulira 360%
kuzungulira 30+20%
kuzungulira 25+44%
kuzungulira 19+89%
Gudumu la ku America, 35 ku 1. Mtengo ndi 36 kugawa ndi chiwerengero cha kuzungulira, kuchotsa 1.

Gudumu ndi Malamulo a Roulette ya ku America

Chifukwa chiyani mwayi waukulu unkamvekabe ngati kutchova juga

Mwayi pa 35 ku 1 umalipira pang’onopang’ono ndi mosafanana. M’modzi mwa alangizi a gululo anachenjeza kuti wosewera wobetcha $100 pa nambala angakhale atataya $10,000 kapena $20,000 mwayi usanaonekere, ndipo masamu akugwirizana nazo: ndi mwayi wa 44% pa manambala amodzi, wosewera amakhalabe pa kutaya pambuyo pa kuzungulira 100 pafupifupi kamodzi pa kanayi. Ndicho chifukwa chake a Eudaemons anayamba pa masenti khumi ndi kumanga ndalama zosewererandalamaNdalama zosewereraNdalama zonse zimene mwazisiyira masewera. Kusamalira ndalama zosewerera ndiko kusankha kuchuluka kwake komwe mungaike pachiopsezo pa betcha lililonse ndi pa gawo lililonse la masewera.Werengani yonse → zawo kuchokera ku phindu, ndipo chifukwa chake Alan Lewis, amene analowa nawo mu 1978, anathera nthawi yake pa kuchuluka kwa ndalama zobetcha. Farmer pambuyo pake anaganiza kuti anali osamala kwambiri. Ndalama zobetcha zazing’ono zinawasunga otetezeka, komanso zinatanthauza kuti zaka za ntchito zinapeza zochepa kwambiri.

Zimene zinawonongedwa ndi zimene zinapindula

Pafupifupi $15,000 zinapita ku zigawo, zida ndi malipiro a Truitt, zambiri kuchokera kwa Farmer ndi kwa Letty Belin, loya amene pambuyo pake anakwatiwa naye. Farmer ankawerengedwa kuti anagwira ntchito maola 3,500, Truitt 3,000 ndipo Packard 2,000. Poyerekeza ndi zimenezo pali madola zikwi zingapo opambanidwa pa ndalama zobetcha zazing’ono. Mu 1983 Farmer analengeza m’magazini ya kutchova juga kufuna osunga ndalama, pofotokoza chitsanzo choyamba chokhala ndi mwayi wotsimikizika ku kasino wa 20 mpaka 40%. Pamene a Eudaemons ankasewera, kufufuza kwa Belin m’malamulo a Nevada sikunapeze kanthu kalikonse koletsa kulosera masewera; mu Meyi 1985 boma linapanga kukhala mlandu kugwiritsa ntchito chipangizo pa zimenezo. Chimene chinakhalitsa chinali sayansi. Kupanga makompyuta kunaphunzitsa Farmer, Packard ndi abwenzi awo kuphunzira chaos, kumene anadzipangira mbiri.

Kuwerenga bukuli lero

Thomas Bass, amene anabetcha pa ulendo womaliza, anafotokoza nkhaniyi mu The Eudaemonic Pie (1985), lomangidwa pa kuyankhulana kwautali ndi gululo, ndipo ndilo gwero la tsamba ili. Mbiri yake yachidule ya roulette si yodalirika ngati nkhani yake ya ntchitoyi. Imabwereza nthano ya alembi asanu ndi mmodzi olembedwa ntchito a Jagger, imene imachokera ku buku la 1901 osati kale kuposa pamenepo (onani Joseph Jagger: Njira ya Roulette ku Monte Carlo), ndipo imaika mayeso a Thorp ndi Shannon ku kasino mu 1962, pamene nkhani za Thorp mwiniwake zimati chilimwe cha 1961.

Mafunso

Kodi a Eudaemons analemera?

Ayi. Anapambana madola zikwi zingapo pa ndalama zobetcha za masenti khumi ndi ma quarter, ndipo anawononga pafupifupi $15,000 ndi maola zikwi zambiri.

Kodi kunali kovomerezeka?

Pamene ankasewera, Nevada inalibe lamulo loletsa kulosera masewera ndi chipangizo. Yakhala nalo kuyambira 1985, ndipo malo ambiri okhala ndi makasino tsopano ali nalo.

Kodi zikanagwira ntchito lero?

Ayi kumene kubetcha kumatsekedwa pamene mpira ukuponyedwa, monga mmene zimakhalira m’ma studio a pompopompo, ndipo kunyamula chipangizo choterocho kulowa mu kasino ndi mlandu m’madera ambiri.

Masamu Osangalatsa

Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.

  1. A Eudaemons ankaganiza kuti kompyuta yawo inali ndi phindu la 44% pa straight upbetchaStraight upNambala imodzi, amalipira 35:1.Werengani yonse → pa gudumu la ku America, kumene betcha limalipira 35 ku 1. Kodi nambala yosankhidwa iyenera kupambana kangati kuti zimenezo zikhale zoona? Ndipo kuneneratu kukanafunika kuchotsa tibowozipangizoKabowoChimodzi mwa tibowo 37 tokhala ndi manambala pa rotor. Kamatchedwanso: slot, cup.Werengani yonse → tingati mwa 38, ngati mpirazipangizoMpiraMpira waung’ono umene umaponyedwa mu njira motsutsana ndi rotor. Mipira yamakono ndi ya ivorine kapena Teflon, 18–21 mm.Werengani yonse → ukanakhala ndi mwayi wofanana wogwera m’kabowo kalikonse mwa totsalato?

    Onetsani yankho

    Yankho Kamodzi pa kuzungulira 25. Zimenezo n’zofanana ndi kuchotsa tibowo 13 ndi kusiya 25.

    ChipindalamaChipiChizindikiro choimira ndalama yokhazikika, choikidwa pa dongosolo la mabetcha kuti mupange betcha. Chimatchedwanso: check.Werengani yonse → chopambana chimabwerera ndi zina 35: machipi 36. Ngati nambala ipambana kamodzi pa kuzungulira n, machipi n obetchedwa amabweza 36, choncho betcha lili ndi mtengo wa 36/n − 1.

    Ikani zimenezo kukhala 0.44: 36/n = 1.44, choncho n = 25. Popanda kuneneratu n ndi 38 ndipo betcha lili ndi mtengo wa 36/38 − 1 = −5.26%.

    Tsopano tiyerekeze kuti kuneneratu kumachotsa tibowo k ndipo mpira uli ndi mwayi wofanana wogwera m’tibowo tina tiliyonse 38 − k. Chipi pa kabowo kamodzi ka iwo chimapambana kamodzi pa kuzungulira 38 − k. Kuti tipeze 44% tikufunika 38 − k = 25, choncho k = 13: kupitirira pang’ono gawo limodzi mwa atatu la gudumu.

    M’bukuli Farmer akutchulidwa akunena kuti 40% imachokera pa kuchotsa tibowo zisanu ndi zitatu. Pa chitsanzo chosavuta ichi zisanu ndi zitatu zimapereka 36/30 − 1 = 20%, choncho chithunzi chenicheni chiyenera kuti chinali chosafanana: tibowo tina totsala tinali totheka kwambiri kuposa tina.

    tibowo tochotsedwatibowo totsalamtengo wa straight up
    038−5.26%
    2360%
    830+20%
    1325+44%
    1919+89%
  2. Tiyerekeze kuti nambala yanu imapambanadi kamodzi pa kuzungulira 25 pa 35 ku 1, phindu la 44%. Mukubetcha chipi chimodzi pa kuzungulira kulikonse. Kodi muli ndi kuthekera kotani kokhala m’mbuyo pambuyo pa kuzungulira 100? Pambuyo pa 500?

    Onetsani yankho

    Yankho Pafupifupi 23% pambuyo pa kuzungulira 100 ndipo ikadali pafupifupi 6% pambuyo pa 500.

    Pambuyo pa kuzungulira 100 mwabetcha machipi 100, ndipo kupambana kulikonse kumabweza 36. Kupambana kawiri kumabweza 72, kutaya kwa 28; katatu kumabweza 108, phindu la 8. Choncho muli m’mbuyo ngati mwapambana kawiri kapena kuchepera.

    Kuthekera kopanda kupambana pa kuzungulira 100 ndi (24/25)¹⁰⁰ = 1.7%. Kupambana kamodzi ndendende: 100 × (1/25) × (24/25)⁹⁹ = 7.0%. Kawiri ndendende: 4,950 × (1/25)² × (24/25)⁹⁸ = 14.5%. Pamodzi 23.2%.

    Pambuyo pa kuzungulira 500 mukufunika kupambana 14 kuti mukhale patsogolo (14 × 36 = 504), ndipo avareji ndi 20. Kuthekera kwa 13 kapena kuchepera ndi pafupifupi 6.2%.

    Iyi ndi mbali ina ya betcha lovuta kupambana. Phindu ndi lalikulu, ndipo pafupifupi m’zotsatizana imodzi mwa zinayi za kuzungulira 100 silioneka. Wosewera amene sakudziwa motsimikiza kuti phindulo lilipo sangathe kusiyanitsa zotsatizana zoipa ndi kompyuta yowonongeka, ndipo umenewo ndi mkhalidwe umene a Eudaemons ankakhala nawo kawirikawiri.

    kuzungulirakupambana kofunikira kuti mukhale patsogolokuthekera kokhala m’mbuyo
    50240.1%
    100323.2%
    200618.6%
    500146.2%
  3. Bukuli likuti ndi phindu la 44%, $100 yobetchedwa ka 50 pa ola iyenera kupeza $2,200 pa ola. Yang’anani. Kenako werengerani zimene phindu lomwelo linapeza pa ndalama zimene gululo linaseweradi: dime pa kuzungulira kulikonse.

    Onetsani yankho

    Yankho $2,200 ndi yolondola pa $100 pa kuzungulira kulikonse. Pa dime pa kuzungulira kulikonse ndi $2.20 pa ola.

    Phindu ndi gawo la chilichonse chobetchedwa. Pa $100 pa kuzungulira kulikonse ndi kuzungulira 50 pa ola, $5,000 imabetchedwa, ndipo 44% ya zimenezo ndi $2,200.

    Pa masenti 10 pa kuzungulira kulikonse, $5 imabetchedwa pa ola, ndipo 44% ya $5 ndi $2.20. Ngakhale kuphimba manambala anayi pa dime iliyonse, ndi $8.80 pa ola kwa anthu awiri.

    Gululo linasewera pa ndalama zochepa chifukwa linkamanga ndalama zosewererandalamaNdalama zosewereraNdalama zonse zimene mwazisiyira masewera. Kusamalira ndalama zosewerera ndiko kusankha kuchuluka kwake komwe mungaike pachiopsezo pa betcha lililonse ndi pa gawo lililonse la masewera.Werengani yonse → kuchokera pa zero ndiponso chifukwa, monga chithunzithunzi chapamwambachi chikusonyezera, phindu la 44% pa 35 ku 1 lingathe kutaya kwa maola ambiri. Mtengo wa kusamala kumeneko unali wakuti njirayo ingathe kugwira ntchito bwinobwino koma n’kulipirabe zochepa kuposa ntchito.

Nthabwala yopumitsa

Fiziki inagwira ntchito. Neon inapambana.

Fiziki inagwira ntchito. Neon inapambana.

Magwero

  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, mutu 465. Gawo 465.075, kugwiritsa ntchito chipangizo kulosera zotsatira za masewera (1985).
zinawunikidwa 2026-09-28chitsanzo: ya ku Ulaya, ziro imodzinjira zowerengera ↗magwero ↗