Ilabhorethri ye-roulette · Ilabhorethri · I-physics · imizuzu 8

Ukwehla kwesivinini

Okuwukuphela kwengxenye yokujikeleza engabikezelwa ngempela.

Impendulo emfushane

Ukwehla kwesivinini sebhola emzileni kulandela ijika elibushelelezi elinqunywa ukuhuquzela nokumelana komoya. Ngezikhathi ezimbalwa zemijikelezo ungalinganisa isikhathi sokuwa ngokunemba okuyingxenye yomzuzwana. Ukuhlakazeka okulandelayo kuqeda iningi lalokho kunemba.

imodeli
v′ = −(a + b·v)
ukubikezeleka emzileni
phezulu
ukubikezeleka ngemva kokuwa
phansi
iphutha lesikhathi sokuwa
0.1–0.3 s kungafinyelelwa

Imodeli

Thatha ibholaokokusebenzaIbholaIbhola elincane eliphonswa emzileni libheke ngakolunye uhlangothi lwe-rotor. Amabhola esimanje enziwa nge-ivorine noma nge-Teflon, angu-18–21 mm.Funda konke → njengelehlisa isivinini ngenxa yenani elingashintshi u-a (ukuhuquzela kokugingqika) kanye nenani elihambisana nesivinini u-b·v (ukumelana komoya nokulahlekelwa okuncike esivinini): dv/dt = −(a + bv). Isixazululo siwukusondela ngokwe-exponential esivinini esibalulekile sokuwa. Ngakho isikhathi somjikelezo u-T = 2πr/v sikhula umjikelezo ngamunye ngenani elikhulayo. Thola u-a no-b emijikelezweni embalwa yokuqala, bese imijikelezo esele, nesikhathi sokuwa, kuyalandela. Akukho lutho olungajwayelekile lapha; yi-mechanics yonyaka wokuqala esetshenziswa ebholeni elisemzileni.

okulinganisiweukufaniswa kwemodeliimijikelezo esele ebikezelweisikhathi sokuwa esibikezelweokwangempela
imijikelezo 1–3: 0.63, 0.67, 0.72 skutholwe u-a no-b912.6 s12.4 s
imijikelezo 1–4ukufanisa kabusha812.5 s12.4 s
imijikelezo 1–6ukufanisa kabusha612.4 s12.4 s
Isibonelo. Umjikelezo ngamunye owengeziwe wenza isilinganiso sinembe kakhudlwana. Empilweni yangempela iphutha elingu-0.1–0.3 s lapho liwa lingafinyelelwa uma umzila uhlanzekile nesandla singanyakazi.

Lokho okutholwa yisilinganiso

Isikhathi sokuwa esinembe ngaphakathi kwemizuzwana engu-0.2, kuhlanganiswe nesivinini se-rotorokokusebenzaI-rotorIngxenye yesondo ejikelezayo ephethe amagodi.Funda konke → samagodiokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → ayi-15 ngomzuzwana, sithola igodi elingaphansi kwendawo yokuwa ngokunemba okucishe kube ngamagodi amathathu. Lezo yizindaba ezinhle kumbikezeli. Izindaba ezimbi ukuthi ibhola bese liwela i-apronokokusebenzaI-apronIndawo ethambekile phakathi komzila webhola namagodi, lapho kuhlala khona ama-deflector.Funda konke →, lishaye i-deflectorokokusebenzaI-deflectorEsinye sezithiyo zensimbi ezisendaweni ye-apron ezihlakaza ibhola eliwayo. Kubuye kuthiwe: canoe, diamond, pin.Funda konke → futhi ligxume liwela ama-fretokokusebenzaI-fretIsihlukanisi sensimbi phakathi kwamagodi amabili esondweni.Funda konke →, kanti igodi lokugcina lisabalala ekusabalaleni okubanzi ngamagodi angu-20 kuya kwangu-30. Ukunemba kwesigaba somzila kuqedwa kakhulu ukuhlakazeka kwesigaba sokuwa.

I-physics yebhola le-rouletteIsivinini se-rotor ye-roulette

Okusalayo

Uma ukusabalala kokuhlakazeka kunendawo evame kakhulu, okwenza ibhola liwele eduze negodi lokuwa kaningi kunangokungahleliwe, khona-ke ukubheja esigabeniisondoIsigabaIngxenye eqhubekayo yamagodi alandelanayo esondweni, ehlukile eqenjini lezinombolo ethebuleni lokubheja.Funda konke → esizungeze igodi elibikezelwe kunikeza inzuzo encane. U-Small no-Tse (2012) bakulinganisa lokhu elabhorethri ngekhamera futhi bathola ukuthi izigaba ezibikezelwe zishaywa kaningi ngokwanele ukuguqula inzuzo yekhasinoizibaloInzuzo yekhasinoIngxenye yenani ngalinye elibhejwayo ikhasino eyigcinayo ngokwesilinganiso: ama-2.70% ku-roulette yaseYurophu.Funda konke → ibe yinzuzo yomdlali engamaphesenti ambalwa. Izimo zabo, ukubona ngokuphelele kusuka phezulu, isondo elaziwayo, ukubheja ngemva kokuqaliswa kwebhola, azikho etafuleni elibukhoma.

Lapho ukunemba kuya khona (isibonelo)amagodi okungaqiniseki
isikhathi sokuwa ±0.2 s × amagodi ayi-15/s
± 3
ukulinganiswa kwesimo se-rotor
± 1
ukushaya i-deflector
± 10
ukugxuma kuma-fret
± 6
amagodi okungaqiniseki
05± 10
Okubili kokuqala kunganciphiswa ngokuzijwayeza nangemishini. Okubili kokugcina kungukwakheka kwesondo.

Okushintshayo ihora nehora

La manani amabili awahlali enjalo njalo esondweni elithile. Ama-Eudaemon, abebala isikhathi sesondo lekhasino iminyaka eminingi ngama-1970, athola ukuthi umoya yiwona owehlisa isivinini kakhulu, ngaphezu komzila, nokuthi ibhola libalulekile: ibhola le-Teflon lalahlekelwa isivinini ngokushesha okuphindwe kabili kunelenziwe ngento yamabhola e-billiard. Babona nokuthi izibikezelo zabo zishelela ngo-5 kuya ku-10% ngehora lapho kuvulwa umnyango noma isimo sezulu sishintsha, ngoba umoya omanzi noma osindayo wehlisa isivinini sebhola masinyane. Ngakho uhlelo lwabo lwalugcina izilungiselelo ezihlukene zezinga lokwehla kwesivinini sebhola nezesivinini eliphuma ngaso emzileni, futhi umdlali wayezisetha kabusha kokubili etafuleni ngalinye nanoma nini lapho izibikezelo ziqala ukuphambuka.

Ama-Eudaemons

Kungani iLabhorethri ichaza lokhu

Hhayi ukuze noma ubani akwenze. Ukubonisa ukuthi ukungahleleki komdlalo kwakhiwe yini ngempela: isigaba esinqunyiwe amakhasino asivikela ngokuvala ukubheja kusenesikhathi nangenani eliphansi kakhulu lemijikelezo, kanye nesigaba esiyisiphithiphithi asivikela ngama-deflector nama-fret aphansi. Umdlali okuqondayo lokhu uyaqonda ukuthi kungani i-2.70% iphephile.

Ukuzenzela izibalo wena

Bala isikhathi sebhola lidlula i-deflector kunoma yikuphi ukusakaza imijikelezo emithathu bese welula isibalo; uzobe usondele ngomjikelezo owodwa ekuweni iningi lesikhathi, okuyisigaba esinqunyiwe sisebenza njengoba kuchaziwe. Bese ubuka ukuthi ibhola liwela kuphi ngempela uma liqhathaniswa negodi elingaphansi kwendawo yokuwa, futhi ugcine amanani okujikeleza okungamashumi amahlanu. Lawo manani awukusabalala kokuhlakazeka, futhi ububanzi bawo buyimpendulo yombuzo othi “kungani lokhu kungehlulwa?”.

I-stopwatch ibala isikhathi sebhola lidlula i-deflector; amanani aqoqiwe aba ukusabalala kokuhlakazeka.

Ifomula

dv/dt = −(a + b·v)
T(umjikelezo) = 2πr / v

Imibuzo

Ingabe imodeli inembile ngokuphelele?

Cha. Ukuhuquzela kuyahluka ngenxa yothuli, umswakama nokuguga. Ababikezeli baphinda bafanise imodeli ekujikelezeni ngakunye.

Udinga imijikelezo emingaki?

Emithathu inikeza isilinganiso esingacacile kahle; emihlanu noma eyisithupha inikeza esihle. Inani eliphansi kakhulu lezitudiyo, imijikelezo emine, lishiya isikhathi esincane sokubheja, futhi ukubheja kuvaliwe noma kunjalo.

Ingabe ukhona owenza imali ngale ndlela?

Abambalwa, isikhashana, ngamadivayisi, ngaphambi kokuthi amakhasino azivumelanise nesimo nemithetho ilandele. Bheka ukudlala ngenzuzo yomdlali.

Ubumnandi bezibalo

Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.

  1. Kumodeli ka-Thorp yokubonisa ibholaokokusebenzaIbholaIbhola elincane eliphonswa emzileni libheke ngakolunye uhlangothi lwe-rotor. Amabhola esimanje enziwa nge-ivorine noma nge-Teflon, angu-18–21 mm.Funda konke → elehlisa ijubane, uma umjikelezo owodwa kumzila uthatha imizuzwana engu-T, ibhola lisele nemijikelezo engu-1/(e^(3T/20) − 1) − 10/3 ngaphambi kokuba lishiye umzila. Mingaki esele ngemuva komjikelezo wengxenye yomzuzwana, nangemuva kowomzuzwana ophelele? Iphutha lokulinganisa isikhathi lemizuzwana engu-0.012 ku-T = 0.8 lisusa ukubikezela kangakanani?

    Bonisa isixazululo

    Impendulo Cishe imijikelezo engu-9.5 ngemuva komjikelezo wengxenye yomzuzwana no-2.85 ngemuva komjikelezo womzuzwana owodwa. Iphutha lisusa ukubikezela cishe ngo-0.12 womjikelezo, cishe amagodiokokusebenzaIgodiEsinye sezikhala ezingu-37 ezinezinombolo ku-rotor. Kubuye kuthiwe: slot, cup.Funda konke → angu-4½.

    T = 0.5: 3T/20 = 0.075 futhi e^0.075 ≈ 1.0779, ngakho 1/0.0779 ≈ 12.84, futhi 12.84 − 3.33 ≈ 9.51 wemijikelezo. T = 1: e^0.15 ≈ 1.1618, 1/0.1618 ≈ 6.18, futhi 6.18 − 3.33 ≈ 2.85. Umjikelezo osheshayo usho imijikelezo eminingi esasele, kanti umjikelezo ohamba kancane kabili ushiya ngaphansi kwengxenye yesithathu yayo.

    Ku-T = 0.8 ifomula inikeza imijikelezo engu-4.51; ku-T = 0.812 inikeza engu-4.39. Iphutha lezingxenye ezingu-12 kwenkulungwane zomzuzwana, cishe isikhathi ibhola elisithathayo ukugingqika ububanzi balo, lisusa ukubikezela ngo-0.12 womjikelezo: cishe amagodi angu-4½ esondweni elinamagodi angu-37. Lelo phutha elilodwa liyingxenye enkulu yamagodi angu-5.5 uhlelo lwamaphutha luka-Thorp oluwavumelayo ekulinganiseni isikhathi sebhola (bheka “Ukudlala ngenzuzo yomdlali ku-roulette”), futhi yingakho iwashi, hhayi izibalo, elikhawulela umbikezeli.

Okokuhlekisa

Kungabikezelwa kuze kufike ukuwa. Bese kufika ama-deflector.

Kungabikezelwa kuze kufike ukuwa. Bese kufika ama-deflector.

Imithombo

  1. Small, M. & Tse, C. K. “Predicting the outcome of roulette.” Chaos 22(3), 2012.
  2. Bass, T. A. The Eudaemonic Pie. Houghton Mifflin, 1985.
  3. Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
kubuyekezwe ngo-2026-09-28imodeli: yaseYurophu, iqanda elilodwaindlela yokusebenza ↗imithombo ↗