Lab yeRoulette · Lab · Fizikisi · maminitsi 8

Kuderera kweKumhanya

Chikamu chimwe chete chekutenderera chinofanotaurika chaizvo.

Mhinduro pfupi

Kuderera kwebhora pamugero kunotevera mutsetse wakatsetseka unotarwa nekukwizana nemhepo. Kubva panguva dzekutenderera kushoma munogona kufungidzira nguva yekuwira kusvika pachikamu chesekondi. Kuparadzira kunotevera kunoparadza zvakawanda zvekunyatsoita ikoko.

modhi
v′ = −(a + b·v)
kufanotaurika pamugero
kwakakwira
kufanotaurika mushure mekuwira
kwakaderera
kukanganisa nguva yekuwira
0.1–0.3 s zvinogoneka

Modhi

Tarisai bhoramidziyoBhoraBhora diki rinokandwa mumugero richienda rimwe divi nerotor. Mabhora emazuva ano ndeeivorine kana Teflon, 18–21 mm.Verengai zvese → serinoderera nekuda kwechikamu chisingachinji a (kukwizana kwekukunguruka) nechikamu chinoenderana nekumhanya b·v (kudzivirirwa nemhepo nekurasikirwa kunoenderana nekumhanya): dv/dt = −(a + bv). Mhinduro ndeyekuswedera kweexponential kukumhanya kwemuganho kwekuwira. Nokudaro nguva yekutenderera T = 2πr/v inowedzera pakutenderera kwega kwega nehuwandu hunokura. Wanai a na b kubva pakutenderera kwekutanga kushoma, uye kutenderera kwasara, nenguva yekuwira, zvinotevera. Hapana chinhu chinoshamisa pano; masvomhu efizikisi egore rekutanga ari kushandiswa kubhora riri pamugero.

zvakayerwakuenzanisa modhikutenderera kwasara kwakafanotaurwanguva yekuwira yakafanotaurwachaiyo
kutenderera 1–3: 0.63, 0.67, 0.72 sa, b zvawanikwa912.6 s12.4 s
kutenderera 1–4kuenzanisa patsva812.5 s12.4 s
kutenderera 1–6kuenzanisa patsva612.4 s12.4 s
Muenzaniso. Kutenderera kwega kwega kwawedzerwa kunonyatsoita kufungidzira. Muchiitiko kukanganisa kwe0.1–0.3 s pakuwira kunogoneka nemugero wakachena neruoko rwakadzikama.

Zvinowanikwa nekufungidzira uku

Nguva yekuwira kusvika pa0.2 sekondi, pamwe nekumhanya kwerotormidziyoRotorChikamu chevhiri chinotenderera chakatakura makomba.Verengai zvese → kwemakombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → 15 pasekondi, kunowana gomba riri pasi penzvimbo yekuwira kusvika pamakomba matatu. Iyo ndiyo nhau yakanaka kumufanotauri. Nhau yakaipa ndeyekuti bhora rinobva rayambuka apronmidziyoApronNzvimbo yakatsetseka pakati pemugero webhora nemakomba, panogara madeflector.Verengai zvese →, rorova deflectormidziyoDeflectorChimwe chezvipingamupinyi zvesimbi paapron zvinoparadzira bhora riri kuwira. Mamwe mazita: canoe, diamond, pin.Verengai zvese → uye rosvetuka richiyambuka mafretmidziyoFretRusvingo rwesimbi pakati pemakomba maviri pavhiri.Verengai zvese →, uye gomba rekupedzisira rinoparadzirwa mukugovaniswa kwakafara makomba 20 kusvika 30. Kunyatsoita kwechikamu chemugero kunonyanya kudyiwa nekuparadzira kwechikamu chekuwira.

Fizikisi yeBhora reRouletteKumhanya kweRotor yeRoulette

Zvinosara

Kana kugovaniswa kwekuparadzira kuine mode, zvekuti bhora rinomhara pedyo negomba rekuwira kazhinji kupfuura zvisina hurongwa, ipapo kubheja chikamu chevhirivhiriChikamu chevhiriRutivi rwemakomba akatevedzana pavhiri, rwakasiyana neboka riri patafura yekubhejera.Verengai zvese → chakatenderedza gomba rakafanotaurwa kunopa mukana mudiki. Small naTse (2012) vakazviyera mulaboratori nekamera vakawana kurova kwechikamu chakafanotaurwa kwakakwira zvakakwana kushandura chikamu chekasinomasvomhuChikamu chekasinoChikamu chemari yega yega yakabhejwa chinochengetwa nekasino paavhareji: 2.70% muRoulette yeEurope.Verengai zvese → kuva mukana wemutambi wezvikamu zvishoma zvepesenti. Mamiriro avo, kuona vhiri rese kubva kumusoro, vhiri rinozivikanwa, mabheti achiiswa bhora ratokandwa, haavepo patafura yemhenyu.

Kunoenda kunyatsoita (muenzaniso)makomba ekusava nechokwadi
nguva yekuwira ±0.2 s × makomba 15/s
± 3
kuyera chikamu cherotor
± 1
kurova deflector
± 10
kusvetuka pamafret
± 6
makomba ekusava nechokwadi
05± 10
Zviviri zvekutanga zvinogona kuderedzwa nekudzidzira nemidziyo. Zviviri zvekupedzisira ndiwo magadzirirwo evhiri.

Zvinochinja paawa neawa

Maconstant maviri haana kutarwa zvachose pavhiri. VaEudaemons, vakayera nguva yevhiri rekasino kwemakore akawanda muma1970, vakaona kuti mhepo ndiyo inonyanya kuderedza bhora, kupfuura mugero, uye kuti bhora rine basa: bhora reTeflon rairasikirwa nekumhanya kaviri nekukurumidza kupfuura rakagadzirwa nezvinhu zvebhora rebhiridha. Vakaonawo kufanotaura kwavo kuchitsauka ne5 kusvika 10% paawa kana musuwo wazarurwa kana mamiriro ekunze achinja, nokuti mhepo ine hunyoro kana inorema inoderedza bhora nekukurumidza. Purogiramu yavo nokudaro yaichengeta zvigadziriso zvakasiyana zvechiyero chekuderera kwebhora nezvekumhanya kwarinobuda nako mumugero, uye mutambi aigadzirisa zvese zviri zviviri patafura imwe neimwe uye zvakare kana kufanotaura kwatanga kutsauka.

The Eudaemons

Nei Lab ichitsanangura izvi

Kwete kuti chero munhu azviite. Kuratidza kuti kusava nehurongwa kwemutambo kunoumbwa nei chaizvo: chikamu chinofanotaurika chinodzivirirwa nemakasino nekuvhara mabheti nekukurumidza nehuwandu hushoma hwekutenderera, nechikamu chemhirizhonga chavanodzivirira nemadeflector nemafret akaderera. Mutambi anonzwisisa izvi anonzwisisa kuti nei 2.70% yakachengeteka.

Kuita masvomhu imi pachenyu

Yerai nguva yebhora richipfuura deflector muvhidhiyo ipi zvayo inotepfenyurwa kwekutenderera kutatu mofungidzira kuenda mberi; kazhinji muchange muri mukati mekutenderera kumwe kwekuwira, ndicho chikamu chinofanotaurika chichishanda sezvatsanangurwa. Ipapo tarisai panomhara bhora chaizvo zvichienzaniswa negomba riri pasi penzvimbo yekuwira, monyora kwekutenderera makumi mashanu. Zvamanyora ikugovaniswa kwekuparadzira, uye upamhi hwako ndihwo mhinduro ku“nei izvi zvisingakundike?”.

Stopwatch inoyera nguva yebhora richipfuura deflector; zvakanyorwa zvinova kugovaniswa kwekuparadzira.

Fomula

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

Mibvunzo

Modhi yakarurama chaizvo here?

Kwete. Kukwizana kunochinja neguruva, hunyoro uye kusakara. Vafanotauri vanoenzanisa patsva pakutenderera kwega kwega.

Munoda kutenderera kungani?

Kutatu kunopa kufungidzira kwekungoti; kushanu kana kutanhatu kunopa kwakanaka. Minimum yemasitudhiyo yekutenderera kuna inosiya nguva shoma yekubheja, uye mabheti anenge akatovharwa.

Pane munhu akamboita mari nenzira iyi here?

Vashoma, kwenguva pfupi, nemidziyo, makasino asati achinja uye mitemo isati yatevera. Onai Kutamba neMukana muRoulette.

Kutamba neMasvomhu

Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.

  1. Mumuenzaniso waThorp wekutsanangura bhoramidziyoBhoraBhora diki rinokandwa mumugero richienda rimwe divi nerotor. Mabhora emazuva ano ndeeivorine kana Teflon, 18–21 mm.Verengai zvese → riri kuderera, kana kutenderera kumwe mumugero kuchitora masekondi T, bhora rine kutenderera kwe1/(e^(3T/20) − 1) − 10/3 kwasara risati rabuda mumugero. Kwasara kungani mushure mekutenderera kwehafu yesekondi, uye mushure mekwesekondi yose? Kukanganisa kwekuyera nguva kwemasekondi 0.012 pa T = 0.8 kunofambisa kufanotaura zvakadii?

    Ratidza mhinduro

    Mhinduro Anenge kutenderera 9.5 mushure mekutenderera kwehafu yesekondi uye 2.85 mushure mekwesekondi imwe. Kukanganisa kunofambisa kufanotaura nechikamu che0.12 chekutenderera, anenge makombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → 4½.

    T = 0.5: 3T/20 = 0.075 uye e^0.075 ≈ 1.0779, saka 1/0.0779 ≈ 12.84, uye 12.84 − 3.33 ≈ kutenderera 9.51. T = 1: e^0.15 ≈ 1.1618, 1/0.1618 ≈ 6.18, uye 6.18 − 3.33 ≈ 2.85. Kutenderera kunokurumidza kunoreva kutenderera kuzhinji kwasara, uye kutenderera kwakanonoka kaviri kunosiya kushoma pane chikamu chimwe muzvitatu.

    Pa T = 0.8 fomula inopa kutenderera 4.51; pa T = 0.812 inopa 4.39. Kukanganisa kwe12 pazviuru zvesekondi, anenge nguva inotorwa nebhora kumonera upamhi hwaro, kunofambisa kufanotaura ne0.12 yekutenderera: anenge makomba 4½ evhiri rine makomba 37. Kukanganisa ikoko kumwe chete ndiko kuzhinji kwemakomba 5.5 anobvumirwa nebhajeti yezvikanganiso yaThorp pakuyera nguva yebhora (onai Advantage Play), uye ndosaka wachi, kwete huverengi, ichiganhurira mufanotauri.

Kuseka zvishoma

Zvinofanotaurika kusvika pakuwira. Ipapo madeflector.

Zvinofanotaurika kusvika pakuwira. Ipapo madeflector.

Zvinyorwa

  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.
yakaongororwa 2026-09-28modhi: yeEurope, zero imwemaitiro ↗zvinyorwa ↗