Laboratuwaar Ruleet · Laboratuwaar · Fiisik · hojomaaji 8

Leeɓnugol

Feccere wootere e taarol nde hiisetee ado e goonga.

Jaabawol rabbiɗngol

Leeɓnugol bal dow laawol ina rewa diidol newɗungol ngol frotomaa e haɗtirde henndu tabintini. E waktuuji tuurji seeɗa, aɗa waawi hiisaade waktu yanugol haa e feccere segonde. Sankitagol caggal ɗuum ina hayra ko ɓuri heewde e ndee peewal.

modeel
v′ = −(a + b·v)
hiisa ado dow laawol
toowɗo
hiisa ado caggal yanugol
lesɗo
juumre waktu yanugol
0,1–0,3 s ina waawi heɓeede

Modeel ngal

Jeewo balkuutorɗeBalBal tokoosal werlaangal e laawol ngol e laawol rotoor ngol. Balli jamaanu hannde ko ivorine walla Teflon, 18–21 mm.Tar fof → ngal no ina leeɓa e geɗal waylotaakal a (frotomaa taarnagol) e geɗal yahdungal e yaawre b·v (haɗtirde henndu e majjere yahdunde e yaawre): dv/dt = −(a + bv). Jaabawol ngol ko ɓadtagol ekspoonansiyel faade e yaawre yanugol keerol. Waktu tuur T = 2πr/v noon ina ɓeydoo e kala tuur e ɓeydaari mawnoori. Hiisa a e b e tuurji adiiɗi seeɗa, tuurji heddiiɗi e waktu yanugol ina njokka. Hay huunde ɗoo haawnaaki; ko mekanik hitaande arandeere jaaɓnaande e bal dow laawol.

ko betaafotndugol modeeltuurji heddiiɗi hiisaaɗi adowaktu yanugol hiisaaɗo adogoonga
tuurji 1–3: 0,63, 0,67, 0,72 sa, b fotndaama912,6 s12,4 s
tuurji 1–4fotndugol kadi812,5 s12,4 s
tuurji 1–6fotndugol kadi612,4 s12,4 s
Misal. Kala tuur ɓeydiiɗo ina ɓeyda peewal hiisa oo. E golle, juumre 0,1–0,3 s e yanugol ina waawi heɓeede so laawol ngol ina laaɓi, jungo kadi ina tabiti.

Ko hiisa oo rokkata

Waktu yanugol haa e 0,2 segonde, kawrudo e yaawre rotoorkuutorɗeRotoorGeɗal taarorde taarotooɗo, roondiiɗo cuuɗi ɗii.Tar fof → cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → 15 e kala segonde, ina holla suudu nde woni les nokku yanugol haa e hedde cuuɗi tati. Ɗum ko kabaaru moƴƴo ngam hiisoowo ado. Kabaaru bonɗo ko bal ngal ina taƴa tellordekuutorɗeTellordeNokku tellungo hakkunde laawol bal e cuuɗi ɗii, ɗo deflektooruuji ɗii ngoni.Tar fof → caggal ɗuum, ina fiya deflektoorkuutorɗeDeflektoorGooto e haɗooji njamndi woodɗi e tellorde ɗi saŋkitinta bal ina jippoo. Ina noddee kadi: kanuu, diyamaa, pinngu.Tar fof → ina diwa dow ceerlekuutorɗeCeeralCeerndorgal njamndi hakkunde cuuɗi ɗiɗi e taarorde.Tar fof →, suudu sakkitiindu kadi ina sankitoo e senndugol njaajeendi mum cuuɗi 20 haa 30. Peewal daawal laawol ina ñaamee ko ɓuri heewde e sankitagol daawal yanugol.

Fiisik Bal RuleetYaawre Rotoor Ruleet

Ko heddii

So senndugol sankitagol ina jogii mood, hono bal ngal ina ɓura tabitaade takko suudu yanugol ko e sahaa, waɗde pari e geɗaltaarordeGeɗal taarordeCeeɓnde cuuɗi takkondirɗi e taarorde, ceertunde e mooftere e tapi.Tar fof → takko suudu hiisaandu ado ina rokka ɓural tokoosal. Small e Tse (2012) betii ɗum e laboratuwaar e kamera, tawi keewal hebgol geɗal hiisaangal ado ina toowi no haanirta ngam waylude ɓural kasinomatematikƁural kasinoGeɗal kala pari ngal kasino jogiiyata e hakkundeere: 2,70% e ruleet Orop.Tar fof → ɓural fijoowo teemedere seeɗa. Ngonkaaji mum, yiyde taarorde fof gila dow, taarorde anndaande, pariiji waɗaaɗi caggal nde bal ngal werlaa, ngalaa e taabal live.

Toon peewal ngal majjata (misal)cuuɗi sikke
waktu yanugol ±0,2 s × cuuɗi 15/s
± 3
betugol nokku rotoor
± 1
fiyagol deflektoor
± 10
diwgol dow ceerle
± 6
cuuɗi sikke
05± 10
Ɗiɗi adiiɗi ɗii ina mbaawi ustaade e ekkitaagol e kuutorɗe. Ɗiɗi sakkitiiɗi ɗii ko mbaadi taarorde ndee.

Ko waylitotoo waktu e waktu

Limooje ɗiɗi ɗee tabitaani e taarorde. Eudaemons, ɓe hiisii waktu taarorde kasino duuɓi keewɗi e duuɓi 1970, tawii ko henndu leeɓnata ko ɓuri heewde, ɓuri laawol ngol, tawi kadi bal ngal ina waɗa huunde: bal Teflon ina leeɓa laabi ɗiɗi ɓuri bal mahaaɗo e kompoosit bal biyaar. Ɓe njiyii kadi hiisa mum ina ooñoo 5 haa 10% e kala waktu so damal udditaama walla weeyo waylitii, sabu henndu ɓuuɓndu walla teddundu ina ɓura yaawde leeɓnude bal ngal. Porogaraam mum noon ina jogii teelnde ceertunde ngam njaawdi leeɓnugol bal ngal e ngam yaawre nde jaltata laawol ngol, fijoowo oo kadi ina fuɗɗitnoo ɗe ɗiɗi fof e kala taabal e kala nde hiisa ɗee fuɗɗii ooñaade.

Eudaemons ɓen

Ko waɗi Laboratuwaar ina firta ɗum

Wonaa ngam kala gooto waawa waɗde ɗum. Ko ngam hollude ko sahaa fijo ngo woni e goonga: daawal anndeteengal ado ngal kasinooji ndenndata e uddugol pariiji law e tuurji les, e daawal jiiɓiiɗal ngal ndenndata e deflektooruuji e ceerle lesɗe. Fijoowo faamɗo ɗum ina faami ko waɗi 2,70% oo ina hisi.

Waɗde hiisa oo hoore maa

Hiisa waktu bal ngal ina payta takko deflektoor e kala widewo live tuurji tati, jokkaa hiisa oo; ko ɓuri heewde aɗa wona haa e tuur gooto e yanugol, ɗum ko daawal anndeteengal ado ina golloo no sifiraa. Caggal ɗuum ndaar toon bal ngal tabitata e goonga e nder suudu nde woni les nokku yanugol, winndaa limto ngam taarle capanɗe joy. Limto oo ko senndugol sankitagol, njaajeendi mum kadi ko jaabawol “ko waɗi ɗum fooɗaaka?”.

Kronomeetar ina hiisa waktu bal ngal ina payta takko deflektoor; limto oo ina wonta senndugol sankitagol.

Formil

dv/dt = −(a + b·v)
T(tuur) = 2πr / v

Naamne

Hol modeel ngal ina feewi timmi?

Alaa. Frotomaa ina waylitoo e pundu, ɓuuɓol e ɓoyɗugol. Hiisooɓe ado ina fotndita e kala taarol.

Tuurji jelu ngoni ko haaniɗaa?

Tati ina rokka hiisa hedde; joy walla jeegom hiisa moƴƴo. Tuurji les nay studio ina accita waktu seeɗa ngam waɗde pari, pariiji kadi uddaama no woorir.

Hol gooto heɓii kaalis e ndee laawol?

Seeɗa, waktu rabbiɗɗo, e kuutorɗe, ado kasinooji fotndaade sariyaaji kadi njokka. Ƴeew Fijo Ɓural e Ruleet.

Weltaare e Matematik

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

  1. E mbaadi hollirteendi Thorp ngam balkuutorɗeBalBal tokoosal werlaangal e laawol ngol e laawol rotoor ngol. Balli jamaanu hannde ko ivorine walla Teflon, 18–21 mm.Tar fof → leelnoowal, so taarol gootol e laawol ngol ina naamnoo segonde T, bal ngal ina heddii taarle 1/(e^(3T/20) − 1) − 10/3 hade mum yaltude e laawol ngol. Taarle njelu heddotoo caggal taarol feccere segonde, e caggal taarol segonde timmunde? Juumre ƴeewndagol sahaa 0,012 segonde e T = 0,8 ina dirna hiinnirgal ngal no foti?

    Hollu jaabawol ngol

    Jaabawol Hono taarle 9,5 caggal taarol feccere segonde e 2,85 caggal taarol segonde wootere. Juumre ndee ina dirna hiinnirgal ngal hono 0,12 taarol, hono cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → 4½.

    T = 0,5: 3T/20 = 0,075 e e^0,075 ≈ 1,0779, ɗum waɗi 1/0,0779 ≈ 12,84, e 12,84 − 3,33 ≈ 9,51 taarle. T = 1: e^0,15 ≈ 1,1618, 1/0,1618 ≈ 6,18, e 6,18 − 3,33 ≈ 2,85. Taarol yaawngol ina firta taarle keewɗe ina heddii, taarol leelngol laabi ɗiɗi ina accoo ko ɓuri famɗude tataɓal.

    E T = 0,8 formil ngol ina addi taarle 4,51; e T = 0,812 ina addi 4,39. Juumre 12 e nder ujunnaaje segonde, hono sahaa mo bal ngal naamnotoo ngam taarnaade yaajeende mum, ina dirna hiinnirgal ngal 0,12 taarol: hono cuuɗi 4½ e taarorde cuuɗi 37. Juumre wootere ndee ko ko ɓuri heewde e cuuɗi 5,5 ɗi bujee juumte Thorp accata ngam ƴeewndagol sahaa bal ngal (ƴeew Fijo Ɓural e Ruleet), ɗum ko waɗi montoor, wonaa limngal, ko keerata hiinnoowo.

Ƴeewndo weltinoowo

Ina hiisee ado haa yanugol. Caggal ɗuum, deflektooruuji.

Ina hiisee ado haa yanugol. Caggal ɗuum, deflektooruuji.

Iwdi

  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.
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ƴeewtaa 2026-09-28misal: ruleet Orop, seero gootolaawol golle ↗iwdi ↗