Yiwuwa a roulette
Kowace yiwuwa a roulette adadin ramuka ne da aka raba da 37.
p = lambobin da caca ta rufe / 37. Lamba ɗaya: 2.70%. Lambobi goma sha takwas: 48.65%. Yiwuwar wani jerin sakamako na musamman tana fitowa ne ta hanyar ninka yiwuwar kowane juyi.
Juyi ɗaya
Kowane ɗaya daga cikin ramukakayan aikiRamiƊaya daga cikin ɗakuna 37 masu lamba a kan rotor. Ana kuma kiransa: slot, cup.Karanta gaba ɗaya → 37 yana da dama iri ɗaya, don haka damar yin nasara a roulette a juyi ɗaya batu ne na ƙirgawa kawai. Cacar da ta rufe lambobi huɗu tana yin nasara sau 4/37, kusan 10.8%. Babu wani abu fiye da wannan a cikin yiwuwalissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya → ta juyi ɗaya, shi ya sa za a iya nazarin wasan gaba ɗaya a kan ƙaramar takarda.
Juye-juye da yawa
Juye-juye ba sa dogara da juna, don haka ana ninka yiwuwar jerin sakamako. JacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → sau biyu a jere: (18/37)² = 23.7%. Ja sannan sifilidabaranSifiliRamin kore guda ɗaya da babu cacar ɗaya zuwa ɗaya, ta dozin ko ta ginshiƙi da ke rufe shi; tushen fifikon gidan caca. Ana kuma kiransa: sifili ɗaya, 0.Karanta gaba ɗaya →: (18/37)(1/37) = 1.3%. Lamba goma sha bakwai sau biyu a jere: (1/37)² = 0.073%, kusan sau ɗaya cikin 1,369. Tsari yana da muhimmanci ga wani jerin sakamako na musamman, amma ba ga ƙidaya ba: “ja sannan baƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya →” 25.0% ne, amma “ja ɗaya da baƙi ɗaya a juyi biyu, ko wane tsari” 50.0% ne.
Aƙalla sau ɗaya
Ku yi amfani da akasin abin. Yiwuwar rashin samun nasara ko sau ɗaya a straight upcacaStraight upLamba ɗaya tak, biya 35:1.Karanta gaba ɗaya → cikin juyi 37 ita ce (36/37)³⁷ = 36.3%, don haka yiwuwar samun nasara aƙalla sau ɗaya 63.7% ce, ba “tabbaci” da ʼyan wasa da yawa ke tsammani daga dama 37 na 1 cikin 37 ba. Lissafi iri ɗaya ya nuna cewa lamba tana da kusan dama 1 cikin 3 na rashin fitowa ko kaɗan cikin juyi 37, shi ya sa allon sakamako koyaushe yake nuna wasu lambobi “masu sanyi”.
Lokacin jira da ake tsammani
A matsakaici, lambar straight up tana fitowa sau ɗaya a kowane juyi 37, amma tsawon jira yana bambanta ƙwarai: tsakiyar tsawon jira (median) kusan juyi 25 ne (rabin lokaci tana zuwa da wuri) kuma jira ɗaya cikin ashirin yana wuce juyi 110. Lokutan jira na tsarin geometric suna da doguwar wutsiya, kuma ɗan wasan da “ya san” cewa lokacin wata lamba ya yi bayan juyi 60 yana bayyana abin da ke faruwa sau ɗaya cikin biyar.
Kurakurai da aka saba yi
Haɗa yiwuwar abubuwan da dukansu za su iya faruwa tare (ja ko mara ba 36/37 ba ne; 26/37 ne, domin lambobi goma suna duka biyun). Ninka yiwuwa ga abubuwan da ke faruwa a juyi ɗaya (ja da mara a juyi ɗaya 10/37 ne, ba 18/37 × 18/37 ba). Ɗaukar juye-juyen da suka wuce a matsayin ɓangare na jerin sakamakon da kuke caca a kansa yanzu: bayan ja sau goma, yiwuwar ja na goma sha ɗaya 18/37 ce, ba (18/37)¹¹ ba.
Mene ne odds a roulette, kuma ta yaya suka bambanta da yiwuwa?
Gidajen caca suna bayyana biyakuɗiBiyaAbin da cacar da ta ci ke dawowa da shi, ana faɗinsa a matsayin “X zuwa 1” a kan kuɗin cacar da aka mayar.Karanta gaba ɗaya → a matsayin odds. Lamba ɗaya tana yin nasara da yiwuwar 1/37, don haka odds na yin nasara a roulette a lamba ɗaya 36 zuwa 1 ne a kan ku. Saboda haka biyan 35 zuwa 1 ya gaza da raka'akuɗiRaka'aKuɗin caca na tushe da tsari ko ɗan wasa ke aiki da shi. Ana bayyana jerin ƙarin caca a raka'a don su yi aiki a kowane tebur.Karanta gaba ɗaya → ɗaya, kuma wannan shi ne fifikon gidan cacalissafiFifikon gidan cacaKason kowane kuɗin caca da gidan caca ke riƙewa a matsakaici: 2.70% a roulette na Turai.Karanta gaba ɗaya → a asalin siffarsa. Juyawa: odds a kan ku = (1 − p)/p; yiwuwa = 1/(odds + 1).
Ƙa'idar lissafi
Tambayoyi
(1/37)² = 1/1369 ≈ 0.073%.
36/37 = 97.3%. Sifili shi ne sauran.
Kowace daga cikin lambobi 37 tana da yiwuwar 1/37. Goma sha bakwai ita ce lambar da aka fi yin caca a kanta, kuma wannan gaskiya ce game da mutane.
Nishaɗi da lissafi
Ku fara gwada waɗannan da kanku. Kowace mafita a naɗe take; ku buɗe ta idan kun shirya.
Kuna sa caca a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →, juyi bayan juyi. Mece ce damar nasararku ta biyar ta zo daidai a juyi na takwas? Kuma ku sami nasara biyar a cikin juye-juye takwas na farko?
Nuna mafita
Amsa 12.9%, kusan 1 cikin 8, ga nasara ta biyar a juyi na takwas. 33.4% ga nasara biyar zuwa lokacin.
Nasara ta biyar a juyi na takwas tana nufin abubuwa biyu: juyi na takwas ya ci, kuma juye-juye bakwai na farko suna ɗauke da nasara huɗu daidai da asara uku, a kowane tsari. Akwai hanyoyi 35 na sa nasara huɗu a cikin juye-juye bakwai.
Don haka damar ita ce 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9%.
Ga nasara biyar zuwa juyi na takwas, ku ƙara irin wannan lissafi ga nasara ta biyar a juyi na biyar, na shida da na bakwai: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%. Masana ƙididdiga suna kiran wannan rarrabawar negative binomial: gwaji nawa ƙayyadadden adadin nasarori ke ɗauka. Taylor (2021) ya warware tambaya iri ɗaya a dabaran roulette na Amurka, 12.2%.
Ɗan barkwanci
Ku ƙirga ramuka. Ku raba da 37. Ku ninka don jerin sakamako. Shi ke nan.
Majiyoyi
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.