Haɗarin ƙarewar jari

Tambayar

Kuna 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 → a ta jarin cacakuɗiJarin cacaJimillar kuɗin da aka ware don wasa. Sarrafa jarin caca shi ne yanke shawarar nawa za a sa a haɗari a kowace caca da kowane zaman wasa.Karanta gaba ɗaya → kuma kuna son kai ga raka'a a + b, kuna yin caca raka'a ɗaya a lokaci ɗaya a cacar ɗaya zuwa ɗayacacaCacar ɗaya zuwa ɗaya (even-money)Ja/baƙi, mara/cika, manya/ƙanana. Lambobi 18, biya 1:1.Karanta gaba ɗaya → mai yiwuwarlissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya → nasara p = 18/37 da yiwuwar asara q = 19/37. Mene ne damar ku kai ga burin kafin ku kai sifili? Pascal, Fermat da Huygens ne suka warware amsar a shekarun 1650, kuma tana ɗaya daga cikin sakamako mafi tsufa a ilimin yiwuwa.

Blaise Pascal: tatsuniyar dabaran roulette

Ƙa'idar lissafi ta ƙarewar jarin ɗan caca

P(kai ga buri) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). Haɗarin ƙarewar jarilissafiHaɗarin ƙarewar jariYiwuwar rasa duka jarin caca kafin a kai wani buri ko wani adadin juye-juye.Karanta gaba ɗaya → shi ne ɗaya a rage wannan. Da q/p = 19/18 ≈ 1.0556, rabon yana ƙaruwa cikin sauri mai ninkawa bisa ga yawan raka'o'i, don haka ƙa'idar lissafin tana hukunta ƙananan raka'o'i sosai: duk yadda cace-cacen da ake buƙata kafin a kai ga burin suka yawaita, haka ake ƙara biyan harajin 2.70% a hanya.

Yadda ake karanta shi

Ƙananan raka'o'i suna cutarwa. Ƙoƙarin ninka $500 da cace-cace na $10 yana yin nasara 6% na lokaci; da caca ɗaya ta $500 yana yin nasara 48.6% na lokaci. Wasa da ƙarfin hali, wato cace-cace kaɗan kuma manya, yana ƙara damar kai ga buri zuwa mafi girma a wasan da ake tsammanin asara, domin yana rage yawan lokutan da ake amfani da fifiko zuwa mafi ƙaranci. Haka kuma yana ƙara bambancin sakamakolissafiBambancin sakamakoMa'aunin yadda sakamako ke yaɗuwa a kewayen ƙimar da ake tsammani. Yana da girma ga straight up, ƙanƙanta ga cace-cacen ɗaya zuwa ɗaya.Karanta gaba ɗaya → na abin da zai same ku zuwa mafi girma, kuma yana ƙare daren da sauri. Ana kiran wannan ƙa'idar lissafi (theorem) “wasa da ƙarfin hali shi ne mafi dacewa” (bold play is optimal), kuma Dubins da Savage ne suka tabbatar da ita a 1965.

Inda matsalar ta fara

Tambayar ta girmi roulette. A 1656, Pascal ya ba Fermat wani wasan wuyar warwarewa: ʼyan wasa biyu suna jefa dice uku, kowannensu yana farawa da alamomi 12; jefa 11 yana motsa alama zuwa gefe ɗaya, jefa 14 kuma zuwa ɗayan gefen. Dukansu sun warware shi, kuma Huygens, wanda ya ji labarinsa ta wata wasiƙa daga masanin lissafi Pierre de Carcavi, ya buga shi a 1657 a matsayin matsala ta biyar ta littafin farko a kan yiwuwa, tare da amsar ba tare da hujja ba. Ana iya jefa goma sha ɗaya ta hanyoyi 27, goma sha huɗu kuma ta hanyoyi 15 kawai, don haka kowace alama tana motsawa zuwa gefen ɗan wasa na farko sau 9 cikin 14, kuma ƙa'idar lissafin da ke sama, da alamomi 12 kowanne, tana sa ya fi yiwuwar cin komai sau kusan 1,157 fiye da rasa komai. Fifiko na 2.70% ya fi ƙanƙanta ƙwarai, amma ƙa'idar lissafi iri ɗaya tana nuna abin da yake yi cikin cace-cace da yawa.

Ainihin caca da ƙarfin hali

A Afrilu 2004, Ashley Revell, wani matashi ɗan Ingila, ya sayar da kusan duk abin da ya mallaka, har da tufafinsa, ya kai $135,300 zuwa Plaza a Las Vegas. Bayan wasu ƙananan cace-cace, ya saka dukan kuɗin a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →, sau ɗaya. Ƙwallokayan aikiƘwalloƘaramin ƙwallon da ake jefawa a hanyarsa a akasin juyawar rotor. Ƙwallayen zamani na ivorine ko Teflon ne, 18–21 mm.Karanta gaba ɗaya → ya faɗi a ja 7, kuma ya fita da $270,600. A dabaran mai 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 → biyu, wannan juyi guda dama ce ta 47.37%, kuma ta jawo masa asarar $7,121 a matsakaici, wato fifiko na 5.26% a kan caca ɗaya. Da an raba shi zuwa cace-cace na $10, da kusan babu begen kai ga wannan buri. Wasa da ƙarfin hali ba ya sa caca ta zama mai kyau; yana sa ta zama gajeriya iyakar yiwuwa.

Haɗarin ƙarewar jari ba tare da buri ba

Idan kawai kuna wasa har jarinku ya ƙare ko ku tsaya bayan juyi N, tambayar ta zama “mene ne damar jarin cacata ya taɓa sifili cikin juyi N?”. Babu ƙa'idar lissafi ta kai tsaye ga N na gaba ɗaya, amma simulator ɗin da ke wannan shafin yanar gizo suna lissafa ta: jarin caca na $500 a $10 a kan ja kusan ba ya ƙarewa cikin juyi 100 (ƙasa da 1%), yana ƙarewa kusan 9% na lokaci cikin juyi 500, kuma kusan 95% na lokaci cikin 5,000. Ba tare da ƙa'idar tsayawa ba, yiwuwar tana kusantar 100%, kuma wannan shi ne nau'in dogon lokaci na fifikon gidan cacalissafiFifikon gidan cacaKason kowane kuɗin caca da gidan caca ke riƙewa a matsakaici: 2.70% a roulette na Turai.Karanta gaba ɗaya →.

Kusantowa a dogon zango: dokar manyan lambobi a roulette

Tsawon lokaci, da nisan riba

Wasu sakamako biyu na gargajiya suna amsa tambayoyin da ʼyan wasa ke yi a zahiri. Ba tare da buri ba, cace-cacen ɗaya zuwa ɗaya masu kuɗi ɗaya suna ɗaukar juyi 37 a matsakaici ga kowace raka'a ta jarin caca a dabaran Turai, da 19 a na Amurka, domin kowane juyi yana ɗaukar 1/37 na raka'a a matsakaici (1/19 a dabaran Amurka): raka'a 100 suna ɗaukar juyi 3,700 a matsakaici, ko da yake rabin irin waɗannan zaman wasa suna ƙarewa cikin 3,134 (ku duba Tsawon zaman wasa da kuɗinsa). Kuma ko yaya girman jarin caca, damar a dabaran Turai ta taɓa samun ribar raka'a k ita ce (18/19)ᵏ. Wannan 95% ne ga raka'a ɗaya da 58% ga goma, amma babu jarin caca, ko yaya zurfinsa, da ke ba da dama daidai-wa-daidai ta taɓa samun ribar raka'a 13; a dabaran Amurka damar ita ce (9/10)ᵏ kuma tana faɗuwa ƙasa da rabi a raka'a 7.

Tsawon zaman wasa da kuɗinsaDabaran da dokokin roulette na Amurka

Jarin caca don dama daidai-wa-daidai

Ku juya tambayar: nawa ne dole ku kawo don ku sami aƙalla dama daidai-wa-daidai ta cin wani adadi kafin ku rasa komai? Don ƙaramar riba, ba da yawa ba. Don babba, jarin cacar da ake buƙata yana hawa da sauri, kuma bayan wani wuri babu jarin caca da ya isa, domin ko marar iyaka ma yana ba da ƙasa da dama daidai-wa-daidai ta taɓa samun irin wannan riba. Taylor (2021) ya faɗe shi ta wata hanya: a dabaran Amurka, don samun dama daidai-wa-daidai ta kai raka'a 100, dole ku fara da 94, kuna saka 94 cikin haɗari don cin 6. A dabaran Turai za ku buƙaci 88.

Darasi na aiki

Ku yanke shawarar abin da kuke ƙoƙarin yi. Idan burin wata riba ce ta musamman, ku yi cace-cace manya kuma kaɗan. Idan burin dogon dare ne, ku yi ƙananan cace-cace kuma ku yarda cewa fifiko zai ɗauki 2.70% nasa daga babbar jimillar cacakuɗiJimillar cacaJimillar kuɗin da aka yi caca da su a cikin zaman wasa ko wani lokaci, har da kuɗin da aka ci aka sake sawa. Ana kuma kiranta: handle, action.Karanta gaba ɗaya →. Idan burin duka biyun ne, dole a sadaukar da ɗaya, kuma yawanci burin ne ake sadaukarwa.

Ƙa'idar lissafi

Tambayoyi