Tatsuniyoyi · Tatsuniyoyi · minti 7

Tatsuniya: dabarar roulette da kullum take cin nasara

“Ina da tsarin da ke cin nasara a kashi 80% na lokaci.” Watakila haka ne. Amma har yanzu yana asarar kuɗi.

Amsa a taƙaice

Tsari zai iya sa zaman wasa masu nasara su yawaita. Ba zai iya sa ƙimar da ake tsammani ta zama riba ba, domin kowace caca da yake sanyawa −1/37 ce na kuɗin cacarta kuma ƙimomin da ake tsammani suna haɗuwa. Tsare-tsaren da suka fi yawan cin nasara su ne suka fi asara idan sun yi asara.

zaman wasa na Martingale masu riba
≈ 80% (gajeru)
matsakaicin sakamakon Martingale
asara
EV na kowane tsari
−2.70% na jimillar caca
hukunci
tatsuniya

Iƙirarin

Imanin: a wani wuri akwai dabarar roulette da kullum take cin nasara, tsarin canza kuɗin caca bisa sakamakon da suka wuce wanda ke mayar da roulette wasan da ake cin nasara. Hujjojin da ake bayarwa: jerin zaman wasa masu nasara, bidiyo kan yadda ake cin roulette kowane lokaci, shaidar wani, takardar lissafin wani mako na sa'a. Yawanci ana yin iƙirarin ne da zuciya ɗaya; mutumin yana yarda da shi domin ya daɗe yana aiki.

Dalilin da ya sa ba daidai ba ne, a layi ɗaya

Ƙimomin da ake tsammanilissafiƘimar da ake tsammaniMatsakaicin sakamako a kowace caca a cikin dogon lokaci. −1/37 na kuɗin caca a kowace cacar Turai ta yau da kullum.Karanta gaba ɗaya → suna haɗuwa. Idan kowace caca tana da EV = −1/37 na kuɗin cacarta, kowane jerin cace-cace yana da EV = −1/37 na jimillar abin da aka sa, ko wace irin doka ce ta zaɓi kuɗin caca. Tsari doka ce ta zaɓar kuɗin caca. Saboda haka kowane tsari yana da EV = −1/37 na 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 →. Wannan ka'idar lissafi ce da aka tabbatar (Doob da Halmos sun tabbatar da shi a shekarun 1930; Thorp 1969 ya bayyana sharuɗɗan), kuma ba shi da keɓancewa ga dokoki masu wayo. Sharaɗi ɗaya da ya kamata a sani shi ne mafi ƙarancin caca: misalin Thorp yana sa $1,000 a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →, sannan cent 90, sannan cent 9 da sauransu, yana raguwa har abada. Da yiwuwar 18/37 caca ta farko tana cin nasara kuma ɗan wasan yana ci gaba da riba har abada, ko da yake sakamakon da ake tsammani har yanzu −1/37 ne na duk abin da aka sa. Mafi ƙarancin caca na ainihin tebur yana hana hakan, kuma tare da shi duk wani fata na ci gaba da riba a dogon lokaci.

Kusantowa a dogon zango: dokar manyan lambobi a roulette

Dalilin da ya sa yake kama da yana aiki

Jerin ƙarin cacadabaraJerin ƙarin cacaDuk wata ƙa'ida da ke canza kuɗin caca bisa sakamakon da ya gabata. Jerin ƙarin caca bayan asara yana ɗaga shi bayan an rasa, na bayan nasara kuma bayan an ci.Karanta gaba ɗaya → bayan asara suna sa zaman wasa masu nasara su yawaita. MartingaledabaraMartingaleJerin ƙarin caca da ke ninka caca bayan kowace asara. Ku duba sashen “Dabarun caca na roulette” don ganin abin da yake yi da wanda ba ya yi.Karanta gaba ɗaya → daga $10 a iyakar $500 yana ƙare kusan kashi 80% na zaman wasa masu juye-juye 100 da ribar ʼyan 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 →. Ɗan wasan da ya yi amfani da shi a zaman wasa ashirin zai ci goma sha shida daga cikinsu kuma zai tuna da hakan. Kowanne daga cikin zaman wasa huɗu masu asara yana rasa fiye da abin da zaman wasa goma masu nasara suke samu, kuma lissafin zaman wasa ashirin asara ne. Tsarin bai canza matsakaicin ba; ya tattara asarorin cikin zaman wasa kaɗan amma manya, inda ya fi sauƙi a kira su rashin sa'a.

Martingale, tushe $10, iyaka $500, juye-juye 100 (kwaikwayo)
zaman wasa masu riba
≈ 78%
zaman wasa mai nasara na yau da kullum
≈ +$40
zaman wasa mai asara na yau da kullum
≈ −$500
matsakaicin sakamako a dukan zaman wasa
≈ −$75
0250≈ −$500
Zaman wasa huɗu masu asara cikin ashirin suna cin kusan $2,000. Zaman wasa goma sha shida masu nasara suna samun kusan $640. Tsarin yana “aiki” a kashi 80% na lokaci.

Gwajin da kowa zai iya yi

Simulator na dabarar roulette a wannan shafin yana gudanar da zaman wasa 10,000 na kowane tsari, ko lambar kwamfutarku, cikin daƙiƙa ɗaya. Ku saita shi zuwa tsarin da kuka yarda da shi ku karanta matsakaicin. Da a ce matsakaicin riba ne a kowane saiti, da wannan shafin ya faɗa. Kowane saiti, kowane tsari, kowace iyakar teburiteburIyakar teburiMafi ƙanƙanta da mafi girman cacar da aka yarda da ita. Mafi girman ita ce ke dakatar da jerin ƙarin caca masu ninkawa.Karanta gaba ɗaya → tana ba da matsakaicin −2.70% na jimillar caca da ɗan bambanci na kwatsam. Shaidun mutane samfuri ne na mutum ɗaya; simulator kuma samfuri ne na dubu goma.

Iyakokin teburin roulette

Tsarin da ba zai iya asara ba

A 1997 marubucin poker Mike Caro ya wallafa tsarin roulette a matsayin barkwanci, kuma Gambling Times ta sake wallafa shi a 2001. Jerin cace-cace ne da za a guje wa: kada a taɓa sa caca a kan ja ko baƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya →, mara ko cika, ko kuma 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 →; babu lambobin ja na mara kuma babu lambobin baƙi na cika; kuma babu komai a kan 30, ko a kan dogon jerin ramukakayan aikiRamiƊaya daga cikin ɗakuna 37 masu lamba a kan rotor. Ana kuma kiransa: slot, cup.Karanta gaba ɗaya → daga 11 bin hanyar agogo har zuwa 14 a dabaran Amurka. Idan aka haɗa dokokin, babu lambar da ta rage. Ramukan da ke wajen wannan jeri kawai su ne 0, 28, 9, 26, 30 da 2; an haramta 30 da sunansa, sauran kuma sifili ne, ko cika da baƙi, ko mara da ja. Ɗan wasan da ke bin tsarin ba ya taɓa yin caca kuma ba ya taɓa asara. Fifikonsa sifili ne, kuma shi ne kawai tsarin roulette da ke faɗin gaskiya game da yadda yake kai wa can.

Yayin da yake bin tsarin da ya hana kowace caca, wani ɗan wasa bai taɓa sa tsabar caca ko ɗaya ba.

Dabaran da dokokin roulette na Amurka

Tsare-tsare masu suna, layi ɗaya kowanne

Tsare-tsaren da ake sayarwa da suna, ko a matsayin dabarar cin roulette, ba su da bambanci. Kowanne tarin cace-cace ne, kuma kowace caca tana biyan dabaran 2.70% ɗinsa. Bollman (2024) ya yi nazarin da dama a kan dabaran Amurka, inda kowanne yake jawo asarar 5.26%; ga su nan a kan na Turai.

tsariabin da yake yiabin da yake yi a zahiri
Bohemia (Cuba, 1959)raka'a 1 a kan baƙi da 1 a kan ginshiƙi na uku, wanda ke ɗauke da lambobin baƙi huɗu kawaiyana ƙarewa da +3, +1, 0 ko −2 raka'a; kowace tsabar caca har yanzu tana jawo asarar 2.70%
Macijin jastraight up a kan lambobin ja 12 da ke karkacewa a kan teburin cacalambobi 12 cikin 37: ɗaya yana cin nasara a kashi 32% na juye-juye; sauran suna asara
Shotwellsix line ɗaya da straight up huɗu da aka zaɓa don su kasance kusa da juna a kan dabaranlambobi 10 cikin 37, kashi 27% na juye-juye, har yanzu 2.70%
Tsani na $450lamba ɗaya: $5 na juye-juye 20, $10 na 20, $15 na 10yana rashin fitowa a duka juye-juye 50 kuma yana rasa $450 a kusan kashi 25% na lokaci
Kryptosyana rubuta juye-juye shida a matsayin manya ko ƙanana, mara ko cika, ja ko baƙi, kuma yana gudanar da Martingale uku lokaci ɗaya, ɗaya a kan kowane haɗin cace-cacen ɗaya zuwa ɗayakuɗin caca ninki uku; kowanne daga cikin ukun yana asara shida a jere kusan sau ɗaya a ƙoƙari 55 kuma yana cin raka'a 63
Famous Las Vegas Gambling Systems (ƙasida)yana caca a kan rabin da bai fito ba sau biyar a jere, ko ginshiƙin da bai fito ba a juye-juye bakwaijira ba ya canza komai; dabaran ba ya tunawa
“Juye-juye 19 suna mayar da shi 50–50”a yi caca a kan lamba ɗaya sau 191 − (36/37)¹⁹ = 41%, ba 50% ba

Sigar gaskiya

Tsare-tsare suna canza siffar zaman wasa: sau nawa kuke cin nasara, yaya girman nasarorin, yaya munin mafi munin yanayi. Waɗannan zaɓuɓɓuka ne na gaske kuma ɗan wasa zai iya fifita wata siffa a kan wata. Abin da tsare-tsare ba sa canzawa shi ne farashi, wato 2.70% na duk abin da aka sa a caca, kuma domin jerin ƙarin caca suna sa kuɗi fiye da caca daidai-wa-daidadabaraCaca daidai-wa-daidaYin caca da adadi ɗaya a kowane juyi. Ma'auni ne da ake kwatanta kowane jerin ƙarin caca da shi.Karanta gaba ɗaya →, suna biyan ƙarin sa.

Dabarar caca iri ɗaya a roulette

Tambayoyi

Amma tsarina ya ci nasara na tsawon watanni shida.

Watanni shida na zaman wasa na kowane mako kusan zaman wasa 25 ne. Martingale yana cin kashi 80% na waɗannan. Zaman wasa masu asara suna zuwa, kuma sun fi girma.

Me game da tsare-tsaren da ke tsayawa yayin da suke da riba?

Dokar tsayawa tana rage jimillar caca don haka tana rage asarar da ake tsammanilissafiAsarar da ake tsammaniƘimar da ake tsammani sau jimillar kuɗin da aka yi caca da su; matsakaicin adadin da ake rasawa a cikin zaman wasa ko wani lokaci.Karanta gaba ɗaya →. Ba ta mayar da ita riba ba.

Akwai keɓancewa: dabarar roulette da ke aiki?

Ba a kan dabaran mai adalci ba. A kan dabaran da ya karkatagwajiDabaran da ya karkataDabaran da lahaninsa na zahiri ke sa wasu ramuka su fi yiwuwa fiye da 1/37. Ba kasafai ake samunsa ba, kuma sai da dubban juye-juyen da aka rubuta ake iya gane shi.Karanta gaba ɗaya →, wanda matsala ce ta ilimin motsi na zahiri, ba tsari ba.

Nishaɗi da lissafi

Ku fara gwada waɗannan da kanku. Kowace mafita a naɗe take; ku buɗe ta idan kun shirya.

  1. Tsarin wasa na barkwanci na Mike Caro na 1997 don dabaran na Amurka yana hana jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → da baƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya →, mara da cika, da sifilaidabaranSifiliRamin 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 →; lambobin mara masu ja da lambobin cika masu baƙi; lamba 30; da kowane ramikayan aikiRamiƊaya daga cikin ɗakuna 37 masu lamba a kan rotor. Ana kuma kiransa: slot, cup.Karanta gaba ɗaya → a jerin daga 11 a hanyar agogo har zuwa 14. Ku yi amfani da dokokin ɗaya bayan ɗaya. Waɗanne lambobi ne suka rage don yin caca?

    Nuna mafita

    Amsa Babu ko ɗaya. Tsarin ba ya taɓa yin caca, don haka fifikonsa sifili ne daidai.

    Hana ja, baƙi, mara, cika da sifilai yana barin lambobi guda-guda da ƙananan rukunoni a cikin 1 zuwa 36.

    Babu lambobin mara masu ja kuma babu lambobin cika masu baƙi yana barin lambobin cika masu ja (12, 14, 16, 18, 30, 32, 34, 36) da lambobin mara masu baƙi (11, 13, 15, 17, 29, 31, 33, 35): lambobi goma sha shida. Hana 30 yana barin goma sha biyar.

    A dabaran na Amurka jerin daga 11 a hanyar agogo zuwa 14 yana rufe 32 daga cikin ramuka 38. Shida da ke wajensa su ne 0, 28, 9, 26, 30 da 2. Duka goma sha biyar da suka rage suna cikin jerin, don haka doka ta ƙarshe tana cire su ma. Tsarin da ba ya taɓa yin caca shi kaɗai ne ba ya taɓa asara, kuma wannan shi ne abin da Caro yake son nunawa.

  2. Kryptos yana gudanar da MartingaledabaraMartingaleJerin ƙarin caca da ke ninka caca bayan kowace asara. Ku duba sashen “Dabarun caca na roulette” don ganin abin da yake yi da wanda ba ya yi.Karanta gaba ɗaya → uku a lokaci ɗaya, ɗaya a kan kowane nau'i na cace-cacen ɗaya zuwa ɗayacacaCacar ɗaya zuwa ɗaya (even-money)Ja/baƙi, mara/cika, manya/ƙanana. Lambobi 18, biya 1:1.Karanta gaba ɗaya → (manya ko ƙanana, mara ko cika, ja ko baƙi), da kuɗin caca 1, 2, 4, 8, 16, 32 da tsayawa bayan asarori shida. Ku ɗauki ɗaya daga cikin ukun a dabaran na Turai. Sau nawa yake rasa duka cace-cace shida, me zagaye ɗaya yake samu a matsakaici, kuma wane kaso ne wannan na kuɗin da aka saka?

    Nuna mafita

    Amsa Yana rasa duka shida kusan sau ɗaya cikin zagaye 55, wato 1.83% na lokaci, kuma wannan yana cin 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 → 63. A matsakaici zagaye ɗaya yana asarar kusan raka'a 0.17 cikin raka'a 6.42 da aka saka: 2.70%, farashin kowace caca a dabaran.

    Caca tana faɗuwa da yiwuwar 19/37, har da sifili. Shida a jere: (19/37)⁶ = 0.0183, kusan 1 cikin 55, sannan kuɗin caca 1 + 2 + 4 + 8 + 16 + 32 = 63 sun tafi. Idan ba haka ba, zagayen yana ƙarewa da nasara da +1 raka'a.

    Matsakaici: 1 × (1 − 0.0183) − 63 × 0.0183 = 1 − 64 × 0.0183 = −0.17 raka'a.

    Kuɗin da aka saka: ana sa caca ta farko koyaushe, ta biyu sai bayan asara kawai, da sauransu: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = raka'a 6.42. Kuma −0.17/6.42 = −2.70%.

    Juye-juye shida da aka rubuta suna yanke wane gefe ne kowace caca take kawai, kuma dabaran ba zai iya sanin su ba. Gudanar da duka ukun yana ninka kuɗin da aka saka sau uku, haka ma matsakaicin asarar. Bollman (2024) ya yi aiki da tsarin a dabaran na Amurka, inda kowanne daga cikinsu yake rasa shida a jere kashi 2.1% na lokaci.

Ɗan barkwanci

Yawan cin nasara da cin kuɗi lambobi ne dabam-dabam.

Yawan cin nasara da cin kuɗi lambobi ne dabam-dabam.

Majiyoyi

  1. Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
  2. Thorp, E. O. The Mathematics of Gambling. Gambling Times / Lyle Stuart, 1984.
  3. Doob, J. L. “Note on probability.” Annals of Mathematics 37(2), 1936.
  4. Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.” Duke Mathematical Journal 5(2), 1939.
  5. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Babi na 13, roulette.
  6. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021. Babi na 2, roulette.
  7. Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed. CRC Press, 2024.
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