Tarihin tsare-tsaren caca na roulette
Ƙarni biyu na mutane suna rubuta dokoki kan yadda za su canja kuɗin cacarsu.

Martingale na ƙarni na 18 ne; D’Alembert an sanya masa sunan masanin lissafin da bai so shi ba; Labouchère abin sha'awar wani ɗan siyasa ne na zamanin Victoria. Babu ɗaya daga cikinsu da ya yi aiki a lokacin ma.
Martingale
Sunan ya fito ne daga kalmar ʼyan caca ta yaren Provençal (à la martegalo, “kamar yadda mutanen Martigues ke yi”, waɗanda aka san su da ganganci) don cacar ninkawa, kuma an rubuta shi a ƙamus-ƙamus na Faransanci tun shekarun 1760. Thorp (1984), bisa ga American Heritage Dictionary, ya ba da wani bayani na gargajiya na biyu: ana yi wa mutanen Martigues ba'a saboda baƙin halaye, ciki har da ɗaure wandonsu ta baya, don haka kalmar ta zo tana nufin “ta hanyar ban dariya”. Tun a ƙarni na 18 a Paris ta riga ta zama labarin gargaɗi: Casanova ya bayyana yadda ya yi asarar dukiya mai yawa yana ninkawa a wasan faro a Venice a shekarun 1750. Lissafin dalilin da ya sa yake gazawa, wato 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 → da 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 → mai iyaka, an fahimce shi kafin shekarun 1770. A ka'idar yiwuwalissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya →, “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 →” ya zama kalmar fasaha a shekarun 1930 don wasa mai adalcilissafiWasa mai adalciWasan da babu ɓangaren da ke da fifiko: kowace caca tana da ƙimar da ake tsammani ta sifili.Karanta gaba ɗaya →, wanda shi ne abu ɗaya da Martingale na roulette ba shi ba.

D’Alembert
Jean le Rond d’Alembert ya yi jayayya a cikin Encyclopédie (1754) cewa bayan jerin “kai” a jefa tsaba, “wutsiya” ta fi yiwuwa, wanda ke ɗaya daga cikin bayanan farko na kuskuren ɗan caca daga wani babban masanin lissafi. Tsarin cacar da ke ƙara 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 bayan asara da rage ɗaya bayan nasara, ʼyan caca na baya waɗanda suka yi imani da haka ne suka sanya masa sunansa. Shi bai ba da shawararsa ba, kuma a lokutan da tunaninsa ya fi kyau, da ya ƙi shi.
Labouchère
Henry LabouchèredabaraLabouchèreTsarin sharewa: a rubuta layin lambobi, a yi caca da jimillar lambobi biyu na ƙarshe, a share su bayan nasara, a ƙara kuɗin cacar da aka rasa bayan asara.Karanta gaba ɗaya → (1831–1912), ɗan jarida, mai gidan wasan kwaikwayo kuma ɗan majalisa na jam'iyyar Liberal, ya yaɗa tsarin sokewa (cancellation) a cikin manyan mutanen London a shekarun 1870, kuma an ruwaito cewa ya yi amfani da shi a Monte Carlo. Hanyar, wato rubuta layin lambobi da yin caca da jimillar lambobin gefe biyu, ta wanzu tun kafin zamaninsa. Sunansa ya manne ne saboda an san shi da wasu abubuwa, kuma saboda tsarin yana da siffar da ba a cika samu ba: yawanci yana aiki, abin da ya sa ya zama abin hira a wajen cin abinci.
Casanova ya yi asara yana ninkawa a faro. Martingale ya riga ya tsufa.
D’Alembert ya wallafa kuskuren tunanin da daga baya aka sanya wa wani tsari sunansa.
Kalmar “Martingale” ta shiga ƙamus-ƙamus na Faransanci a matsayin kalmar ʼyan caca.
Labouchère ya yaɗa tsarin sokewa a London.
Jerin ƙarin caca na Fibonacci da Paroli sun bayyana a littattafan jagorar caca.
Ana sayar da tsare-tsaren “sector” bisa tsarin dabaran ta hanyar aika wasiƙa.
Halmos, ɗalibin Doob, ya tabbatar cewa babu tsarin caca da zai iya mayar da wasa mara amfani ga ɗan wasa ya zama mai amfani.
Kwamfutoci sun kwaikwayi kowane tsari. Duka sun nuna −1/37 na jimillar caca.
Tsare-tsaren iri ɗaya ake sayarwa a intanet da sakamako iri ɗaya, kuma ana kwaikwayon su cikin burauza a wannan shafin.
Ƙarni na 20
FibonaccidabaraFibonacciJerin ƙarin caca da ke bin jerin lambobi 1, 1, 2, 3, 5, 8, 13…: mataki ɗaya gaba bayan asara, matakai biyu baya bayan nasara.Karanta gaba ɗaya → da ParolidabaraParoliJerin ƙarin caca bayan nasara: a ninka bayan nasara, a koma farko bayan asara ko bayan nasarori uku a jere. Ana kuma kiransa: reverse Martingale.Karanta gaba ɗaya → sun shiga littattafan jagorar caca a kusan 1900. Tsakiyar ƙarnin ta kawo tsare-tsaren da ake sayarwa ta wasiƙa, kowanne da shaidar wani mutum da alkawarin mayar da kuɗi, da kwaikwayo na farko da kwamfuta, waɗanda suka nuna abin da lissafi ya riga ya faɗa. Hujjar cewa babu tsarin da zai yi aiki ta riga ta kasance: Joseph Doob (1936) da Paul Halmos (1939) sun nuna cewa babu wata doka ta zaɓar lokacin caca da yawan kuɗin caca da ke canja sakamakon da ake tsammani na wasa mai adalci ko mara amfani ga ɗan wasa, kuma binciken Thorp na 1969 ya bayyana sharuɗɗan ta yadda ʼyan caca ke haɗuwa da su. Tun daga lokacin tsare-tsaren ba su canja ba; tallarsu ce ta koma daga ƙasidu zuwa bidiyo.

Tatsuniya: dabarar roulette da kullum take cin nasaraDabarar Fibonacci a roulette
Dalilin da ya sa suke ci gaba da wanzuwa
Tsari yana ba ɗan wasa abin yi da labarin da zai ba da. Yawancin zaman wasa a ƙarƙashin yawancin tsare-tsare suna ƙarewa da ƙaramar nasara, wanda labari ne mafi daɗi fiye da lissafi. Zaman wasa na asara ba su da yawa kuma ana tunawa da su a matsayin rashin sa'a. Talla ba ta buƙatar yin ƙarya game da yiwuwar cin nasara; tana buƙatar nuna zaman wasa ɗaya na nasara kawai, kuma akwai su da yawa. Hujjar akasin haka, 2.70% 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 →, tana nan tun 1796 kuma ba ta taɓa gamsarwa kamar dare ɗaya na sa'a ba.
Tsare-tsaren da ake sayarwa
Kasuwancin ƙarni na 20 ya ƙara nasa dabaru, kowanne sabon tsari na cace-cace iri ɗaya marasa amfani ga ɗan wasa. An sayar da Phase One a kan $25 da 10% na abin da mai saye ya ci, tare da alkawarin Phase Two idan an biya $500 da kuma “Inner Circle” a kan $5,000. Babu ɗaya daga cikinsu da ke canja lissafin: ƙimar 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 → ta jerin cace-cace ita ce jimillar ƙimar da ake tsammani ta kowace caca.
Wanda ba tsari ba ne
Dokokin tsayawa: yanke shawara tun da wuri kan yawan kuɗin da za a yi asara ko a ci, sannan a tafi. Ana yawan sayar da su a matsayin wani ɓangare na tsari, kuma su ne kawai ɓangaren da ke yin wani abu, domin suna rage jimillar caca. Ba a sanya musu sunan kowa ba, wanda ya dace.
Tambayoyi
Martingale, da ƙarni ɗaya ko fiye. Ninkawa bayan asara shi ne tunani na farko da kowa ke yi.
D’Alembert ne ya fi kusa, ba da gangan ba. Pascal, Fermat, Huygens, Bernoulli da Laplace duka sun bayyana dalilin da ya sa suke gazawa.
Domin yawancin zaman wasa suna ƙarewa da nasara, kuma bidiyon zaman wasa na nasara ba shi da tsada a yi.
Ɗan barkwanci

Ƙarni biyu na sunaye. Lamba ɗaya.
Majiyoyi
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- d’Alembert, J. “Croix ou pile.”
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.