Misali: yammaci da D’Alembert
Ƙarin raka'a ɗaya bayan asara, ragin raka'a ɗaya bayan nasara, ja a kowane juyi na tsawon juye-juye ɗari. Tsarin da ya fi taushi, da kuma abin da taushin yake ci.

Zaman wasa na kwaikwayo na D’Alembert mai juye-juye 100, $5 a kowace raka'a. Kuɗin caca ya koma $5 sau biyar, ya hau a hankali zuwa $80 a lokacin wani mummunan ɓangare, kuma ya ƙare a $55 da zaman wasan a asarar $40. Tsarin da ke jin kamar daidaito amma ba haka yake ba.
Ku bi tsarin mataki-mataki
Asara tana hawa mataki ɗaya. Nasara tana komawa baya mataki ɗaya.
Kuɗin caca da sakamako suna cikin raka'o'in cacar tushe.
Shirin
A fara 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, $5, a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →. Bayan asara a ƙara raka'a; bayan nasara a cire ɗaya, amma kada a sauka ƙasa da ɗaya. Ra'ayin, wanda ba d’Alembert ne ya gabatar da shi ba amma ana ɗora masa laifi, shi ne cewa nasarori da asarori suna daidaita juna, don haka a kowane haɗin asara ɗaya da nasara ɗaya muna samun ribar raka'a ɗaya. Lissafi ya ce ja yana cin nasara a kashi 48.65% na juye-juye, don haka asarori sun fi nasarori da kusan ɗaya cikin arba'in, kuma kuɗin caca yana hawa a hankali a tsawon lokaci.
Juye-juye 1–30
Ja goma sha huɗu, baƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya → goma sha biyar, 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 → ɗaya. Kuɗin caca ya hau zuwa $20 a lokacin jerin asara uku, ya koma $5 zuwa juyi na 18, kuma ya hau zuwa $25 a ƙarshen wannan ɓangare. Sakamakon tsaf +$20. Kowane haɗin asara da nasara ya ba da raka'a ɗaya tsaf kamar yadda aka faɗa; ƙarin asarorin sun cinye su. Yana ji kamar famfo mai tafiya a hankali wanda galibi yake aiki.
Juye-juye 31–65
Mummunan ɓangaren. Ja goma sha uku a kan waɗanda ba ja ba ashirin da biyu, har da jerin asara bakwai. Daga $5 a juyi na 41 kuɗin caca ya hau raka'a ɗaya-ɗaya zuwa $80, kuma kowace asarar $75 ta shafe goma sha biyar daga cikin nasarorin $5 na baya. Sakamakon tsaf −$485 a wannan ɓangare; jimilla ya zuwa yanzu −$465. Babu wani abin ban mamaki da ya faru a kowane juyi guda; hawan a hankali ne ya yi aikin.
- p10 −$500
- p25 −$500
- tsakiya −$500
- p75 −$500
- p90 +$885

Juye-juye 66–100
Ja ashirin a kan waɗanda ba ja ba goma sha biyar, kuɗin caca yana sauka daga $80 zuwa $55 da matakan $5. Kowace nasara a babban kuɗin caca ta dawo da kuɗi na gaske: nasarar $75 bayan asarar $70 haɗi ne da ke ba da +$5 tsaf, amma haɗin babba ne. Sakamakon tsaf +$425 a wannan ɓangare; ƙarshe −$40.
Lissafin kuɗi
Matsakaicin kuɗin caca kusan $37, don haka jimillar caca kusan $3,670, idan aka kwatanta da $500 ga wanda ke caca daidai-wa-daida da $5. 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 → a kan $3,670 ita ce $99; ainihin sakamako −$40, ƙasa da standard deviationlissafiStandard deviationTushen murabba'i na bambancin sakamako; nisan da sakamako ke yawan yi daga ƙimar da ake tsammani.Karanta gaba ɗaya → ɗaya. Hawan girman kuɗin caca a hankali shi ne dukan tasirin tsarin: ƙarin kuɗi a kan tebur, 2.70% iri ɗaya daga kowace dala, da rarrabuwar sakamako mafi faɗi.
Abin da zaman wasan ya nuna
D’Alembert shi ne kuskuren ɗan caca da aka rubuta a matsayin dokar kuɗin caca: yana ɗauka cewa nasarori da asarori za su daidaita da wuri har kuɗin caca ya sauko. Suna daidaita ne a dogon lokaci ta hanyar narkewa a cikin yawa, ba ta gyara ba, kuma kuɗin caca ba shi da dalilin komawa raka'a ɗaya. Tsari ne mai tafiya a hankali ba tare da faɗuwa kwatsam ba, kuma wannan jinkirin ne ya sa ʼyan wasa suke yarda da shi.
Tambayoyi
Ba kasafai ba. Kuɗin caca yana ƙaruwa da raka'a ɗaya a kowace asara, ba ninkawa ba, don haka sai an yi dogon mummunan jeri kafin a kai iyakar.
Eh, kuma iyakar tana mayar da shi 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 → a wannan iyaka bayan mummunan jeri. Kowace iyaka tana da kyau; babu wadda ke canza fifikon gidan caca.
A 1754 ya yi hujjar cewa wutsiya tana ƙara yiwuwa bayan jerin kai. ʼYan caca da suka yarda da shi suka sa wa tsarin sunansa. Da ya ji kunya.
Ɗan barkwanci

Tsarin da ya fi taushi. Yana hawa a hankali maimakon faɗuwa kwatsam.
Majiyoyi
- d’Alembert, J. “Croix ou pile.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.