Bambancin sakamako
Me ya sa straight up da cacar ja masu 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 → iri ɗaya suke ji kamar wasanni daban-daban.

Bambancin sakamako yana auna yadda sakamako ke watsuwa a kewayen ƙimar da ake tsammani. A kan kowace raka'a ta kuɗin caca, kusan 34 ne ga straight up kuma kusan 1 ga ja.
Ƙa'idar lissafi ga caca ɗaya
Ga cacar da ke biyan W zuwa 1 da yiwuwalissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya → p, sakamakon kowace 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 → +W ne da yiwuwa p, kuma −1 da yiwuwa 1 − p. 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 → ita ce pW − (1 − p) = −1/37. 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 → shi ne E[X²] − EV² = pW² + (1 − p) − (1/37)². Ga straight upcacaStraight upLamba ɗaya tak, biya 35:1.Karanta gaba ɗaya →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. Ga jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Abin da yake nufi ga zaman wasa
Bambance-bambancen sakamako suna haɗuwa a kan juye-juye da ba sa dogara da junalissafiJuye-juye masu zaman kansuKowane juyi yana da yiwuwa iri ɗaya komai abin da ya faru a baya. Tushen kowane lissafi a wannan shafin.Karanta gaba ɗaya →, don haka a cikin juyi N da kuɗin caca ƙayyadadde, bambancin sakamako na jimilla shi ne N × kuɗin caca² × σ², kuma standard deviationlissafiStandard deviationTushen murabba'i na bambancin sakamako; nisan da sakamako ke yawan yi daga ƙimar da ake tsammani.Karanta gaba ɗaya → shi ne σ × kuɗin caca × √N. Juyi 100 a $10: standard deviation kusan $584 ne ga straight up kuma $100 ga ja, a kewayen sakamako iri ɗaya da ake tsammani na −$27. Ɗan wasa ɗaya yana ganin sakamako na hawa da sauka da ɗaruruwa; ɗayan yana ganin sauyi a hankali kaɗan-kaɗan. Dukansu suna biyan farashi iri ɗaya.
Bambancin sakamako da tsare-tsaren caca
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 → ba ya canza EV a kan kowace raka'a da aka yi caca da ita, amma yana canza duka yawan kuɗin da aka yi caca da shi da kuma siffar rarrabuwar sakamako. 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 → yana rage bambancin sakamako na yawancin zaman wasa (ƙananan nasarori da yawa) kuma yana ƙara wutsiya mai kauri (babbar asara da ba kasafai ake gani ba); jimillar bambancin sakamako a kan duk zaman wasa ya fi na caca da kuɗi ɗayadabaraCaca 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 → yawa saboda wannan wutsiya. 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 → yana yin akasin haka. Zaɓar tsarin caca zaɓar siffar bambancin sakamako ne; matsakaici ba ya cikin abin da ake iya zaɓa.
- p10 −$500
- p25 −$500
- tsakiya −$500
- p75 +$40
- p90 +$1,120
Dabarar caca iri ɗaya a rouletteDabarar Paroli a roulette (Martingale a juye)
Me ya sa yake da muhimmanci ga ɗan wasa
Bambancin sakamako shi ne ke sa gajerun zaman wasa su zama marasa tabbas, dogaye kuma su zama masu tabbas. Da σ = $100 da EV = −$27 a cikin juyi 100, fifiko kashi ɗaya cikin huɗu ne na hayaniyar sakamako, kuma zaman wasa da ya ƙare da riba abu ne na yau da kullum. A cikin juyi 10,000, EV −$2,700 ne kuma σ $1,000 ne; yanzu fifiko ya kusa ninka hayaniyar sau uku, kuma jerin nasara abu ne na sigma uku (three-sigma). Bambancin sakamako abokin ɗan wasa ne a ɗan gajeren lokaci, na gidan caca kuma a dogon lokaci.
Bambancin sakamako na haɗin cace-cace
Ga cace-cace da yawa a juyi ɗaya, sakamakonsu yana da alaƙa (nasara a 17 nasara ce kuma a baƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya → da dozincacaDozin1–12, 13–24 ko 25–36, biya 2:1.Karanta gaba ɗaya → na biyu), don haka bambance-bambancen sakamako ba a iya haɗa su kai tsaye kawai. Kayan aikin Mai haɗa caca yana lissafa ainihin rarrabuwar sakamako ga kowane rukunin tsabobin cacakuɗiTsabar cacaAlamar da ke wakiltar ƙayyadadden adadin kuɗi, wadda ake ajiyewa a kan teburin caca don yin caca. Ana kuma kiranta: check.Karanta gaba ɗaya → ta hanyar ƙirga duk sakamako 37, wadda ita ce kaɗai hanya madaidaiciya ta yin hakan.
Ƙa'idar lissafi
Tambayoyi
A'a. Kowace caca tana da ƙimar da ake tsammani iri ɗaya. Bambancin sakamako mafi girma yana nufin hawa da sauka mafi faɗi a kewayenta.
Cace-cacen ɗaya zuwa ɗayacacaCacar ɗaya zuwa ɗaya (even-money)Ja/baƙi, mara/cika, manya/ƙanana. Lambobi 18, biya 1:1.Karanta gaba ɗaya →, da σ ≈ 1 a kowace raka'a. Ya ma fi ƙasa tare da la partageƙa'idaLa partageƘa'idar Faransa: idan sifili ya fito, ana mayar da rabin kuɗin cacar ɗaya zuwa ɗaya (even-money). Tana rage fifikon gidan caca a kan waɗannan cace-cace da rabi, zuwa 1.35%.Karanta gaba ɗaya →, wanda kuma yake inganta matsakaici.
Ribar da ake tsammani iri ɗaya ce a kowace dala; bambancin sakamako yana shafar yadda kuɗin shigar gidan caca ke zuwa da hawa da sauka ne kawai, kuma gidan caca yana da dubban ʼyan wasa da ke daidaita shi.
Nishaɗi da lissafi
Ku fara gwada waɗannan da kanku. Kowace mafita a naɗe take; ku buɗe ta idan kun shirya.
ʼYan wasa biyu kowannensu yana sa caca ta $1 a kowane juyi na juye-juye 100 a dabaran roulette na Turai, ɗaya koyaushe a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →, ɗayan koyaushe a kan 17. Wa ya fi yiwuwar kasancewa a gaba a ƙarshe?
Nuna mafita
Amsa Ɗan wasan da ke kan 17: 50.9%, idan aka kwatanta da 35.5% ga ja. Duka biyun suna rasa $2.70 a matsakaici.
Ja: ɗan wasan yana a gaba da nasara 51 ko fiye cikin 100, kowace da yiwuwalissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya → 18/37. Rarrabawar binomial tana ba da 35.5%, kuma nasara 50 daidai, ba riba ba asara, ƙarin 7.7%.
Lamba 17: kowace nasara tana mayar da $36, don haka nasara biyu (−$28) ba su isa ba, uku (+$8) kuma sun isa. Damar samun nasara uku ko fiye a juye-juye 100 a 1/37 ita ce 50.9%.
Ɗan wasan straight up yana kasancewa a gaba sau da yawa, amma sakamakon yana da tsalle-tsalle: nasara ɗaya fiye ko ƙasa tana motsa sakamakon da $36, kuma ʼyan wasan da ke a baya galibi sun fi nisa a baya. Bollman (2024) ya ba da alƙaluman na Amurka, 26.5% da 49.2%.
Ɗan barkwanci

Asarar da ake tsammani iri ɗaya. Ɗaya daga cikinsu yana gaya muku da babbar murya.
Majiyoyi
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.