Kyaututtuka, tallace-tallace da mayar da kuɗi a roulette
Kyaututtukan roulette kamar takardun matchplay, tsabobin caca da ba za a iya canjawa zuwa kuɗi ba da mayar da wani ɓangare na asara suna mayar da ɗan kuɗi kaɗan daga gidan caca zuwa ɗan wasa. Idan aka lissafa farashinsu daidai, wasu daga cikinsu sun fi abin da dabaran ke ɗauka daraja.
Takardar da ke ninka biyan cacar ɗaya zuwa ɗaya tana da darajar kusan 46% na cacar a dabaran Turai. Tsabar caca ta talla da ake amfani da ita sau ɗaya tana da darajar (36 − n)/37 na ƙimar da aka rubuta a kanta a cacar da ke rufe lambobi n: 95% a straight up, 49% a ja. Mayar da rabin asarar tsaf tana sa gajeren zaman wasa a kan ja ya cancanci a buga. Babu ɗaya daga cikin waɗannan da ke canja dabaran; suna canja wanda ke biya ne kawai.
Dalilin da ya sa talla za ta iya fin fifikon
Fifikon gidan cacalissafiFifikon gidan cacaKason kowane kuɗin caca da gidan caca ke riƙewa a matsakaici: 2.70% a roulette na Turai.Karanta gaba ɗaya → farashi ne a kan 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 → da aka saka: 2.70% a dabaran Turai. Kyautar roulette tana ƙara kuɗi a gefe ɗaya na caca, kuma idan ta ƙara fiye da 2.70% na kuɗin caca, ƙimar da ake tsammani ta wannan cacar tana sama da sifili muddin tallar tana ci gaba. Gidajen caca suna bayar da su duk da haka saboda suna da iyaka: takarda ɗaya a kowace ziyara, 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 → da za a iya yin caca da su amma ba za a iya canjawa zuwa kuɗi ba, mayar da kuɗi ga ʼyan wasan da ke asarar maƙudan kuɗi kawai. Lissafin daidai yake da ko'ina a wannan shafin: dama sau biyakuɗiBiyaAbin da cacar da ta ci ke dawowa da shi, ana faɗinsa a matsayin “X zuwa 1” a kan kuɗin cacar da aka mayar.Karanta gaba ɗaya →, an haɗa su a dukkan sakamako.
Takardun matchplay
Takardar matchplay tana zama kusa da cacar kuɗi kuma tana ninka abin da cacar ke biya idan ta ci; ko an ci ko an yi asara, gidan caca yana riƙe takardar. Bollman (2024) ya lissafa farashin wata takarda ta Las Vegas daga 2022 wadda ke ƙara daidai har zuwa $50 a kan cacar ɗaya zuwa ɗayacacaCacar ɗaya zuwa ɗaya (even-money)Ja/baƙi, mara/cika, manya/ƙanana. Lambobi 18, biya 1:1.Karanta gaba ɗaya →. A dabaran Turai, $50 a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → tare da takardar tana cin $100 da dama ta 18/37 kuma tana asarar $50 da dama ta 19/37: abin da ake tsammani +$22.97, ko 45.9% na cacar. A dabaran Amurka +$21.05 ne, 42.1%. A straight upcacaStraight upLamba ɗaya tak, biya 35:1.Karanta gaba ɗaya → (cacar lamba ɗaya) takarda iri ɗaya za ta ninka daraja sau biyu, shi ya sa ake iyakance takardun ga cace-cacen ɗaya zuwa ɗaya.
Tsabobin caca da ba za a iya canjawa zuwa kuɗi ba
Tsabobin caca na talla, waɗanda ake kira non-negotiable chips, ana iya yin caca da su amma ba za a iya musanya su da kuɗi ba. Dokar da aka saba ita ce amfani sau ɗaya: cacar da ta ci ana biyan ta da tsabobin caca na yau da kullum kuma ana karɓe tsabar cacar talla; wadda ta yi asara ma ana karɓe ta. Tsabar caca ta $100 a kan cacar da ke rufe lambobi n tana cin (36 − n)/n × $100 da dama ta n/37, don haka darajarta (36 − n)/37 ce na ƙimar da aka rubuta a kanta. Ƙimar tsabar cacar kanta ba ta taɓa dawowa, sai dai ribar kawai, kuma cacar da ba kasafai take cin nasara ba amma tana biyan mai yawa ita ce ta fi ƙarancin asara ta wannan hanya: $94.59 a straight up, $48.65 a ja. Inda tsabar cacar za ta iya zama a kan shimfiɗar teburikayan aikiTeburin caca (layout)Ragar caca da aka buga a kan tebur. Ana kuma kiransa: table, felt, cloth.Karanta gaba ɗaya → har sai ta yi asara, cacar ɗaya zuwa ɗaya tana da darajar 18/19 na ƙimarta a dabaran Turai da 9/10 a na Amurka (Bollman, 2024).
Mayar da tsabobin caca zuwa kuɗi
Daraja matsakaici ce; ɗan wasa da ke son kuɗin tabbas zai iya saye shi da kariya (hedge). Misalin Bollman daga tsohon gidan caca na Vegas World ne: $1,000 na tsabobin caca na amfani sau ɗaya a dabaran Amurka, $500 a kan ja da $500 a kan baƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya →, tare da $20 na kuɗi a kan kowanne daga cikin 0 da 00. Ja ko baƙi yana cin $500 kuma yana asarar $40 na kuɗi: +$460. 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 → yana asarar tsabobin caca biyun kuma yana biyan $700 a kan kuɗin: +$680. Ɗan wasan yana tabbatar da aƙalla $460, kuma matsakaicin, $471.58, 99.6% ne na darajar tsabobin cacar a kan ja kaɗai. Inda dokoki suka yarda a saka tsabobin caca a kan lamba ɗaya-ɗaya, dabaran Turai yana ba da kariya mafi kyau: tsabobin caca na $25 a kan dukkan lambobi 36 ($900) da $25 na kuɗi a kan sifili. Duk lambar da ta fito tana biyan $875, kuma kuɗin da ke kan sifili yana ɓacewa sai dai idan sifili ne ya fito, don haka ɗan wasan yana riƙe aƙalla $850, 94% na ƙimar tsabobin cacar, ba tare da wani haɗari ba.
Mayar da wani ɓangare na asara
Ana yawan ba ʼyan wasa masu saka maƙudan kuɗi rangwame: wani kaso na asarar tsaf da suka yi ana mayar musu a ƙarshen zaman wasa da aka amince da shi. Rangwame yana biya ne kawai idan kun yi asara, don haka ya fi daraja lokacin da sakamako ke kaɗawa sosai kuma zaman wasa gajere ne har fifikon bai riga ya yi rinjaye ba. Epstein (2013) ya yi lissafin ga dabaran Amurka; namu adadin na dabaran Turai suna biye. Idan aka mayar da rabin asarar tsaf, caca da kuɗi ɗaya a kan ɗaya zuwa ɗaya ta cancanci a buga har zuwa juye-juye 103, kuma ta fi kyau a 25, inda darajarta +0.51 na kuɗin caca ce a matsakaici. A straight up kaɗawar tana da girma sosai har zaman wasa yana ci gaba da kasancewa mai riba har kusan juye-juye 3,600, kuma ya fi kyau a 882, inda darajarsa +17.25 na kuɗin caca ce. Da mayar da 10% wanda aka fi saba gani, ɗaya zuwa ɗaya tana da riba ne kawai a juyi ɗaya, yayin da straight up ya fi kyau a juye-juye 20, inda darajarsa +0.62 na kuɗin caca ce.
Dokokin tallan roulette: abin da gidan caca ke dogara da shi
Kowace talla tana da iyaka, kuma iyakar tana kare gidan caca: takarda ɗaya a kowace ziyara, tsabobin caca da ake bayarwa a ƙayyadadden adadi, rangwame da ake amincewa da shi ne kawai da ʼyan wasan da asarar da ake tsammani daga gare su a tafiya ɗaya ta fi mayarwar nesa ba kusa ba. Ɗan wasa da ya yi amfani da takardar sannan ya zauna na yammaci yana saka $50 a kan ja zai mayar da $22.97 ɗin cikin juye-juye 17, a $1.35 a kowane juyi. Darajar gaskiya ce ga ɗan wasan da ya karɓe ta ya tafi, ko wanda dama zai yi wasa har haka.
Ƙa'idar lissafi
Tambayoyi
Ga cacar guda ɗaya da take tare da ita, e. Kowace caca dabam har yanzu tana kashe 2.70% na kuɗin caca.
ʼYan wasa kaɗan ne ke tunanin ta, tsabobin caca suna da iyaka, kuma gidan caca ya riga ya lissafa farashin tallar a matsayin talla.
Ba kasafai ba. Sharaɗi ne na manyan ʼyan caca, wanda yawanci ake amincewa da shi tare da mai kula da baƙi na gidan caca kuma ake biya a kan asarar tsaf a tafiya ɗaya.
Nishaɗi da lissafi
Ku fara gwada waɗannan da kanku. Kowace mafita a naɗe take; ku buɗe ta idan kun shirya.
An ba ku tsabar 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 talla ta $25 wadda ake karɓewa bayan caca ɗaya, ko an ci ko an rasa. Ina ya kamata ta tafi: a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →, a kan dozincacaDozin1–12, 13–24 ko 25–36, biya 2:1.Karanta gaba ɗaya → ko a kan lamba ɗaya?
Nuna mafita
Amsa A kan lamba ɗaya. A can darajarta $23.65 ce a matsakaici; a kan dozin $16.22, a kan ja kuma $12.16.
Ita tsabar cacar kanta ba ta dawowa, sai abin da ta ci kawai. A kan ja tana cin $25 da damar 18/37: $12.16. A kan dozin tana cin $50 da damar 12/37: $16.22. A kan lamba ɗaya tana cin $875 da damar 1/37: $23.65.
Gabaɗaya, caca a kan lambobi n tana da darajar (36 − n)/37 na tsabar cacar, don haka idan lambobin suka yi ƙasa, ya fi kyau. Da tsabar caca ta yau da kullum wannan ba shi da bambanci, domin kuɗin caca yana dawowa a kowace nasara kuma kowace caca tana da darajar 36/37 nata. Ɗauke kuɗin caca yana cutar da cace-cacen da ke yawan cin nasara kuma da ƙyar yake taɓa cacar da ke nasara sau ɗaya cikin 37.
Wani gidan caca zai mayar da rabin asarar ku ta tsaf bayan juyi ɗaya daidai. Shin $100 a kan ja ya cancanci a buga? Kuma $100 a kan lamba ɗaya fa?
Nuna mafita
Amsa Duka biyun: kusan +$22.97 a kan ja da +$45.95 a kan lambar.
A kan ja kuna cin $100 da damar 18/37 kuma, bayan mayarwa, kuna rasa $50 da damar 19/37: (1,800 − 950)/37 = +$22.97.
A kan lamba ɗaya kuna cin $3,500 da damar 1/37 kuma kuna rasa $50 da damar 36/37: (3,500 − 1,800)/37 = +$45.95.
Waɗannan su ne alƙaluman matchplay kuma. Cacar $100 da ke rasa $50 kawai tana cin $100 ko tana rasa $50, daidai kamar cacar $50 da coupon da ke ninka nasararta biyu. A cikin zaman wasa mai tsawo, ana biyan mayarwar ne a kan sakamakon tsaf kawai, nasarori da asarori suna soke juna kafin a biya ta, darajar kuma tana raguwa; ga ja da mayar da rabi, juye-juye 25 su ne mafi kyawun tsawo.
Gidan cacar zai mayar da rabin asarar ku ta tsaf bayan ƙayyadadden adadin cace-cace na $100 a kan ja, da aka zaɓa tun da farko: juyi 1, 2 ko 3. Wanne ne ya fi daraja?
Nuna mafita
Amsa Juye-juye uku: kusan +$31.45. Juyi ɗaya yana da darajar +$22.97, biyu kuma +$20.96 kawai.
Juyi ɗaya: ku ci $100 da damar 18/37, ko ku rasa $100 ku dawo da $50 da damar 19/37: +$22.97, kamar a atisayen da ke sama.
Juye-juye biyu: duka biyu sun ci (sau 324 cikin 1,369), +$200. Ɗaya-ɗaya (sau 684), $0, babu abin da za a mayar. Duka biyu sun rasa (sau 361), −$200, −$100 bayan mayarwa. Matsakaici: (200 × 324 − 100 × 361)/1,369 = +$20.96. Mayarwar tana biya ne kawai a kan asara, kuma juye-juye biyu suna mayar da asarori da yawa na juyi ɗaya zuwa canjaras.
Juye-juye uku ba za su taɓa yin canjaras ba. Nasara uku (sau 5,832 cikin 50,653): +$300. Nasara biyu (18,468): +$100. Nasara ɗaya (19,494): −$100, an mayar zuwa −$50. Babu (6,859): −$300, an mayar zuwa −$150. Matsakaici: +$31.45.
Mayarwar tana ƙara daraja idan kuka ɗauki alƙawari mai tsawo, yayin da fifikon gidan caca ke jawo asarar $2.70 kawai a kowane juyi, don haka darajar tana hawa zuwa kusan +$51 a juye-juye 25 (duba teburin da ke sama), kuma adadin juye-juye na mara koyaushe yana doke na cika da ke biye da shi.
Wani gidan caca a Las Vegas ya taɓa raba coupon: ku sa caca ta $5 a kan 00 kuma, idan ta ci, za a biya ku $250 maimakon $175 da aka saba. Mece ce darajar cacar $5 da coupon ɗin, a matsayin kaso na kuɗin caca, a dabaran sa 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?
Nuna mafita
Amsa Kusan +34%: cacar tana da darajar +$1.71 a matsakaici. Idan $250 ɗin ya haɗa da $5 da aka mayar, +31.6% ne.
00 yana cin nasara sau ɗaya cikin juye-juye 38. Da coupon: +$250 sau ɗaya, −$5 sauran sau 37. Matsakaici: (250 − 37 × 5)/38 = 65/38 = +$1.71, wato 34.2% na $5. Ba tare da coupon ba: (175 − 185)/38 = −$0.26, −5.26% da aka saba.
Idan $250 shi ne jimillar abin da aka mayar, nasarar $245 ce kuma matsakaicin (245 − 185)/38 = +$1.58, ko 31.6%.
Bollman (2024) ya sa wannan coupon, daga gidan caca na Lady Luck (yanzu Downtown Grand), a matsayin atisaye; amsar da aka buga tare da shi, 7.89%, ba ta dace da ko ɗaya daga cikin fassarorin biyu ba. Kamar coupon na matchplay, yana da daraja sau ɗaya: ku buga shi ku tsaya.
Ɗan barkwanci
Talla ta fi daraja ga ɗan wasan da ya karɓe ta ya koma gida.
Majiyoyi
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.