Misali: dabarar dozin biyu a roulette
Dala goma a kan kowane ɗaya daga cikin dozin biyu, wato lambobi 24 a rufe, na tsawon juye-juye hamsin. Dabarar dozin biyu a roulette ita ce cacar rufe lambobi da ke cin nasara a juye-juye biyu cikin uku, amma har yanzu tana jawo asarar 2.70%.

Zaman wasa na kwaikwayo mai juye-juye 50 na $10 a kan dozin na farko da na biyu. Nasara talatin da ɗaya ta $10, asara goma sha tara ta $20 (dozin na uku ko sifili). Sakamakon tsaf −$70, bayan an kai riba ta $90. Cacar da ke jin kamar ba ta da haɗari domin tana yawan cin nasara, amma farashinta daidai yake da na kowace caca.
Shirin: dabarar dozin biyu a roulette
$10 a kan dozincacaDozin1–12, 13–24 ko 25–36, biya 2:1.Karanta gaba ɗaya → na farko da $10 a kan na biyu. Lamba daga 1 zuwa 24 tana biyan dozin ɗaya $20, ɗayan kuma ya yi asarar $10: +$10. Lamba daga 25 zuwa 36, ko 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 →, tana sa duka biyun su yi asara: −$20. 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 →: (24 × 10 − 13 × 20)/37 = −20/37 = −$0.54 a kowane juyi, wato 2.70% na $20. Yawan nasara 64.9%, kuma wannan adadin ne ke sa ake sayar da cacar.
Juye-juye 1–25
Nasara goma sha takwas, asara bakwai: +$180 − $140 = +$40. Asarori bakwai ɗin sun haɗa da sifili sau ɗaya da jerin lambobi uku na dozin na uku a juye-juye 11–13 da suka jawo asarar $60 a jere, kuma suka ji kamar abin da ba a saba ba. Amma 35.1% ne kawai ya zo a dunƙule, kuma abubuwa kan zo a dunƙule.

Juye-juye 26–50
Nasara goma sha uku, asara goma sha biyu: +$130 − $240 = −$110. Asara goma sha biyu a juye-juye 25 abu ne da ke faruwa a kashi 20%, ba abin mamaki ba ne. Ƙarshe −$70; mafi girma +$90 a juyi na 31. Cacar ba ta taɓa kawo babban sauyi a kowace hanya ba, domin nasara $10 ce, asara kuma $20; kawai tana niƙa a hankali.
- p10 −$500
- p25 −$500
- tsakiya −$280
- p75 −$40
- p90 +$170
Lissafin kuɗi
Jimillar caca $1,000 a juye-juye 50. 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 → $27; ainihin sakamako −$70, kusan standard deviationlissafiStandard deviationTushen murabba'i na bambancin sakamako; nisan da sakamako ke yawan yi daga ƙimar da ake tsammani.Karanta gaba ɗaya → ɗaya ƙasa da haka (σ a kowane juyi kusan $14 ne, don haka kusan $100 a juye-juye 50). Irin wannan $20 a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → da yana da abin da ake tsammani iri ɗaya da σ mafi girma, kusan $140 a dukan zaman wasan: dozin biyu hanya ce ta rasa adadi iri ɗaya da ƙaramin 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 →.
Abin da zaman wasan ya nuna
Rufe lambobi 24 yana sa roulette ya ji kamar wasan da kuke yawan cin nasara a ciki, kuma haka ne: kashi 64.9% na juye-juye. An tsara biyankuɗiBiyaAbin 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 → ta yadda kashi 35.1% da kuke rasawa yake cin ninki biyu na abin da nasarori ke biya, kuma tsarin teburin cacakayan aikiTeburin caca (layout)Ragar caca da aka buga a kan tebur. Ana kuma kiransa: table, felt, cloth.Karanta gaba ɗaya → ya daidaita wannan rabo zuwa −1/37 na jimillar kuɗin caca. Ku ƙara 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 → a kan sifili a matsayin “inshora”, fifikon gidan caca na haɗe zai kasance 2.70% har yanzu, domin an saka wa inshorar farashin 2.70% ita ma. Shafin Matsala: dozin biyu da tsabar caca ɗaya yana yin lissafin dalla-dalla.
Tambayoyi
Lissafi iri ɗaya: lambobi 24, +1 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 → idan an ci, −2 idan an rasa. GinshiƙaicacaGinshiƙiLambobi goma sha biyu a cikin ginshiƙi ɗaya a tsaye na teburin caca, biya 2:1.Karanta gaba ɗaya → suna watsa lambobin da aka rufe a kan dabaran; dozin kuma suna tara su wuri ɗaya a kan teburin caca. Babu bambanci a tsakaninsu.
Tana rufe lambobi 25; yanzu sifili yana ba da +$16 tsaf maimakon −$20, da kuɗin $1 a kowane juyi. Ƙimar da ake tsammani −$0.57 ce a kan $21, har yanzu 2.70%.
Haka ne, kuma an daidaita biyan da shi. Mafi yawan lokaci kuna cin $10. Wani lokaci kuna rasa $20. Matsakaicin shi ne fifikon gidan cacalissafiFifikon gidan cacaKason kowane kuɗin caca da gidan caca ke riƙewa a matsakaici: 2.70% a roulette na Turai.Karanta gaba ɗaya →.
Ɗan barkwanci

Ku ci juye-juye biyu cikin uku. Ku rasa ninki biyu a na ukun. Sakamakon shi ne 2.70%.
Majiyoyi
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.