Asarar da ake tsammani
Ƙimar da ake tsammani sau jimillar abin da kuke caca da shi: abin da zaman wasa ke ci a matsakaici.

Asarar da ake tsammani = jimillar caca × 1/37. Kuɗin caca $10, juyi 100: an yi caca da $1,000, asarar da ake tsammani $27. Jerin ƙarin caca yana yin caca da kuɗi mafi yawa, don haka asararsa ta fi yawa.
Jimillar caca, ba jarin caca ba
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 → ta dogara ne da yawan kuɗin da ke wucewa a kan teburi, ba da yawan abin da kuka kawo ba. 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 → na $100 da aka sake yin caca da shi sau da yawa zai iya ɗaukar 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 → ta $2,000 da asarar da ake tsammani ta $54; jarin caca na $10,000 da aka yi caca da shi sau ɗaya a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → yana ɗaukar jimillar caca ta $10,000 da $270. Kuɗin shigar gidan caca haraji ne a kan zirga-zirga, kuma zirga-zirgar ita ce kowace 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 kowane juyi.
Ƙa'idar lissafin
E[asara] = Σ kuɗin caca / 37. Ga mai caca da kuɗi ɗaya, wannan shi ne kuɗin caca × juye-juye / 37. Ga 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 →, matsakaicin kuɗin caca ne × juye-juye / 37, kuma matsakaicin kuɗin caca ya fi kuɗin tushe yawa, domin kuɗin caca yana hawa a lokutan jerin asara. 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 → daga tushe na $10 a iyakar $500 yana da matsakaicin kusan $28 a kowane juyi a dogon zaman wasa, don haka yana asarar kusan ninki uku na cacar $10 da kuɗi ɗaya, ba tare da ya canza damar kowace caca ɗaya ba.
Sauri
Teburan kai tsaye suna yin juyi 40–60 a sa'a, zauren gidajen caca 30–50, teburan gaggawa 90 ko fiye, teburan RNG kuma da saurin da kuke danna. Da kuɗin caca iri ɗaya, sauri shi ne babban abu guda da ke shafar asarar da ake tsammani a kowace sa'a: komawa daga teburi mai jinkiri a zauren gidan caca zuwa teburin RNG da ake wasa da shi juyi 200 a sa'a yana ninka kuɗin daren sau huɗu ba tare da wani canji a dama ba.
Cikin shekara ɗaya
Ɗan wasa na yau da kullum da ke wasa sa'o'i biyu a mako a $10 a teburi kai tsaye mai juyi 50 yana yin jimillar caca ta $52,000 a shekara kuma yana biyan kusan $1,400 na asarar da ake tsammani a dabaran Turai, $700 a na Faransa, $2,700 a na Amurka. Lissafin ba shi da armashi, amma sakamakon ba haka yake ba: zaɓin dabaran da teburi ya fi kowane tsarin caca daraja da ninkin marar iyaka, domin tsare-tsaren caca darajarsu daidai 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 → ce.
Wasan da ya fi kowane banki daraja
Wasan St. Petersburg, wanda Nicolaus Bernoulli ya gabatar a 1713, yana jefa kwabo har sai ya faɗi a fuska, kuma yana biyan $2 idan jefi ɗaya ne, $4 idan biyu, $8 idan uku, yana ninkawa kowane lokaci. Kowane tsawo da zai yiwu yana ƙara $1 ga 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 →, don haka a takarda wasan yana da darajar marar iyaka. Babu bankin da zai iya biyan kyaututtuka marasa iyaka, kuma da zarar an ƙayyade kyaututtuka zuwa abin da bankin ke da shi, darajar tana rugujewa: da banki na $1 miliyan wasan yana da darajar kusan $21, da $1 biliyan kusan $31. Martingale wasan nan ne dai, amma an kalle shi daga ɗayan gefen. Yana cin 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 kusan a kowane zagayen tsarin kuma yana rasa komai a wani dogon jeri da ba kasafai ake gani ba; ba tare da iyaka ba, da dogayen jerin za a biya su da nasarori masu ƙara girma koyaushe, amma da iyaka ba haka ba ne, shi ya sa 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 → ke yanke yadda Martingale zai gaza, amma ba ko zai gaza ba.

Asarar da ake tsammani ba ita ce sakamakon ba
Kowane zaman wasa guda zai bambanta da asarar da ake tsammani a gare shi, sau da yawa da fiye da asarar da ake tsammani kanta. Cikin juyi 100 na cacar ɗaya zuwa ɗaya a $10, standard deviationlissafiStandard deviationTushen murabba'i na bambancin sakamako; nisan da sakamako ke yawan yi daga ƙimar da ake tsammani.Karanta gaba ɗaya → $100 ne idan aka kwatanta da −$27 da ake tsammani; zaman wasa da ya ƙare da riba ba abin mamaki ba ne. Asarar da ake tsammani ita ce farashi; 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 marufi; sakamakon wani dare samfuri ne na guda ɗaya.
Ƙa'idar lissafi
Tambayoyi
A'a. 2.70% na duk abin da kuke caca da shi. Idan kuka sake yin caca da abin da kuka ci, an sake yin caca da shi ke nan.
A kowace sa'a, e, a sauri iri ɗaya. A kowane buri da aka kai, a'a: ku duba haɗarin ƙarewar jarilissafiHaɗarin ƙarewar jariYiwuwar rasa duka jarin caca kafin a kai wani buri ko wani adadin juye-juye.Karanta gaba ɗaya →.
Gidajen caca suna ƙididdige asarar da kuke tsammani daga matsakaicin cacarku da lokacin da kuka yi wasa, kuma suna mayar da wani ɓangare nata a matsayin comps. Suna mayar da wani ɓangare na farashin ne, ba wai suna ba ku fifiko ba.
Ɗan barkwanci

Jimillar caca × 1/37. Agogo yana cikin ƙa'idar lissafin.
Majiyoyi
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.