Lissafi · Muhimmin ra'ayi · minti 7

Ƙimar da ake tsammani a roulette

Ƙimar da ake tsammani a roulette ita ce matsakaicin sakamakon caca idan za a iya maimaita ta har abada. A roulette na Turai iri ɗaya ce ga kowace caca ta yau da kullum: kuna rasa 1/37 na kowane kuɗin caca, a matsakaici, a kowane juyi.

A sauƙaƙe

Ku yi tunanin sanya caca iri ɗaya ta $10 a kan ja sau miliyan ɗaya. Wasu juye-juye suna cin $10, wasu suna rasa $10. Ku haɗa kowane sakamako ku raba da miliyan ɗaya: za ku sami kusan −$0.27. Wannan lambar ita ce ƙimar da ake tsammani ta cacar roulette. Ba abin da ke faruwa a kowane juyi ɗaya ba ne; matsakaici ne na dogon zango a kowane juyi.

Amsa a taƙaiceEV = yiwuwar cin nasara × adadin da aka ci − yiwuwar asara × adadin da aka rasa. Ga kowace cacar roulette ta yau da kullum, wannan yana zama −2.70% na kuɗin caca.

Ƙa'idar lissafin EV na cacar roulette

EV = p · W − (1 − p) · S
p = n/37 · W = S·(36/n − 1) · n = lambobin da aka rufe · S = kuɗin caca

Ku maye gurbin dokar biyan roulette, 36/n − 1, kuma n zai soke kansa. Wannan shi ne dukan labarin fifikon gidan caca a layi ɗaya:

EV = (n/37)·S·(36/n − 1) − ((37−n)/37)·S
= S·(36 − n − 37 + n)/37
= −S/37

Ku gwada: na'urar lissafin ƙimar da ake tsammani a roulette

Ku zaɓi lambobi nawa cacar take rufewa. Yiwuwa da biya suna canzawa; ƙimar da ake tsammani ba ta canzawa.

an rufe lamba 1 · biya 35:1kuɗin caca $10

asara 97.3%

p(nasara)1/37 = 2.70%

nasara tana biyan+$350

asara tana cin−$10

EV = p·W − (1−p)·S0.0270·$350 − 0.9730·$10

ƙimar da ake tsammani−$0.27 a kowane juyi · −2.70%

Yadda yake kama a tsawon lokaci

Matsakaicin sakamako a kowane juyi ga cacar $10 a kan ja, yayin da juye-juye ke ƙaruwa. Da farko, sa'a ce ke rinjaye; matsakaicin mai gudana yana daidaita zuwa −$0.27 yayin da samfurin ke girma. Wannan ita ce kusantowa a dogon zango da gidan caca ke dogara da ita.

Juyi bayan juyi, matsakaicin da ke gudana yana daina kaɗawa kuma yana tsayawa ƙasa da sifili kaɗan.

Kuskuren fahimta da aka saba

“EV da ke ƙasa da sifili yana nufin zan yi asara a kowane zaman wasa.”

A'a. Yana nufin matsakaicin zaman wasa da yawa asara ne. Zaman wasa ɗaya-ɗaya suna bambanta sosai, musamman ga cace-cace masu babban bambancin sakamako kamar straight up.

“Gidan caca yana buƙatar dogon lokaci kafin ya ci.”

Fifikon gidan caca yana aiki a kowane juyi; abin da dogon zango ke yi shi ne sa sakamakon ya zama abin hasashe. A zaman wasa ɗaya, sa'a ce ta fi ƙarfi.

“Wasu cace-cace suna da EV mafi kyau fiye da wasu.”

Ba a roulette na Turai ba, sai dai akwai banda ɗaya: ƙarƙashin la partage ko en prison, cace-cacen ɗaya zuwa ɗaya suna da rabin fifikon gidan caca da aka saba.

Ɗan barkwanci

$Ba abin da ke faruwa a juyi ɗaya ba. Matsakaicin dukansu ne.$

Ba abin da ke faruwa a juyi ɗaya ba. Matsakaicin dukansu ne.