Ƙarin bayani · Ilimi · minti 7

Roulette da koyar da lissafi

Dabaran roulette yana sa yiwuwa ta zama mai sauƙin hangowa. Ga yadda ake amfani da shi a darasi ba tare da ƙarfafa caca ba.

Amsa a taƙaice

Sakamako talatin da bakwai masu yiwuwa daidai, ƙayyadaddun biya, rashin dogaro da juna, sanannen tsammanin asara da kuma dogon tarihin kuskuren ɗan Adam. Roulette yana bayyana tsammani, 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 →, dokar manyan lambobilissafiDokar manyan lambobiMatsakaicin sakamako masu zaman kansu yana kusantar ƙimar da ake tsammani yayin da yawan gwaje-gwaje ke ƙaruwa.Karanta gaba ɗaya →, kuskuren ɗan caca, gwajin hasashe da matsalar ranar haihuwa fiye da yadda kuɗin ƙarfe ko ɗan lido ke yi.

sararin sakamako
37, daidai gwargwado
ra'ayoyin da aka koyar
≥ 8
kayan aiki a wannan shafin
kyauta, a cikin burauza
darasi na sifili
EV = −1/37, kullum

Me ya sa roulette

Kuɗin ƙarfe yana da sakamako biyu, ɗan lido kuma shida; duka biyun sun yi ƙanƙanta wajen nuna matsalar ranar haihuwalissafiMatsalar ranar haihuwaMutane nawa ake buƙata kafin ya fi yiwuwa biyu daga cikinsu su kasance da ranar haihuwa ɗaya, ko juye-juye nawa kafin ya fi yiwuwa wata lamba ta maimaitu. A dabaran mai ramuka 37, juyi 8 ya isa a sami damar da ta fi rabi.Karanta gaba ɗaya → ko gwajin chi-squaregwajiGwajin chi-squareGwajin ƙididdiga da ke kwatanta yawan faɗuwar ƙwallo da aka gani a kowane rami da abin da ake tsammani, n/37. Ana amfani da shi don tantance ko dabaran ya karkata.Karanta gaba ɗaya → da wani abin burgewa. Katunan wasa suna da ƙwaƙwalwa. Roulette yana da sakamako 37 masu yiwuwa daidai, ƙayyadaddun 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 → da ke sa lissafin tsammani ya zama layi ɗaya, rashin dogaro da juna bisa tsarin zahiri, da fifiko ƙarami har ya ɓoye a zaman wasa ɗaya amma babba har ya mamaye shekara guda. Haka kuma yana da ƙarnoni biyu na kurakuran tunani da aka rubuta don a yi nazari a kansu.

Kuɗin ƙarfe, ɗan lido da katunan wasa suna ba da wuri ga sakamako 37 masu yiwuwa daidai na roulette.

Gwajin chi-square

Jerin darussa

darasira'ayimisalin roulettekayan aiki a wannan shafin
1yiwuwa a matsayin ƙirgep(caca) = n/37Na'urar lissafin damar nasara a roulette
2tsammaniEV = (n/37)(36/n − 1) − (37 − n)/37 = −1/37Mai haɗa caca
3rashin dogaro da juna da dokar ninkawa(18/37)² don ja biyuYiwuwar jerin sakamako iri ɗaya a roulette
4kishiya da “aƙalla sau ɗaya”1 − (36/37)³⁷ = 63.7%Yiwuwa a roulette
5bambancin sakamako da standard deviationσ = 5.84 (straight up) da 1.00 (ja), EV iri ɗayaBambancin sakamako
6dokar manyan lambobi (da abin da ba ta faɗa ba)matsakaici yana kusantowa; jimilla tana nisantawaKusantowa a dogon zango
7kuskuren ɗan cacabaƙi 26, 1913Kuskuren ɗan caca
8tafiya ta kwatsam da ƙarewar jariƙa'idar lissafin ƙarewar jarin ɗan cacaNa'urar lissafin haɗarin ƙarewar jari
9gwajin hasashechi-square a kan ramuka 37Mai nazarin karkatar dabaran roulette
10matsalar ranar haihuwamaimaitawa a cikin juye-juye 8, 56%Matsala: dabaran ranar haihuwa
11kwaikwayon Monte Carlozaman wasa 10,000 a cikin daƙiƙa ɗayaSimulator na dabarar roulette
12me ya sa tsare-tsare ke kasawaƙa'idar haɗa tsammaniZa a iya cin roulette?

Koyarwa ba tare da koyar da caca ba

Ku yi amfani da kuɗin wasa da Wasan gwaji, wanda ba shi da kuɗin caca na gaske. Ku fara da 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 → kuma ku ci gaba da komawa gare ta: kowane atisaye yana ƙarewa da “kuma ƙimar da ake tsammani ita ce −1/37 na kuɗin caca”. Ku yi amfani da tsare-tsaren a matsayin misalan kuskure, ba a matsayin hanyoyin bi ba: atisayen shi ne a nemo aibin, kuma simulator yana nuna aibin cikin daƙiƙoƙi. Ku haɗa da tarihin mutanen da suka yi asara. Darasin shi ne cewa lissafi ne ke yin nasara, wanda shi ne akasin talla.

Atisayen da ke aiki

Ku sa ɗalibai su yi hasashen juye-juye nawa kafin maimaitawa, sannan su gudanar da Wasan gwaji sau goma (matsalar ranar haihuwa). Ku sa su rubuta “tsari” a editan dabara su gudanar da zaman wasa 10,000 (ƙa'idar haɗa tsammani). Ku sa su lissafa yiwuwarlissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya → jerin na 1913 sannan na faruwar jerin a wani wuri a cikin shekaru hamsin na Monte Carlo (bambancin takamaiman al'amari da wani al'amari kowane iri). Ku sa su nemo ramikayan aikiRamiƊaya daga cikin ɗakuna 37 masu lamba a kan rotor. Ana kuma kiransa: slot, cup.Karanta gaba ɗaya → “mai karkata” a cikin tarihin juye-juye na adalci sannan su gauraya bayanan (kwatance da yawa).

Yadda hasashen ɗalibai ke saurin yin kuskure (hasashen aji na yau da kullum da gaskiya)
juye-juye kafin maimaitawa: hasashe ≈ 19, gaskiya 8
8 da 19
p(fitowa ≥1 a juye-juye 37): hasashe 100%, gaskiya 63.7%
63.7% da 100%
p(ja bayan ja 10): hasashe “ƙasa”, gaskiya 48.65%
48.65%
zaman wasa da riba, Martingale: hasashe ≈ 95%, gaskiya ≈ 78%
78% da 95%
matsakaicin sakamako, Martingale: hasashe “riba”, gaskiya asara
asara
050100
Kowane giɓi darasi ne. Na ƙarshe shi ne dukan kwas ɗin.

Karanta tarihin juye-juyen da aka wallafaMuhimmancin ƙididdiga

Me ya sa yake zama a zuciya

Ɗalibai suna tunawa da baƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya → 26, dabaran Jagger, da lokacin da simulator ya nuna tsarinsu yana asara. Ana manta yiwuwa ta ka'ida zalla kafin jarrabawa ta zo; dabaran ba a mantawa da shi. Iyakar ɗabi'a a bayyane take: ku koyar da lissafin da ke sa wasan ya zama mummunar caca, ta amfani da wasan, kuma ɗaliban da za su yi caca daga baya aƙalla za su san farashin.

Shahararrun ʼyan wasan roulette

Tambayoyi

Shin ya dace da ɗaliban makaranta?

Da kuɗin wasa, da bayyana a fili cewa fifikon gidan cacalissafiFifikon gidan cacaKason kowane kuɗin caca da gidan caca ke riƙewa a matsakaici: 2.70% a roulette na Turai.Karanta gaba ɗaya → shi ne darasin, manhajojin karatu da yawa sun riga sun yi amfani da ɗan lido da lotto; roulette sigar abu ɗaya ce mai zurfi.

Wane shafi ya kamata malami ya fara da shi?

Fifikon gidan caca a roulette, sannan Wasan gwaji, sannan Simulator na dabarar roulette.

Shin Wasan gwaji yana da aminci ga aji?

Ba shi da kuɗi na gaske, ba shi da asusu, kuma ba shi da hanyoyin haɗi zuwa kamfanonin caca.

Ɗan barkwanci

Sakamako talatin da bakwai, fifiko ɗaya, ƙarnoni biyu na kurakurai da za a koya daga gare su.

Sakamako talatin da bakwai, fifiko ɗaya, ƙarnoni biyu na kurakurai da za a koya daga gare su.

Majiyoyi

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, bugu na 3, 1968. Ƙarewar jarin ɗan caca, babi na XIV.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Babi na 13, roulette.
an duba 2026-09-28samfuri: na Turai, sifili ɗayahanyar aiki ↗majiyoyi ↗