Standard deviation a roulette
Standard deviation na roulette, wato tushen murabba'i na 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 nisan da aka saba gani tsakanin sakamako da abin da ake tsammani.
A kowace $1 ta kuɗin caca, σ 5.84 ne ga straight up kuma 1.00 ga ja. Ku ninka shi da kuɗin caca da kuma tushen murabba'i na yawan juye-juye don samun na zaman wasa.
Ƙa'idar ƙiyasi mai sauƙi
Kusan kashi biyu cikin uku na zaman wasa suna faɗuwa cikin σ ɗaya daga abin da ake tsammani, kuma 95% cikin biyu. Ga juyi 100 a jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → da $10 (ana tsammanin −$27, σ = $100), yawancin zaman wasa suna faɗuwa tsakanin −$127 da +$73, kuma kusan duka tsakanin −$227 da +$173. Sakamakon da ya fita daga wannan iyaka ba shaida ba ce ta komai, sai dai cewa zaman wasa ɗaya cikin ashirin yana yin haka.
Me ya sa √N
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 → tana ƙaruwa daidai da N; watsuwar sakamako kuma tana ƙaruwa daidai da √N. Idan N ƙarami ne, watsuwa ta fi rinjaye, kuma zaman wasa kamar jefa kwabo ne mai ɗan karkata. Idan N babba ne, asara ta wuce watsuwa. Wurin da suke haɗuwa, inda asarar da ake tsammani ta yi daidai da standard deviationlissafiStandard deviationTushen murabba'i na bambancin sakamako; nisan da sakamako ke yawan yi daga ƙimar da ake tsammani.Karanta gaba ɗaya → ɗaya, yana a N = (σ/fifiko)² = (1/0.027)² ≈ juyi 1,370 ga cacar ɗaya zuwa ɗaya, da (5.84/0.027)² ≈ 46,800 ga straight upcacaStraight upLamba ɗaya tak, biya 35:1.Karanta gaba ɗaya →. Ƙasa da waɗannan adadi, sa'a ce ke yanke hukunci; sama da su, fifiko ne.
Yadda ake amfani da shi
Don sanin ko zaman wasa ya kasance na ban mamaki, ku lissafa (sakamako − EV)/σ. Ɗan wasan da ke cacar ja da $10 wanda ya kammala juyi 100 da +$150 yana a (150 + 27)/100 = 1.77σ, sakamako na ɗaya cikin 25: sa'a ce, ba abin mamaki ba. Ɗan wasan straight up da +$150 iri ɗaya yana a 0.3σ: dare ne na yau da kullum. Sakamako iri ɗaya a dala yana nufin abubuwa daban-daban a cace-cace daban-daban.
Standard error na kaso
Lissafi iri ɗaya yana nuna yawan juye-juyen da ake buƙata kafin a ga fifiko a cikin bayanai. Standard error na kason nasara da aka gani shi ne √(p(1 − p)/N). Ga ja da N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Bambanci tsakanin kwabo na adalci da ja 1.35% ne, don haka bayan juyi 1,000 har yanzu ba za ku iya bambance su da tabbaci ba. Bayan juyi 10,000, standard error ya zama 0.5% kuma za ku iya. Wannan ma shi ya sa gano karkatar dabaran ke buƙatar juye-juye da yawa haka.
Gargaɗi game da karkata
Sakamakon straight up ya yi nisa da normal distribution a gajeren zaman wasa: yawancin zaman wasa asara ce ta −$10 a kowane juyi ba tsayawa, tare da tsalle na +$350 lokaci zuwa lokaci. Ƙa'idar ±1σ tana bayyana watsuwar daidai, amma ba ya bayyana siffar da kyau har sai N ya kai ɗaruruwa. Ga cace-cacen ɗaya zuwa ɗayacacaCacar ɗaya zuwa ɗaya (even-money)Ja/baƙi, mara/cika, manya/ƙanana. Lambobi 18, biya 1:1.Karanta gaba ɗaya →, ƙiyasi ta hanyar normal distribution yana da kyau tun daga kusan juyi 30.
Ƙa'idar lissafi
Tambayoyi
Shaida ce cewa kun yi zaman wasa kusan 40, ko kuma kuna cikin ɗaya mai sa'a cikin arba'in. Ku sake yi.
Hawa da saukarsa tana ƙara raguwa: standard error na matsakaici shi ne σ/√N. A N = 10,000, 1% ne na kuɗin caca.
Nishaɗi da lissafi
Ku fara gwada waɗannan da kanku. Kowace mafita a naɗe take; ku buɗe ta idan kun shirya.
A cikin juye-juye 100 na dabaran roulette na Turai, 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 a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → tana a gaba da aƙalla nasara 51, raka'a ɗaya a kan straight upcacaStraight upLamba ɗaya tak, biya 35:1.Karanta gaba ɗaya → (cacar lamba ɗaya) kuma tana a gaba idan lambarta ta fito aƙalla sau 3. Ku yi amfani da lanƙwasar ƙararrawa (bell curve) don ƙiyasta duka damar biyu, sannan ku kwatanta su da ainihin amsoshin.
Nuna mafita
Amsa Ja: lanƙwasar ƙararrawa tana ba da 35.6%, ainihin amsar kuma ita ce 35.5%. Straight up: lanƙwasar ƙararrawa tana ba da 55.0%, ainihin amsar kuma ita ce 50.9%. Gajeriyar hanyar tana aiki ga ja amma tana kuskure ga lamba ɗaya.
Ja: nasarori suna da matsakaicin 100 × 18/37 = 48.6, da yaɗuwa ta √(100 × 18/37 × 19/37) = 5.0. Kasancewa a gaba yana nufin 51 ko fiye; alamar rabin hanya, 50.5, tana sama da matsakaicin da yaɗuwa 0.37, kuma lanƙwasar ƙararrawa tana sa 35.6% a sama da hakan. Haɗa ainihin damar nasara 51, 52 … 100 yana ba da 35.5%.
Straight up: fitowa suna da matsakaicin 100/37 = 2.70, da yaɗuwa ta √(100 × 1/37 × 36/37) = 1.62. Fitowa uku ko fiye yana nufin sama da 2.5, yaɗuwa 0.12 ƙasa da matsakaicin: 55.0% bisa lanƙwasar ƙararrawa. A ainihin lissafi, 1 ne a cire damar fitowa 0, 1 da 2, 6.5% + 17.9% + 24.7%, wanda ke barin 50.9%.
Lanƙwasar ƙararrawa tana buƙatar sakamako da yawa a ɓangarorin biyu na matsakaicin. Ja yana da su bayan juye-juye 100; lambar da ke fitowa ƙasa da sau uku a matsakaici ba ta da su. Lanƙwasar har ma tana ba da 8.7% ga “babu fitowa”, inda ainihin damar 6.5% ce. Taylor (2021) ya sa binomial da lanƙwasar ƙararrawa gefe da gefe ta hanya iri ɗaya.
Ɗan barkwanci
Zaman wasa ɗaya cikin ashirin yana wajen sigma biyu. Koyaushe akwai wani a kan wutsiya.
Majiyoyi
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.