Itandukaniro Risanzwe muri Ruleti
Itandukaniro risanzwe kuri ruleti, umuzi kare w'ihindagurika ry'ivyavuyemwoimibareIhindagurika ry'IvyavuyemwoIgipimo c'ukuntu ivyavuyemwo bikwiragira kure y'agaciro kitezwe. Kinini kuri straight up, gito ku matego ya rimwe kuri rimwe.Soma vyose →, ni intera isanzwe iri hagati y'ivyavuyemwo n'ivyitezwe.
Kuri buri $1 yateze, σ ni 5,84 kuri straight up na 1,00 ku nomero zitukura. Kuba n'amahera y'itego n'umuzi kare w'igitigiri c'inzunguruka kugira uronke ic'igihe c'ugukina.
Itegeko ryoroshe
Nka bibiri vya gatatu vy'ibihe vyo gukina birangira biri mu ntera ya σ imwe y'ivyitezwe, na 95% mu ntera ya zibiri. Mu nzunguruka 100 ku nomero zitukuraitegoGitukuraItego rya rimwe kuri rimwe ku nomero 18 zitukura. Mu gifaransa: rouge.Soma vyose → kuri $10 (vyitezwe −$27, σ = $100), ibihe vyinshi vyo gukina birangira hagati ya −$127 na +$73, kandi hafi vyose hagati ya −$227 na +$173. Ivyavuyemwo biri hanze y'iyo ntera ntibigaragaza ikintu na kimwe, kiretse ko igihe kimwe c'ugukina muri makumyabiri kibigira.
Ni kubera iki √N
Igihombo citezweimibareIgihombo citezweAgaciro kitezwe gakubwe n'amahera yose yateze; ni amahera y'impuzandengo atakara mu gihe c'ugukina canke mu gihe runaka.Soma vyose → kiyongera kingana na N; ikwiragira riyongera ringana na √N. Iyo N ari gito, ikwiragira ni ryo ritegeka kandi ibihe vyo gukina ni nko gutera igiceri gihengamye gato. Iyo N ari kinini, igihombo kirenza ikwiragira. Aho bihurira, aho igihombo citezwe kingana n'itandukaniro risanzweimibareItandukaniro risanzweUmuzi kare w'ihindagurika ry'ivyavuyemwo; intera isanzwe iri hagati y'ivyavuyemwo n'agaciro kitezwe.Soma vyose → rimwe, ni kuri N = (σ/inyungu ya kazino)² = (1/0,027)² ≈ inzunguruka 1.370 ku matego ya rimwe kuri rimwe na (5,84/0,027)² ≈ 46.800 kuri straight upitegoStraight upInomero imwe gusa, iriha 35:1.Soma vyose →. Munsi y'ivyo bitigiri, amahirwe ni yo atsinda; hejuru yavyo, inyungu ya kazino ni yo itsinda.
Kubikoresha
Kugira umenye nimba igihe c'ugukina cari kidasanzwe, harura (ivyavuyemwo − EV)/σ. Umukinyi ateze $10 ku nomero zitukura arangiza inzunguruka 100 ari kuri +$150 aba ari kuri (150 + 27)/100 = 1,77σ, ivyavuyemwo biba incuro imwe muri 25: yagize amahirwe, si igitangaza. Umukinyi wa straight up ari kuri +$150 nyene aba ari kuri 0,3σ: ijoro risanzwe. Ivyavuyemwo bingana mu madolari bisobanura ibintu bitandukanye ku matego atandukanye.
Ikosa risanzwe ry'igice
Iryo harura nyene rikubwira inzunguruka zingahe zikenewe kugira ngo inyungu ya kazino iboneke mu makuru. Ikosa risanzwe ry'igice c'intsinzi cabonetse ni √(p(1 − p)/N). Ku nomero zitukura na N = 1.000: √(0,4865 × 0,5135 / 1000) ≈ 1,6%. Itandukaniro riri hagati y'igiceri kitabogamye n'inomero zitukura ni 1,35%, ku buryo inyuma y'inzunguruka 1.000 utarashobora kubitandukanya ufise icizere. Inyuma ya 10.000, ikosa risanzwe ni 0,5% kandi urashobora. Ni co gituma kandi gutahura ukubogama kw'uruziga gukenera inzunguruka nyinshi cane.
Ukwiyubara ku kubogama kw'ikwiragira
Ivyavuyemwo vya straight up biri kure y'ikwiragira risanzwe mu gihe gito c'ugukina: ibihe vyinshi vyo gukina ni −$10 bidahinduka kuri buri kuzunguruka, hamwe n'ugusimba kwa +$350 rimwe na rimwe. Itegeko rya ±1σ risobanura neza ikwiragira, ariko nabi ishusho yaryo gushika N ishitse mu majana. Ku matego ya rimwe kuri rimweitegoItego rya rimwe kuri rimweGitukura/cirabura, igiharwe/igiharuro, binini/bito. Inomero 18, riha 1:1.Soma vyose →, ikigereranyo c'ikwiragira risanzwe ni ciza guhera nko ku nzunguruka 30.
Ingingo y'imibare
Ibibazo
Ni icemezo c'uko wakinnye ibihe vyo gukina nka 40, canke ko wari muri kimwe c'amahirwe muri mirongo ine. Subiramwo.
Irahindagurika bike na bike: ikosa risanzwe ry'impuzandengo ni σ/√N. Kuri N = 10.000, ni 1% vy'amahera y'itego.
Twinezwe n'Imibare
Banza ubigerageze wewe nyene. Inyishu yose irapfutse; yugurure igihe witeguye.
Mu kuzunguruka 100 kw'uruziga rw'i Buraya, igiceamaheraIgiceAmahera y'itego y'ishingiro uburyo canke umukinyi akoresha. Iyongerekana ridondorwa mu bice kugira ngo rikore ku meza ayo ari yo yose.Soma vyose → kimwe kuri gitukuraitegoGitukuraItego rya rimwe kuri rimwe ku nomero 18 zitukura. Mu gifaransa: rouge.Soma vyose → kiba imbere n'amatsinzi nibura 51, kandi igice kimwe kuri straight upitegoStraight upInomero imwe gusa, iriha 35:1.Soma vyose → kiba imbere iyo inomero yaco isohotse nibura incuro 3. Koresha umurongo w'inzogera (bell curve) kugira ngo uharure ugushoboka kwompi, hanyuma ubigereranye n'inyishu nyakuri.
Erekana inyishu
Inyishu Gitukura: umurongo w'inzogera utanga 35,6% kandi inyishu nyakuri ni 35,5%. Straight up: umurongo w'inzogera utanga 55,0% kandi inyishu nyakuri ni 50,9%. Iyo nzira ngufi ikora kuri gitukura igahusha ku nomero imwe.
Gitukura: amatsinzi agira impuzandengo ya 100 × 18/37 = 48,6, n'ukwiragira kwa √(100 × 18/37 × 19/37) = 5,0. Kuba imbere bisobanura 51 canke birenga; ikimenyetso c'agati, 50,5, kiri ku kwiragira 0,37 hejuru y'impuzandengo, kandi umurongo w'inzogera ushira 35,6% hejuru y'aho. Guteranya ugushoboka nyakuri kw'amatsinzi 51, 52 … 100 bitanga 35,5%.
Straight up: amafata agira impuzandengo ya 100/37 = 2,70, n'ukwiragira kwa √(100 × 1/37 × 36/37) = 1,62. Amafata atatu canke arenga bisobanura hejuru ya 2,5, ukwiragira 0,12 munsi y'impuzandengo: 55,0% ukurikije umurongo w'inzogera. Neza neza, ni 1 ukuyemwo ugushoboka kw'amafata 0, 1 na 2, 6,5% + 17,9% + 24,7%, bigasigaza 50,9%.
Umurongo w'inzogera ukeneye ivyavuyemwo vyinshi ku mpande zompi z'impuzandengo. Gitukura kibifise inyuma y'ukuzunguruka 100; inomero isohoka munsi y'incuro zitatu ku mpuzandengo ntivyo ifise. Umurongo uha mpaka 8,7% “nta fata”, aho ugushoboka nyakuri ari 6,5%. Taylor (2021) ashira binomiale n'umurongo w'inzogera iruhande y'uko nyene.
Agakuru ko gutwenga
Igihe kimwe c'ugukina muri makumyabiri kiri hanze ya sigma zibiri. Hama hari umuntu ku murizo.
Aho Twakuye
- 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.