Ikinyuranyo Gisanzwe muri Roulette
Ikinyuranyo gisanzwe muri roulette, umuzi wa kabiri w'ihindagurikaimibareIhindagurikaIgipimo cy'uko ibisubizo bikwirakwira kure y'agaciro gateganyijwe. Riri hejuru kuri straight up, hasi ku matega yishyura kimwe ku kindi.Soma byose →, ni intera isanzwe iri hagati y'igisubizo n'ibiteganyijwe.
Kuri buri $1 ritegewe, σ ni 5,84 kuri straight up na 1,00 ku mutuku. Kuba n'itega n'umuzi wa kabiri w'umubare w'amazunguruka ku mukino.
Itegeko ry'igereranya
Hafi bibiri bya gatatu by'imikino birangirira muri σ imwe y'ibiteganyijwe, naho 95% muri ebyiri. Ku mazunguruka 100 ku mutukuitegaUmutukuItega ryishyura kimwe ku kindi ku mibare 18 y'umutuku. Mu Gifaransa: rouge.Soma byose → ya $10 (biteganyijwe −$27, σ = $100) imikino myinshi iri hagati ya −$127 na +$73, kandi hafi yose iri hagati ya −$227 na +$173. Igisubizo kiri hanze y'urwo rugero si ikimenyetso cy'ikintu na kimwe uretse ko umukino umwe muri makumyabiri ubikora.
Kuki √N
Igihombo giteganyijweimibareIgihombo giteganyijweAgaciro gateganyijwe gakubye amafaranga yose yategewe; igihombo mpuzandengo mu mukino umwe cyangwa mu gihe runaka.Soma byose → cyiyongera mu rugero rumwe na N; ikwirakwira ryiyongera mu rugero rumwe na √N. Kuri N nto ikwirakwira riraganza kandi imikino iba nko gutera igiceri gifite ukubogama guto. Kuri N nini igihombo kirusha ikwirakwira umuvuduko. Aho bihurira, aho igihombo giteganyijwe kingana n'ikinyuranyo gisanzweimibareIkinyuranyo gisanzweUmuzi wa kare w'ihindagurika; intera isanzwe y'igisubizo uvuye ku gaciro gateganyijwe.Soma byose → kimwe, ni kuri N = (σ/inyungu ya kazino)² = (1/0,027)² ≈ amazunguruka 1.370 ku matega yishyura kimwe ku kindi na (5,84/0,027)² ≈ 46.800 kuri straight upitegaStraight upUmubare umwe, yishyura 35:1.Soma byose →. Munsi y'iyo mibare, amahirwe ni yo agena; hejuru yayo, inyungu ya kazino ni yo igena.
Kugikoresha
Kugira ngo umenye niba umukino wari udasanzwe, bara (igisubizo − EV)/σ. Umukinnyi utega $10 ku mutuku urangiza amazunguruka 100 afite +$150 aba ari kuri (150 + 27)/100 = 1,77σ, igisubizo kiba rimwe muri 25: amahirwe, si igitangaza. Umukinnyi utega straight up ufite +$150 imwe aba ari kuri 0,3σ: ijoro risanzwe. Igisubizo kimwe mu madolari gisobanura ibintu bitandukanye ku matega atandukanye.
Ikosa risanzwe ry'igipimo
Iryo barura rimwe rikubwira amazunguruka bisaba kugira ngo inyungu ya kazino igaragare mu makuru. Ikosa risanzwe (standard error) ry'igipimo cy'intsinzi cyabonetse ni √(p(1 − p)/N). Ku mutuku hamwe na N = 1.000: √(0,4865 × 0,5135 / 1000) ≈ 1,6%. Ikinyuranyo hagati y'igiceri kiboneye n'umutuku ni 1,35%, bityo nyuma y'amazunguruka 1.000 ntushobora kubitandukanya wizeye. Nyuma ya 10.000, ikosa risanzwe ni 0,5% kandi urabishobora. Ni na yo mpamvu gutahura ukubogama k'uruziga bisaba amazunguruka menshi cyane.
Kwitonda ku kubogama kw'ikwirakwira
Ibisubizo bya straight up biri kure cyane y'ikwirakwira rya normal mu mukino mugufi: imikino myinshi ni −$10 ihoraho kuri buri zunguruka n'ugusimbuka kwa +$350 rimwe na rimwe. Itegeko rya ±1σ risobanura neza ikwirakwira ariko nabi ishusho kugeza N igeze mu magana. Ku matega yishyura kimwe ku kindiitegaItega ryishyura kimwe ku kindiUmutuku/umukara, itabangikanye/ibangikanye, minini/mito. Imibare 18, ryishyura 1:1.Soma byose → igereranya rya normal riba ryiza guhera ku mazunguruka agera kuri 30.
Formula
Ibibazo
Ni gihamya ko wakinnye imikino igera kuri 40, cyangwa ko wari muri wa mukino umwe w'amahirwe muri mirongo ine. Bisubiremo.
Ihindagurika buke buke: ikosa risanzwe ry'impuzandengo ni σ/√N. Kuri N = 10.000 ni 1% by'itega.
Kwishimisha n'Imibare
Banza ubigerageze ubwawe. Buri gisubizo kirapfunyitse; ugifungure igihe witeguye.
Mu mazunguruka 100 y'uruziga rw'i Burayi, niteamafarangaIniteItega ry'ibanze uburyo cyangwa umukinnyi akoresha. Impererekane z'amatega zisobanurwa mu nite kugira ngo zikoreshwe ku meza ayo ari yo yose.Soma byose → imwe ku mutukuitegaUmutukuItega ryishyura kimwe ku kindi ku mibare 18 y'umutuku. Mu Gifaransa: rouge.Soma byose → iba iri imbere iyo itsinze nibura 51, naho nite imwe kuri straight upitegaStraight upUmubare umwe, yishyura 35:1.Soma byose → iba iri imbere iyo umubare wayo usohotse nibura incuro 3. Koresha umurongo w'inzogera ugereranye amahirwe yombi, hanyuma uyagereranye n'ibisubizo nyabyo.
Erekana igisubizo
Igisubizo Umutuku: umurongo w'inzogera utanga 35,6% kandi igisubizo nyacyo ni 35,5%. Straight up: umurongo w'inzogera utanga 55,0% kandi igisubizo nyacyo ni 50,9%. Inzira ngufi ikora ku mutuku ikananirwa ku mubare umwe.
Umutuku: intsinzi zigira impuzandengo ya 100 × 18/37 = 48,6, n'ikwirakwira rya √(100 × 18/37 × 19/37) = 5,0. Kuba imbere bivuze 51 cyangwa kurenza; ikimenyetso cy'icya kabiri, 50,5, kiri ikwirakwira 0,37 hejuru y'impuzandengo, kandi umurongo w'inzogera ushyira 35,6% hejuru yaho. Guteranya amahirwe nyayo y'intsinzi 51, 52 … 100 bitanga 35,5%.
Straight up: gufata kugira impuzandengo ya 100/37 = 2,70, n'ikwirakwira rya √(100 × 1/37 × 36/37) = 1,62. Gufata gatatu cyangwa kurenza bivuze hejuru ya 2,5, ikwirakwira 0,12 munsi y'impuzandengo: 55,0% ku murongo w'inzogera. Neza, ni 1 ukuyemo amahirwe yo gufata 0, 1 na 2, 6,5% + 17,9% + 24,7%, bigasiga 50,9%.
Umurongo w'inzogera ukenera ibisubizo byinshi ku mpande zombi z'impuzandengo. Umutuku urabifite nyuma y'amazunguruka 100; umubare usohoka munsi y'incuro eshatu ku mpuzandengo ntubifite. Umurongo ndetse uha 8,7% “kudafata na rimwe”, aho amahirwe nyayo ari 6,5%. Taylor (2021) ashyira binomial n'umurongo w'inzogera iruhande rumwe mu buryo bumwe.
Akanya k'urwenya
Umukino umwe muri makumyabiri uri hanze ya sigma ebyiri. Hahora hari umuntu uri ku murizo.
Inkomoko
- 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.