Ekar-tip dan roulet
Ekar-tip dan roulet, rasinn kare varyansmatematikVaryansEnn mezir lor kouma bann rezilta dispers otour valer atandi. For pou pari lor enn sel nimero, ba pou pari peman egal.Lir tou →, se distans tipik ant enn rezilta ek so lesperans.
Par $1 miz, σ se 5.84 pou enn sel nimero ek 1.00 pou rouz. Pou enn sesion, miltipliye par miz-la ek par rasinn kare nonb tour.
Regleman pratik
Apepre de-tier bann sesion tom dan enn σ otour lesperans ek 95% dan de. Pou 100 tour lor rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → a $10 (atandi −$27, σ = $100) laplipar sesion tom ant −$127 ek +$73, ek preske tou ant −$227 ek +$173. Enn rezilta deor sa linterval-la pa prev nanye, apart ki enn sesion lor ven fer sa.
Kifer √N
Pert atandimatematikPert atandiValer atandi miltiplie par total larzan ki ou parye; montan mwayen ki ou perdi lor enn sesion ouswa enn peryod.Lir tou → ogmante an proporsion avek N; dispersion ogmante an proporsion avek √N. Pou enn N tipti, dispersion domine ek sesion-la kouma zwe pil ouswa fas avek enn ti pant. Pou enn N gran, pert-la depas dispersion-la. Pwen kroizman, kot pert atandi egal enn ekar-tipmatematikEkar-tipRasinn kare varyans; distans tipik ant enn rezilta ek valer atandi.Lir tou →, se N = (σ/lavantaz)² = (1/0.027)² ≈ 1,370 tour pou peman egal ek (5.84/0.027)² ≈ 46,800 pou pari lor enn sel nimeropariPari lor enn sel nimeroEnn sel nimero, peye 35:1.Lir tou →. Anba sa bann nonb-la, sans ki deside; lao zot, se lavantaz-la.
Kouma servi li
Pou zize si enn sesion ti inabityel, kalkil (rezilta − EV)/σ. Enn zwer ki parye $10 lor rouz ek fini 100 tour a +$150 se a (150 + 27)/100 = 1.77σ, enn rezilta enn lor 25: li ena sans, me pa extraordiner. Enn zwer lor enn sel nimero avek mem +$150 se a 0.3σ: enn aswar ordiner. Mem rezilta an dolar pa vedir mem zafer lor diferan pari.
Erer standar enn proporsion
Mem kalkil-la dir ou komie tour bizin pou trouv lavantaz-la dan bann done. Erer standar enn proporsion gin ki ou obzerve se √(p(1 − p)/N). Pou rouz avek N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Diferans ant enn pil ouswa fas zis ek rouz se 1.35%, alor apre 1,000 tour ou pa kapav ankor diferansie zot avek konfians. Apre 10,000, erer standar se 0.5% ek ou kapav. Se pou sa osi ki pou detekte enn rou ki ena defo bizin telman boukou tour.
Fer atansion ar asimetri
Rezilta lor enn sel nimero lwin pou ena enn distribision normal dan enn ti sesion: laplipar sesion se enn −$10 regilie par tour avek detanzanta enn so +$350. Regleman ±1σ dekrir dispersion-la bien me so form mal ziska ki N arive dan bann santenn. Pou pari peman egalpariPari peman egalRouz/nwar, inper/per, ot/ba. 18 nimero, peye 1:1.Lir tou → aproksimasion normal-la bon depi apepre 30 tour.
Formil
Kestion
Li prouve ki ou finn zwe apepre 40 sesion, ouswa ki ou ti dan sa enn lor karant ki ena sans-la. Refer li.
Li balanse touletan mwins: erer standar mwayenn-la se σ/√N. Kan N = 10,000, li 1% miz-la.
Lamizman ar matematik
Esey rezoud zot ou mem avan. Sakenn solision kase; ouver li kan ou pare.
Lor 100 tour enn rou eropeen, enn initelarzanIniteMiz baz ki enn sistem ouswa enn zwer servi. Bann progresion dekrir an inite pou ki zot aplik lor nenport ki latab.Lir tou → lor rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → devan avek omwin 51 gin, ek enn inite lor enn pari lor enn sel nimeropariPari lor enn sel nimeroEnn sel nimero, peye 35:1.Lir tou → devan si so nimero sorti omwin 3 fwa. Servi kourb Gauss pou estim toulede sans, apre kompar zot ar bann repons egzak.
Montre solision-la
Repons Rouz: kourb Gauss donn 35.6% ek repons egzak-la se 35.5%. Enn sel nimero: kourb Gauss donn 55.0% ek repons egzak-la se 50.9%. Rakoursi-la marse pou rouz ek li rate pou enn sel nimero.
Rouz: bann gin fer enn mwayenn 100 × 18/37 = 48.6, avek enn dispersion √(100 × 18/37 × 19/37) = 5.0. Devan vedir 51 ouswa plis; pwen lamwatie-sime, 50.5, se 0.37 dispersion par-anler mwayenn-la, ek kourb Gauss met 35.6% par-anler sa. Kan ou adisionn sans egzak 51, 52 … 100 gin, ou gagn 35.5%.
Enn sel nimero: bann kout fer enn mwayenn 100/37 = 2.70, avek enn dispersion √(100 × 1/37 × 36/37) = 1.62. Trwa kout ouswa plis vedir par-anler 2.5, 0.12 dispersion anba mwayenn-la: 55.0% dapre kourb Gauss. Egzakteman, se 1 mwins sans 0, 1 ek 2 kout, 6.5% + 17.9% + 24.7%, ki les 50.9%.
Kourb Gauss bizin ase rezilta lor toulede kote mwayenn-la. Rouz ena zot apre 100 tour; enn nimero ki sorti mwins ki trwa fwa an mwayenn pena. Kourb-la mem donn 8.7% a “okenn kout”, kot vre sans-la se 6.5%. Taylor (2021) met binomial ek kourb Gauss kot-a-kot dan mem fason.
Enpe riye
Enn sesion lor ven deor de sigma. Touzour ena enn kikenn lor lake-la.
Sours
- 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.