Konverzans lor enn long dire: lalwa gran nonb dan roulet
Kouma mwayenn-la stabiliz ver −2.70%, ek kifer sa pran plis letan ki lintiision krwar.
Pert mwayenn par tour konverz ver −1/37 amezir ki tour akimile, avek enn dispersion ki retresi kouma 1/√N. Apre 1,000 tour lor rouz, mwayenn-la zeneralman res dan ±3% so lesperans.
Lalwa gran nonb
Mwayenn kimilatif bann pari independan tann ver valer atandimatematikValer atandiRezilta mwayen par pari lor enn long dire. −1/37 miz-la pou sak pari eropeen standar.Lir tou →. Apre N tour lor pari peman egal avek 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 →, rezilta mwayenn par tour ena enn lesperans −1/37 ek enn ekar-tipmatematikEkar-tipRasinn kare varyans; distans tipik ant enn rezilta ek valer atandi.Lir tou → 1/√N. Kan N = 100, sa dispersion-la vo 10% miz-la, preske kat fwa siyal 2.7% la. Kan N = 1,000, li vo 3.2%, apepre parey kouma siyal-la. Kan N = 10,000, li vo 1%, ek lavantaz kazino vizib kler. Dan enn sesion ou pa trouv lavantaz-la; lor enn lane li pa kapav kasiet.
Seki konverze ek seki pa konverze
Mwayenn par tour konverze. Total-la non: li deriv pli lwin ki zero amezir ki N grandi, apepre 2.7% N an lesperans, avek enn dispersion √N otour sa. Enn zwer ki inn zwe 10,000 tour a $10 atann li pou perdi $2,700, plis ouswa mwins $1,000. Proporsion kimilatif rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → inn stabiliz depi lontan pre 48.65%; balans kimilatif pa inn stabiliz okenn kote.
- p10 −$440
- p25 −$280
- medyann −$140
- p75 +$0
- p90 +$140
Kifer lintiision tronp nou
Dimounn atann ki lavantaz kazino pou paret vit akoz 2.70% sonn boukou, ek atann ki bann long seri pou “egalize” akoz lalwa gran nonbmatematikLalwa gran nonbMwayenn bann rezilta independan aprose valer atandi kan nonb lesey ogmante.Lir tou → dir ki mwayenn konverze. Le de lintiision-la tronp lor lekel: lavantaz-la tipti par raport ar varyansmatematikVaryansEnn mezir lor kouma bann rezilta dispers otour valer atandi. For pou pari lor enn sel nimero, ba pou pari peman egal.Lir tou → enn sel tour (σ = 1 inite kont EV = 0.027), alor bizin (1/0.027)² ≈ 1,400 tour pou li vinn vizib a enn sigma. Ek konverzans mwayenn-la pa ramenn total-la ditou; li zis dilye bann fliktiasion ki finn pase.
Konverzans pou lezot pari
Pou bann pari lor enn sel nimeropariPari lor enn sel nimeroEnn sel nimero, peye 35:1.Lir tou → σ = 5.84, alor mem kalkil-la donn (5.84/0.027)² ≈ 47,000 tour pou lavantaz-la ariv enn sigma. Enn zwer ki zwe lor enn sel nimero kapav zwe pandan plizir lane san ki so prop rezilta montre lavantaz-la diferan ar lasans, alor ki li pe pey egzakteman mem 2.70% ki zwer rouz ki trouv li dan enn pe semenn.
Seki sa vedir pou test bann sistem
Ninport kisannla ki dir enn sistem marse bizin kapav montre li lor 10,000 tour ouswa plis, avek enn mwayenn pozitif dokimante. Lor 1,000 tour, enn mwayenn pozitif lor peman egal arive enn fwa lor sink sou lipotez nil; lor 100 tour li preske pil ou fas. Bann similater lor sa sit-la zwe 2,000 sesion lalonger ou swazir dan enn segonn, sa plis prev ki okenn temwaniaz.
Formil
Kestion
ProbabilitematematikProbabiliteSans enn rezilta, depi 0 ziska 1 ouswa depi 0% ziska 100%. Enn nimero: 1/37 = 2.70%.Lir tou → pou enn zour retrouv ou an avans bes ver zero amezir ki ou zwe. Total-la deriv anba san limit.
Non. Sa vedir ki bann fliktiasion ki finn pase vinn enn pli tipti fraksion enn pli gro lesantiyon.
Pou peman egal, apepre 10,000 avan ki lavantaz kazino vizib kler. Pou pari lor enn sel nimero, apepre 50,000.
Lamizman ar matematik
Esey rezoud zot ou mem avan. Sakenn solision kase; ouver li kan ou pare.
De kamarad zwe 20 round enn zwe zismatematikZwe zisEnn zwe kot okenn kote pena lavantaz: sak pari ena enn valer atandi zero.Lir tou →, enn zet pies ouswa rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → kont nwarpariNwarPari peman egal lor 18 nimero nwar. An franse: noir.Lir tou → avek bann zerorouZeroSel kaz ver ki okenn pari peman egal, douzenn ouswa kolonn pa kouver; sours lavantaz kazino. Osi: enn sel zero, 0.Lir tou → ranbourse, ek zot gard enn skor ki pe kontinie. Kont bann round kot sakenn devan (enn egalite konte pou seki ti devan zis avan). Lekel pli probab: ki laplas devan partaze 10 round kont 10, ouswa ki enn kamarad devan tou 20?
Montre solision-la
Repons Enn kamarad devan tou 20 round boukou pli probab: 35.2%, nimport lekel kamarad, kont 6.1% pou enn partaz egal 10 kont 10.
Sans ki enn skor zis egal apre 2k round se u = C(2k, k)/2²ᵏ: 0.246 apre 10 round ek 0.176 apre 20. Enn rezilta klasik, lalwa ark-sinis, dir ki sans ki enn kamarad ki finn nome devan pou egzakteman 2k lor 2n round se u(2k) × u(2n − 2k).
Devan tou 20: u(20) × u(0) = 0.176 pou sakenn kamarad, 35.2% pou nimport lekel. Enn partaz egal: u(10) × u(10) = 0.246² = 6.1%, partaz mwins probab ki tou.
Alor dan enn zwe zis laplas devan pa sanz lame souvan. Enn zwer ki finn devan tou laswaret, ouswa deryer tou laswaret, pa finn trouv nanye ki sorti lordiner, ek sa pa dir nanye lor rou-la ouswa lor labilite. Epstein (2013) donn mem lalwa-la pou zwe pli long: lamwatie di tan kote ki ena plis lasans res devan pou plis ki 85% zwe-la.
Enpe riye
Mwayenn-la konverze. Total-la zis al so sime.
Sours
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.