Egzanp pa-a-pa: enn sesion Martingale
Dis dolar lor rouz, doub apre sak pert, lor enn latab $500. Tour par tour, ziska tour ki fini tou.
Enn sesion Martingale simile avek enn kapital zwe $1,000. Karant-enn ti gin, apre sis pert ki swiv ek enn setyem pari ki latab refize. Sesion-la fini avek $220 pert apre ki nou ti dan gin $410, ek se sa mem ki sistem-la fer.
Plan-la
Parye $10 lor rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou →. Apre enn pert, doub. Apre enn gin, retourn a $10. Limit latablatabLimit latabPari minimom ek maksimom ki permet. Maksimom-la se seki aret bann progresion ki doub.Lir tou → $500, alor bann miz se 10, 20, 40, 80, 160, 320 ek apre enn pari $640 ki latab pou refize. Sis pert ki swiv kas sistem-la; sak sey ena (19/37)⁶ ≈ 1.8% sans pou fer sa, ek enn sesion 100 tour ena apepre 50 sey. Atandi: apepre 60% sans pou kase dan 100 tour, ek enn pert $630 kan sa arive.
Tour 1–30
MartingalestrateziMartingaleProgresion ki doub pari-la apre sak pert. Get seksion Stratezi pou kone seki li fer ek seki li pa fer.Lir tou → ordiner: seri enn a trwa pert, sakenn fini par enn gin ki donn +$10 net. O tour 30 nou finn gagne 17 fwa, sakenn ferm enn sik, ek nou dan gin $170. Pli gro miz ziska la ti $80 apre trwa pert. Li donn linpresion enn masinn ki inprim bann biye $10.
Tour 31–60
Plis mem zafer, avek enn sik kat pert (miz ziska $160, apre enn gin) ki pandan enn ti moman inn met $310 lor latab ek ki ti paret kouma kouraz. Apre 60 tour: 41 sik konplete, $410 dan gin, ek pli ba nivo kapital zwelarzanKapital zweTotal larzan ki ou met de kote pou zwe. Zesion kapital zwe vedir deside komie ladan ou riske par pari ek par sesion.Lir tou → depi tour 30 ti $1,040. Istogram tou sesion Martingale resanble sa pandan laplipar so longer.
Tour 61–66
Perdi Perdi Perdi Perdi Perdi Perdi. Miz 10, 20, 40, 80, 160, 320: $630 perdi. Prosin pari ti pou $640; limit-la se $500. Sistem-la kase. Nou kapav parye $500 (ek si li gagne, nou ankor $130 dan pert lor sik-la) ouswa retourn a $10 ek aksepte pert-la. Sis nwarpariNwarPari peman egal lor 18 nimero nwar. An franse: noir.Lir tou → ouswa zerorouZeroSel kaz ver ki okenn pari peman egal, douzenn ouswa kolonn pa kouver; sours lavantaz kazino. Osi: enn sel zero, 0.Lir tou → ki swiv ena enn probabilitematematikProbabiliteSans enn rezilta, depi 0 ziska 1 ouswa depi 0% ziska 100%. Enn nimero: 1/37 = 2.70%.Lir tou → 1.8% par sik. Nou ti fer apepre 45 sik. Sans pou ariv isi kikpar dan 45 sik ti apepre 55%. Se pa ti move lisans; se ti medyann.
- p10 −$1,000
- p25 −$1,000
- medyann −$1,000
- p75 +$790
- p90 +$1,690
Bann kont
$410 dan gin apre 60 tour, $220 dan pert apre 66. Total parye: apepre $2,100 lor 66 tour, kont $660 pou enn zwer avek miz fix $10. Pert atandimatematikPert atandiValer atandi miltiplie par total larzan ki ou parye; montan mwayen ki ou perdi lor enn sesion ouswa enn peryod.Lir tou → lor $2,100 total paryelarzanTotal paryeTotal larzan ki ou parye lor enn sesion ouswa enn peryod, ek bann gin ki ou reparye ladan. Osi: handle, action.Lir tou → se $57; nou vre rezilta −$220 apepre enn tier ekar-tipmatematikEkar-tipRasinn kare varyans; distans tipik ant enn rezilta ek valer atandi.Lir tou → anba sa, ek sa pa extraordiner pou enn sistem kot distribision-la ena enn long lake agos. Si nou ti arete o tour 60 avek enn limit ginstrateziLimit ginEnn lobzektif profi fixe davans kot ou aret sesion-la.Lir tou → $400, nou ti pou ale avek $410 gin, ek prosin sesion ti pou ena mem 1.8% par sik.
Seki sesion-la montre
Martingale transform enn pari 48.65% an enn sekans ki gagne 98% so bann sik ek ki perdi 63 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 lezot 2%. Li pa sanz pert atandi par dolar; li miltipli bann dolar. Zwer avek miz fix akote nou inn parye enn tier sa montan-la ek inn perdi, an mwayenn, enn tier sa montan-la. Zwer ki servi sa sistem-la pandan enn lane pou gagne laplipar lasware ek pou perdi lane-la.
Konbien souvan enn seri pert vini
Enn pari peman egal lor enn rou enn sel zero perdi 19 tour lor 37. Sakenn ranze montre sans ki enn seri tour donn tou perdi, ek konbien enn zwer Martingale, ki doub apre sakenn pert, inn perdi ziska la.
| pert youn deryer lot | sans | apepre 1 lor | perdi ziska ler | pari swivan |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Sans-la se 19/37 miltipliye par li-mem enn fwa par pert, konte depi enn tour donn. Enn long sesion ena boukou tour kot enn seri koumsa kapav koumanse, alor lor enn lasware li boukou pli probab ki seki enn ranze fer krwar.
Kestion
Nef pert kas li olie sis: 0.25% par sik, ek $5,110 perdi kan sa arive. Falez pli rar, falez pli o, mem −2.70%.
Li ti pou gagne 48.65% di tan ek kan mem les sik-la a −$130. Pena okenn bon kout apre enn Martingale kase; ena zis miz ki ou swazir apre.
Wi, pou sa sesion-la. Pa pou mwayenn lor tou sesion.
Lamizman ar matematik
Esey rezoud zot ou mem avan. Sakenn solision kase; ouver li kan ou pare.
Lor enn latab $1 ziska $500, enn zwer MartingalestrateziMartingaleProgresion ki doub pari-la apre sak pert. Get seksion Stratezi pou kone seki li fer ek seki li pa fer.Lir tou → koumanse avek $1 lor rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → lor enn rou enn zerorouZeroSel kaz ver ki okenn pari peman egal, douzenn ouswa kolonn pa kouver; sours lavantaz kazino. Osi: enn sel zero, 0.Lir tou →. Komie pert ennswit-lot aret doubleman-la, komie li finn perdi ziska la, ek komie souvan sa arive?
Montre solision-la
Repons Nef pert: $511 perdi, ek prosin pari ti pou $512. Sa arive enn fwa lor apepre 403 sekans.
Bann miz se 1, 2, 4, 8, 16, 32, 64, 128 ek 256: ansam $511. Dizyem-la ti pou $512, lao limit-la. Enn pari $500 ki gagne touzour les zwer-la $11 anba; enn ki perdi les li $1,011 anba.
Rouz perdi avek sans 19/37, alor nef pert ennswit-lot ena enn sans (19/37)⁹ ≈ 0.25%, enn fwa lor apepre 403 sekans. Sakenn sekans konple gagn $1, alor zwer-la atann apepre $402 ti gin avan sa sel pert $511-la, ek 2.70% lor tou seki parye touzour perdi an mwayenn.
Lor enn rou doub zero sans-la se (20/38)⁹, enn fwa lor apepre 323. Bollman (2021) enprim “apepre 1 lor 833”, ki se (18/38)⁹, sans nef gin ennswit-lot.
Enpe riye
Karant-enn ti gin ek enn gro pert. Sa mem tou sistem-la.
Sours
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”