Dambudziko: Muganho weTafura
Martingale ye$10 patafura ye$500. Inoputsika kangani, inorasikirwa zvakadii kana yaputsika, uye kukwidza muganho kunobatsira here?
Kurasikirwa katanhatu kwakatevedzana kunoiputsa: 1.8% pakutenderera kwedenderedzwa rimwe, anenge 60% yemasesheni ekutenderera 100. Kuputsika kunodhura $630. Kukwidza muganho kusvika $5,000 kunoita kuti kuputsika kusawanzoitika (0.25% padenderedzwa) asi kuve kukuru ($5,110). Kurasikirwa kunotarisirwa padhora rakabhejwa i2.70% pamuganho upi neupi.
Dambudziko
Mutambi anobheja $10 patsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → uye anopeta kaviri mushure mekurasikirwa kwega kwega, odzokera kumavambo mushure mekukunda. Mari yepamusoro-soro yetafura i$500. (a) Kurasikirwa kungani kwakatevedzana kunoputsa progressionnziraProgressionMutemo upi zvawo unochinja mari yekubheja zvichienderana nemhedzisiro yakapfuura. Maprogression anokwira mushure mekurasikirwa anoikwidza kana mukarasikirwa; maprogression anokwira mushure mekukunda anoikwidza kana mukakunda.Verengai zvese →? (b) MukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → padenderedzwa ndeupi? (c) Chii chinorasikirwa pakuputsika? (d) Muganho we$5,000 unochinja sei mhinduro? (e) Pane muganho upi neupi unoita kuti sisitimu ive nepurofiti here?
Mhinduro (a)–(c)
Mari dzakabhejwa: 10, 20, 40, 80, 160, 320. Yechinomwe yaizova 640 > 500, saka kurasikirwa katanhatu kunoiputsa. (b) p(kurasikirwa) = 19/37 patsvuku; (19/37)⁶ = 0.0183, anenge 1.8% padenderedzwa. Denderedzwa rinogara kutenderera kunenge kuviri paavhareji, saka sesheni yekutenderera 100 ine madenderedzwa anenge 50 uye p(kuputsika kamwe chete zvishoma) ≈ 1 − 0.9817⁵⁰ ≈ 60%. (c) 10 + 20 + 40 + 80 + 160 + 320 = $630, iri mayunitimariYunitiMari yehwaro inoshandiswa nesisitimu kana nemutambi. Maprogression anotsanangurwa nemayuniti kuitira kuti ashande patafura ipi zvayo.Verengai zvese → ekutanga 63, pane $10 yaiedzwa kukundwa nedenderedzwa.
Mhinduro (d)
Pa$5,000: mari kusvika 2,560 inobvumirwa; yegumi, 5,120, inorambwa. Kurasikirwa kapfumbamwe kunoiputsa: (19/37)⁹ ≈ 0.25% padenderedzwa, anenge 11% yemasesheni ekutenderera 100. Kurasikirwa pakuputsika: 10 + 20 + … + 2,560 = $5,110. Mutambi atenga njodzi isingawanzoitiki pamutengo wenjodzi huru. Pamasesheni mazhinji mutengo unotarisirwa wekuputsika i p × kurasikirwa ≈ 0.0183 × 630 = $11.5 padenderedzwa pamuganho we$500 uye 0.0025 × 5,110 = $12.8 pa$5,000; inhamba imwe chete, kunze kwekutenderedza, uye ndiko kurasikirwa kunotarisirwamasvomhuKurasikirwa kunotarisirwaKukosha kunotarisirwa kwakapetwa nemari yose yakabhejwa; mari yepakati inorasika musesheni kana munguva yakati.Verengai zvese → kwedenderedzwa pamwe ne$10 inowanikwa nemadenderedzwa anokunda.
Mhinduro (e)
Kwete. Kurasikirwa kunotarisirwa padenderedzwa = (mari yose inotarisirwa kubhejwa mudenderedzwa) / 37, pamuganho upi neupi, nekuti bheti rega rega riri −1/37 raro pacharo. Muganho unongosarudza kuti kurasikirwa kunoparadzirwa sei pakati pekukunda kudiki kwakawanda nekurasikirwa kukuru kushoma. Pasina muganho uye nemari yekutambamariMari yekutambaMari yose yakachengeterwa kutamba. Kutonga mari yekutamba kuri kusarudza kuti mungaisa pangozi yakawanda sei pabheti rimwe nepasesheni imwe.Verengai zvese → isingaperi progression yaizo“shanda”, mupfungwa yekuti yaisazombopwanyika, uye yaizobhejawo mari isina muganho nekurasikirwa kunotarisirwa kwe2.70% yemari iyoyo isina muganho. Muganho wetafuratafuraMuganho wetafuraBheti diki nerikuru kupfuura ese anobvumirwa. Rikuru ndiro rinomisa maprogression ekupeta kaviri.Verengai zvese → hausi iwo unotadzisa MartingalenziraMartingaleProgression inopeta bheti kaviri mushure mekurasikirwa kwega kwega. Onai chikamu cheNzira kuti munzwisise zvainoita nezvaisingaite.Verengai zvese → kushanda. Masvomhu ndiwo.
Matafura maviri chaiwo
Muenzaniso waThorp itafura ye$1 ine $1,000 yepamusoro-soro, apo mutambi anovimba kukunda $30 yekudya kwemanheru dhora rimwe panguva. Mari 1, 2, 4 … 512 dzinobvumira mabheti gumi, saka kurasikirwa kagumi kwakatevedzana kunoputsa progression: kamwe pamadenderedzwa 785 pavhiri reEurope (kamwe pa613 pavhiri reAmerica), pamutengo we$1,023. Madenderedzwa makumi matatu anobudirira ese 96.2% yenguva. Imwe 3.8% inorasikirwa anenge $1,000, uye mhedzisiro yepaavhareji yemanheru iri −$9.17, iri chaizvo 1/37 ye$339 inobhejwa nemadenderedzwa makumi matatu paavhareji. Tafura ye$5 ine $2,000 yepamusoro-soro haina kusiyana: mari kusvika $1,280 dzinobvumira mabheti mapfumbamwe, uye kuputsika kunouya kamwe pamadenderedzwa 403 pavhiri reEurope (kamwe pa323 pavhiri reAmerica) uye kunodhura $2,555.
Mutambi akapfuma
Ipai progression mari yekutamba yakadzama pane muganho wakaderera: mayuniti 1,000, yuniti imwe yekutanga nekutenderera 1,000 patsvuku, ichitangazve payuniti imwe kana kupeta kunotevera kwapfuura zvasara. Takaedza manheru akadaro miriyoni. Pavhiri reEurope 52% inopedza iri mberi, 21% inorasikirwa nezvose, uye mhedzisiro yepaavhareji imayuniti −124. Kunyange mumutambo usina zerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese →, apo bheti rega rega rakaenzana, anenge 60% chete aizopedza ari mberi. Manheru akajairika kukunda kudiki; avhareji inobhadharwa nemanheru anopera pazero.
Chidzidzo
Makasino anoisa miganho kuti aganhurire musiyanomasvomhuMusiyanoChiyero chekuti mhedzisiro yakapararira zvakadii kutenderedza kukosha kunotarisirwa. Wakakwirira pastraight up, wakaderera pamabheti emubhadharo wakaenzana.Verengai zvese → wawo, kwete kukunda masisitimu. Kukunda Martingale mhedzisiro yepadivi yavanofara kuva nayo, uye masvomhu aizoikunda zvisinei. Mutambi anofunga kuti muganho ndiwo dambudziko awana mawere akaafunga semateru.
Fomula
Mibvunzo
Inokubvumirai kupona kusvika pamuganho wakakwira, apo kuputsika kusingawanzoitiki asi kuri kukuru. Kurasikirwa kunotarisirwa padhora hakuchinji.
Mari 10, 30, 70, 150, 310: muganho we$500 unosvikwa mushure mekurasikirwa kashanu, uye kuputsika kunodhura $570. 2.70% imwe chete.
Kuti mutambi mumwe asabheja kupfuura zvinogona kubhadharwa zvakasununguka nemari yakachengetwa nekasino. Kutonga musiyano.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
MartingalenziraMartingaleProgression inopeta bheti kaviri mushure mekurasikirwa kwega kwega. Onai chikamu cheNzira kuti munzwisise zvainoita nezvaisingaite.Verengai zvese → inotanga ne$100 patsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → uye inozvibvumira mabheti asingapfuuri n padenderedzwa: mushure mekurasikirwa n kwakateverana inorega yotangazve. Nyorai mhedzisiro yepaavhareji yedenderedzwa rimwe sefomula ye n, moiverenga pamabheti 5, 6 ne7 pavhiri reEurope.
Ratidza mhinduro
Mhinduro Avhareji i100 × (1 − (38/37)ⁿ): −$14.26 pamabheti 5, −$17.35 pa6 uye −$20.52 pa7. Kubvumira mabheti akawanda kunoita kuti denderedzwa repaavhareji riwedzere kuipa, kwete kunaka.
Denderedzwa rinokunda $100 kunze kwekunge mabheti ose n arasikirwa, izvo zvinoitika nemukana we qⁿ, apo q = 19/37. Kana ose akarasikirwa, mari dzakabhejwa 100, 200 … 100 × 2ⁿ⁻¹ dzinosvika 100 × (2ⁿ − 1). Saka avhareji i100 × (1 − qⁿ) − 100 × (2ⁿ − 1) × qⁿ = 100 × (1 − (2q)ⁿ).
Pano 2q = 38/37, zvishoma kupfuura 1, saka (2q)ⁿ inokura ne n uye avhareji inodonha: n = 5 inopa 1.1426 uye −$14.26; n = 6 inopa 1.1735 uye −$17.35; n = 7 inopa 1.2052 uye −$20.52. Manera marefu anorasikirwa kashoma, mu3.6%, 1.8% ne0.9% yemadenderedzwa, asi kurasikirwa kwega kwega kwakapetwa kaviri, uye mari yakawanda inoyambuka tafura padenderedzwa rega rega, pa2.70% yebheti rega rega.
Pavhiri reAmerica 2q = 40/38 uye nhamba dziri −$29.24, −$36.04 uye −$43.20 (Taylor, 2021). Mumutambo usina zerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → 2q = 1, uye denderedzwa rega rega rine avhareji iri zero chaiyo kunyange manera akareba sei.
“Grand Martingale” inopeta kaviri mari yekubheja mushure mekurasikirwa uye yowedzera yunitimariYunitiMari yehwaro inoshandiswa nesisitimu kana nemutambi. Maprogression anotsanangurwa nemayuniti kuitira kuti ashande patafura ipi zvayo.Verengai zvese → imwe, saka mari dzekubheja dzinofamba 1, 3, 7, 15, 31 … Muri pamusoro nemarii kana kukunda kwekutanga kukauya pabheti re1, re2, re3 kana re k? Neyuniti ye$10 nemuganho wepamusoro we$500, denderedzwa rinoputsika kangani, uye denderedzwa rinodhura marii paavhareji?
Ratidza mhinduro
Mhinduro Kukunda pabheti re k kunokusiyai muri pamusoro nemayuniti k: +1, +2, +3 zvichidaro. Pa$10 ne$500 denderedzwa rinoputsika mushure mekurasikirwa kushanu, 3.57% yemadenderedzwa, zvichiita −$570. Paavhareji denderedzwa rinorasikirwa $2.32 pa$85.73 yakabhejwa: 2.70%.
Mari yekubheja ye k i2ᵏ − 1 mayuniti: 1, 3, 7, 15, 31. Mari k − 1 dzekutanga dzinosvika 2ᵏ − 2 − (k − 1) = 2ᵏ − k − 1. Kukunda pabheti re k kunobhadhara 2ᵏ − 1, saka denderedzwa rinopera (2ᵏ − 1) − (2ᵏ − k − 1) = mayuniti k pamusoro: yuniti imwe yekuwedzera pakurasikirwa kwega kwega kusati kwauya kukunda.
Pa$10 payuniti mari dzekubheja ndi$10, $30, $70, $150 ne$310; inotevera, $630, iri pamusoro pemuganho we$500. Kurasikirwa kushanu kwakateverana, (19/37)⁵ = 3.57%, kunodhura 10 + 30 + 70 + 150 + 310 = $570.
Avhareji: kukunda kunounza $10 × k nemukana we(19/37)ᵏ⁻¹ × 18/37 pa k = 1 kusvika 5, uye kuputsika kunotora $570 nemukana we3.57%; pamwe chete −$2.32. Mari yakabhejwa ine avhareji ye$85.73 padenderedzwa, uye 2.32/85.73 = 2.70%. Martingale yakajairwa patafura imwe chete inoputsika mushure mekurasikirwa kutanhatu, 1.83% yemadenderedzwa, zvichiita −$630, uye inorasikirwa $1.74 pa$64.20 yakabhejwa: 2.70% zvakare.
Mutambi anoronga Martingale patsvuku nebheti rekutanga re$1 patafura ine muganho we$1,000, saka mabheti gumi anogoneka: $1, $2, $4 zvichidaro kusvika $512. Denderedzwa rinorasikirwa ose gumi kangani, izvozvo zvinotora nguva yakareba sei paavhareji, uye manheru emabheti 200 anopera saizvozvo kangani?
Ratidza mhinduro
Mhinduro Denderedzwa rinorasikirwa ose gumi kamwe chete pa784, izvo zvinodhura $1,023. Ndiwo mabheti anenge 1,600 paavhareji, uye manheru emabheti 200 anorova madziro anenge 11% yenguva. Denderedzwa richiri kurasikirwa $0.31 paavhareji pa$11.31 yakabhejwa: 2.70%.
Bheti patsvuku rinorasikirwa nemukana we19/37, zero ichisanganisirwa. Gumi akateverana: (19/37)¹⁰ ≈ 0.00128, anenge 1 pa784. Mari dzakabhejwa 1 + 2 + 4 + … + 512 dzinosvika $1,023.
Denderedzwa rinotora mabheti 2.05 paavhareji, saka madenderedzwa 784 anotora mabheti anenge 1,600. Tichiverenga kutenderera nekutenderera, mutsara wekurasikirwa gumi unobuda pane imwe nzvimbo mumabheti 200 11.3% yenguva.
Pakati penjodzi mutambi anokunda $1 padenderedzwa: anenge $783 isati yasvika yakaipa, wozoita −$1,023, anenge −$240 panguva yose. Padenderedzwa: 1 × (1 − 0.00128) − 1,023 × 0.00128 ≈ −$0.31. Mari yakabhejwa padenderedzwa: 1 + 2 × (19/37) + 4 × (19/37)² + … + 512 × (19/37)⁹ ≈ $11.31. Uye −0.31/11.31 = −2.70%.
Enzanisai nebheti rekutanga re$10 pamuganho we$500, mabheti matanhatu: madziro anouya kamwe chete pamadenderedzwa 55, uye manheru emabheti 200 anoasangana nawo 84% yenguva. Muganho wakakwirira unoita kuti kuputsika kuve kushoma uye kukuru, kwete kwakachipa.
Kuseka zvishoma
Zvisingawanzoitiki asi zvikuru, pamuganho wega wega. Chigadzirwa hachichinji.
Zvinyorwa
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.