Muenzaniso: Sesheni yeMartingale
Madhora gumi patsvuku, anopetwa kaviri mushure mekurasikirwa kwega kwega, patafura ine muganho we$500. Kutenderera nekutenderera, kusanganisira kutenderera kunozvipedza.
Sesheni yeMartingale yakasimulatwa kubva pamari yekutamba ye$1,000. Kukunda kudiki makumi mana nekumwe, ipapo kurasikirwa kutanhatu kwakatevedzana nebheti rechinomwe rakarambwa. Sesheni inopera yadzikira $220 mushure mekunge yakambokwira $410, ndizvo zvinoitwa nesisitimu.
Hurongwa
Bhejai $10 patsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese →. Mushure mekurasikirwa, petai kaviri. Mushure mekukunda, dzokerai ku$10. Muganho wetafuratafuraMuganho wetafuraBheti diki nerikuru kupfuura ese anobvumirwa. Rikuru ndiro rinomisa maprogression ekupeta kaviri.Verengai zvese → i$500, saka mari yakabhejwa i10, 20, 40, 80, 160, 320 yozoita bheti re$640 richarambwa netafura. Kurasikirwa kutanhatu kwakatevedzana kunoputsa sisitimu; kuedza kwega kwega kune (19/37)⁶ ≈ 1.8% yekuzviita, uye sesheni yekutenderera 100 ine kuedza kunenge 50. Zvinotarisirwa: mukana unenge 60% wekuputswa mukati mekutenderera 100, uye kurasikirwa kwe$630 kana zvaitika.
Kutenderera 1–30
MartingalenziraMartingaleProgression inopeta bheti kaviri mushure mekurasikirwa kwega kwega. Onai chikamu cheNzira kuti munzwisise zvainoita nezvaisingaite.Verengai zvese → yakajairika: mitsara yekurasikirwa kumwe kusvika kutatu, mumwe nemumwe uchipedzwa nekukunda kunopa +$10. Pakutenderera 30 tine kukunda 17, kumwe nekumwe kuchivhara denderedzwa, uye tiri pamusoro ne$170. Mari yakakura kupfuura yose yakabhejwa kusvika parizvino yaive $80 mushure mekurasikirwa kutatu. Zvinonzwika semuchina wekudhinda mabhiri e$10.
Kutenderera 31–60
Zvimwe zvakafanana, nedenderedzwa rimwe rekurasikirwa kuna (mari yakabhejwa kusvika pa$160, ipapo kukunda) rakaisa $310 patafura kwechinguva rikanzwika sehushingi. Mushure mekutenderera 60: madenderedzwa 41 apera, tiri pamusoro ne$410, uye nzvimbo yakaderera yomari yekutambamariMari yekutambaMari yose yakachengeterwa kutamba. Kutonga mari yekutamba kuri kusarudza kuti mungaisa pangozi yakawanda sei pabheti rimwe nepasesheni imwe.Verengai zvese → yaive $1,040. Histogram yesesheni yega yega yeMartingale inoita seizvi kwenguva zhinji yayo.
Kutenderera 61–66
R R R R R R. Mari yakabhejwa 10, 20, 40, 80, 160, 320: $630 yarasika. Bheti rinotevera raizova $640; muganho i$500. Sisitimu yaputsika. Tinogona kubheja $500 (uye kana rakunda, tichiri pasi ne$130 padenderedzwa) kana kudzokera ku$10 togamuchira kurasikirwa. NhemabhetiNhemaBheti remubhadharo wakaenzana panhamba 18 nhema. ChiFrench: noir.Verengai zvese → kana mazerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → matanhatu akatevedzana ane mukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → we1.8% padenderedzwa rega rega. Takanga tapfuura madenderedzwa anenge 45. Mukana wekusvika panguva iyi kumwe kwemadenderedzwa 45 waive unenge 55%. Rakanga risiri rombo rakaipa; yaive median.
- p10 −$1,000
- p25 −$1,000
- median −$1,000
- p75 +$790
- p90 +$1,690
Maakaundi
Pamusoro ne$410 mushure mekutenderera 60, pasi ne$220 mushure me66. Mari yose yakabhejwa: inenge $2,100 mukutenderera 66, kuchienzaniswa ne$660 yemunhu anobheja $10 zvakaenzana. Kurasikirwa kunotarisirwamasvomhuKurasikirwa kunotarisirwaKukosha kunotarisirwa kwakapetwa nemari yose yakabhejwa; mari yepakati inorasika musesheni kana munguva yakati.Verengai zvese → pa$2,100 yemari yose yakabhejwamariMari yose yakabhejwaMari yese yakabhejwa musesheni kana munguva yakati, kusanganisira mari yakakundwa yakabhejwazve. Mamwe mazita: handle, action.Verengai zvese → i$57; −$220 yedu chaiyo iri inenge chikamu chimwe muzvitatu chestandard deviationmasvomhuStandard deviationMudzi wesikweya wemusiyano; chinhambwe chakajairwa chemhedzisiro kubva pakukosha kunotarisirwa.Verengai zvese → pasi peizvo, zvisingashamisi kusisitimu ine kugovera kune muswe murefu kuruboshwe. Dai takamira pakutenderera 60 nemuganho wekukundanziraMuganho wekukundaChinangwa chepurofiti chakatarwa pamberi apo munopedza sesheni.Verengai zvese → we$400, tingadai takaenda tiri pamusoro ne$410, uye sesheni inotevera ingadai yakatakura 1.8% imwe chete padenderedzwa rega rega.
Zvinoratidzwa nesesheni
Martingale inoshandura bheti re48.65% kuva mutsara unokunda 98% yemadenderedzwa awo worasikirwa mayunitimariYunitiMari yehwaro inoshandiswa nesisitimu kana nemutambi. Maprogression anotsanangurwa nemayuniti kuitira kuti ashande patafura ipi zvayo.Verengai zvese → 63 pa2% yasara. Haichinji kurasikirwa kunotarisirwa padhora rega rega; inowanza madhora. Munhu anobheja zvakaenzana aive padivi pedu akabheja chikamu chimwe muzvitatu uye akarasikirwa, paavhareji, chikamu chimwe muzvitatu. Mutambi anoshandisa sisitimu iyi kwegore achakunda manheru mazhinji worasikirwa negore.
Mutsara wekurasikirwa unouya kangani
Bheti remubhadharo wakaenzana pavhiri rezero imwe rinorasikirwa kutenderera 19 pa37. Mutsara wega wega mukana wekuti kutenderera kwakatevedzana kwakapihwa kwese kurasikirwe, uye zvakarasikirwa nemutambi weMartingale, anopeta kaviri mushure mekurasikirwa kwega kwega, panguva iyoyo.
| kurasikirwa zvakatevedzana | mukana | kanenge 1 pa | zvarasika kusvika pari zvino | bheti rinotevera |
|---|---|---|---|---|
| 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 |
Mukana i19/37 wakawanzwa nawo pachawo kamwe pakurasikirwa kwega kwega, kuverengwa kubva pakutenderera kumwe kwakapihwa. Sesheni refu ine kutenderera kwakawanda panogona kutanga mutsara wakadai, saka mumanheru ose zvinogoneka zvikuru kupfuura zvinoratidzwa nemutsara mumwe.
Mibvunzo
Kurasikirwa kupfumbamwe kunoiputsa panzvimbo pekutanhatu: 0.25% padenderedzwa rega rega, uye $5,110 inorasika kana zvaitika. Mawere asingawanzoitika, mawere akadzika, −2.70% imwe chete.
Raizokunda 48.65% yenguva uye rosiya denderedzwa riri pa −$130 zvakadaro. Hapana danho rakanaka mushure meMartingale yaputsika; pane mari chete yamunosarudza kubheja inotevera.
Hongu, pasesheni iyoyo. Kwete paavhareji yemasesheni ese.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
Patafura ye$1 kusvika $500, mutambi weMartingalenziraMartingaleProgression inopeta bheti kaviri mushure mekurasikirwa kwega kwega. Onai chikamu cheNzira kuti munzwisise zvainoita nezvaisingaite.Verengai zvese → anotanga ne$1 patsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → pavhiri rine zerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → imwe. Kurasikirwa kangani kwakateverana kunomisa kupeta kaviri, mari yakarasikirwa yakadii panguva iyoyo, uye zvinoitika kangani?
Ratidza mhinduro
Mhinduro Kurasikirwa kupfumbamwe: $511 yakarasikirwa, uye bheti rinotevera raizova $512. Zvinoitika kamwe chete pamitsara inenge 403.
Mari dzakabhejwa ndi1, 2, 4, 8, 16, 32, 64, 128 ne256: pamwe chete $511. Yechigumi yaizova $512, pamusoro pemuganho. Bheti re$500 rinokunda richiri kusiya mutambi ari pasi ne$11; rinorasikirwa rinomusiya ari pasi ne$1,011.
Tsvuku inorasikirwa nemukana we19/37, saka kurasikirwa kupfumbamwe kwakateverana kune mukana we(19/37)⁹ ≈ 0.25%, kamwe chete pamitsara inenge 403. Mutsara wega wega wapera unokunda $1, saka mutambi anotarisira kukunda kudiki kunenge $402 kurasikirwa kumwe kwe$511 kusati kwauya, uye 2.70% yezvose zvakabhejwa ichiri kurasikirwa paavhareji.
Pavhiri rine zero mbiri mukana i(20/38)⁹, kamwe chete pa323. Bollman (2021) anodhinda “anenge 1 pa833”, iyo i(18/38)⁹, mukana wekukunda kupfumbamwe kwakateverana.
Kuseka zvishoma
Kukunda kudiki makumi mana nekumwe nekurasikirwa kukuru kumwe. Ndiyo sisitimu yese.
Zvinyorwa
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”