Mukana weMitsara yeMhedzisiro muRoulette
Mitsara mirefu yeruvara rumwe chete inowanzoitika. Uyezve haina zvainoreva pakutenderera kunotevera.
Tsvuku shanu dzakatevedzana: 2.7%. Gumi: 0.074%. Musesheni yekutenderera 200, mutsara wematanhatu eruvara rumwe unobuda kazhinji kupfuura kusabuda.
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.
Mutsara mumwe
MukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → wekuti kutenderera k kunotevera kwose kuve tsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → i(18/37)ᵏ. Mbiri: 23.7%. Shanu: 2.7%. Gumi: 0.074%, zvinenge 1 pa1,350. Makumi maviri: 1 pamamiriyoni 1.8. Makumi maviri nenhanhatu, rekodhi yeMonte Carlo: 1 pamamiriyoni 137. Iyi ndiyo mikana yemutsara wakati unotanga pakutenderera kwakati, uye ndiwo mubvunzo usingabvunzwi nemunhu angangoita.
Musesheni
Mubvunzo unorehwa nevanhu ndewekuti “mutsara wek uchabuda kumwe kunhu musesheni yangu here?”, uye mhinduro yakakura zvikuru kupfuura (18/37)ᵏ nokuti sesheni yekutenderera 200 inopa nzvimbo dzinenge 200 dzekuti mutsara utange. Mutsara wematanhatu kana kupfuura weruvara rumwe, tsvuku kana nhemabhetiNhemaBheti remubhadharo wakaenzana panhamba 18 nhema. ChiFrench: noir.Verengai zvese →, unobuda musesheni yekutenderera 200 zvinenge 94% yenguva; misere kana kupfuura zvinenge 47%; gumi kana kupfuura zvinenge 14%. Mukadoma ruvara pamberi, mikana inodzikira, kusvika zvinenge 75%, 27% ne7%. Mutambi anogara manheru ose achaona mitsara mirefu manheru ega ega.
Sei Martingale ichizvifunga
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 → yega yega inowedzera mushure mekurasikirwa ine kureba kwemutsara kunoiputsa: kurasikirwa kutanhatu kubva pa$10 yekutanga pamuganho we$500, gumi paFibonaccinziraFibonacciProgression inotevera nhevedzo 1, 1, 2, 3, 5, 8, 13…: nhanho imwe kumberi mushure mekurasikirwa, nhanho mbiri kumashure mushure mekukunda.Verengai zvese →, kushanu pakuwanza katatu pamadozenibhetiDozeni1–12, 13–24 kana 25–36, rinobhadhara 2:1.Verengai zvese →. Mukana wemutsara wekurasikirwa kutanhatu pamubhadharo wakaenzana i(19/37)⁶ ≈ 1.8% pakuedza kwega kwega, uye sesheni yekutenderera 200 ine pamwe kuedza 100, saka kuputsika kunosvika mumasesheni anenge mana pashanu ekureba ikoko. Mukana wemitsara muRoulette ndicho chikonzero mawere aya asingawanzoshayikwi.
Nhamba dzinopisa nedzinotonhora
Arithmetic imwe chete iyi inoshanda pamastraight upbhetiStraight upNhamba imwe chete, rinobhadhara 35:1.Verengai zvese →. Mukutenderera 300 huwandu hunotarisirwa panhamba imwe neimwe i8.1; standard deviationmasvomhuStandard deviationMudzi wesikweya wemusiyano; chinhambwe chakajairwa chemhedzisiro kubva pakukosha kunotarisirwa.Verengai zvese → inenge 2.8. Imwe nhamba ichabuda ka15 uye imwe ka2 nerombo chete, nguva dzose. Bhodhi remhedzisiro rinoratidza nhamba “dzinopisa” riri kuratidza pamusoro pekugoverwa kwenormal. Lab inotsanangura kuti kunoda kutenderera kwakawanda sei nhamba inopisanganoNhamba inopisaNhamba yabuda kakawanda kupfuura zvaitarisirwa munguva pfupi yapfuura. Pavhiri rakarurama haifanotauri chinhu.Verengai zvese → isati yareva chimwe chinhu (zviuru, kubva pavhiri rimwe rinozivikanwa).
Kuzvimirira ndiyo pfungwa yose
Mutsara wetsvuku gumi hauiti kuti nhema ive nemukana wakakura, uye hauiti kuti tsvuku ive nemukana wakakura zvakare. Dzose dziri pa18/37. Mitsara chimiro chekutevedzana kusina hurongwa uye kusavapo kwayo ndiko kwaizonyumwirwa: kutevedzana kwekutenderera 200 kusina mutsara wakareba kupfuura mana kwaizova humbowo hwakasimba zvikuru hwekubiridzira kupfuura kune mutsara wegumi nembiri.
Fomula
Mibvunzo
Nhema 26 kuMonte Carlo musi wa18 Nyamavhuvhu 1913 ndiwo une mukurumbira. Tsvuku 32 dzakatevedzana dzakashumwa mukasino yekuAmerica muna 1943. Zvose zviri zviviri zvinoenderana nerombo kana tichifunga kutenderera kwakawanda kunoitwa nemakasino.
I18/37 chero zvakadii. Bhejai zvinotaurwa nehurongwa hwenyu, kana kuti musabheja.
Kwete. Kutsauka kunooneka semakombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → mamwe achibuda kazhinji mukutenderera kwezviuru, kwete semitsara yeruvara.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
Zvinotora kutenderera kwakawanda sei kwevhiri reEurope, paavhareji, nhamba dzese 37 dzisati dzabuda kamwe chete zvishoma?
Ratidza mhinduro
Mhinduro Anenge kutenderera 155 paavhareji; median i147.
Verengai kumirira nhamba itsva imwe panguva. Kutenderera kwekutanga kunogara kuchiratidza nhamba itsva. Kana maona nhamba 1, makombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → 36 pa37 matsva, saka nhamba itsva inotevera inotora kutenderera 37/36 paavhareji. Kana maona nhamba k, zvinotora 37/(37 − k).
Sanganisai kumirira: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = kutenderera 155.5.
Zvizhinji zvazvo zviri kumagumo. Nhamba yekupedzisira yoga inotora kutenderera 37 paavhareji, uye shanu dzekupedzisira anenge 85. Pavhiri reAmerica sumu imwe chete inopa anenge 161. Iri idambudziko re“coupon collector”; avhareji imwe chete inobuda pakuverenga kwakajairwa.
Pakutenderera 37 kwevhiri reEurope, kutenderera kumwe pagomba rimwe nerimwe, munofanira kutarisira kuona nhamba dzakasiyana dzinoverengeka sei?
Ratidza mhinduro
Mhinduro Anenge 23.6. Chikamu chimwe chete muzvitatu chenhamba, dzinenge 13, hadzibudi zvachose.
Torai nhamba imwe, semuenzaniso 17. Pakutenderera kumwe nekumwe haibudi nemukana we36/37, saka inopotsa kutenderera kwese 37 nemukana we(36/37)³⁷ ≈ 0.363.
Nhamba yega yega ine mukana mumwe chete, saka paavhareji 37 × 0.363 ≈ 13.4 nhamba hadzibudi uye 37 − 13.4 ≈ 23.6 dzinobuda, dzakawanda dzacho kaviri kana kupfuura.
Vatambi veRoulette vanozvidaidza kuti “mutemo wezvikamu zvitatu”. Hausi mutemo, isvomhu yekudzokororwa chete: pakutenderera kwakareba sevhiri, chikamu chimwe muzvitatu chenhamba hachibudi, pavhiri rakaenzana sepane rimwe ripi zvaro. Pamakomba 38 chikamu ichi i(37/38)³⁸ ≈ 0.363 zvakare; pavhiri guru chinogadzikana pedyo ne1/e ≈ 0.368.
Shamwari inokuratidzai zvinyorwa zviviri zvemavara 50, tsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → kana nhemabhetiNhemaBheti remubhadharo wakaenzana panhamba 18 nhema. ChiFrench: noir.Verengai zvese →, chimwe nechimwe chinonzi chakabva pavhiri pasina mazerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese →. Chimwe chinochinja ruvara ka25 uye mutsara wacho wakareba kwazvo ndewetanhatu. Chimwe chinochinja ka35 uye hachimbopfuuri mutsara wetatu. Ndechipi chakagadzirwa?
Ratidza mhinduro
Mhinduro Chechipiri. Chinyorwa chechokwadi chinochinja kanenge 24 kana 25. Chine shanduko 35 chinobuda kamwe chete pazvinyorwa zvinenge 500, uye chisina mutsara unopfuura wetatu kaviri chete pa100.
Ruvara rutsva rwega rwega runodzokorora rwekupedzisira kana kuchinja, hafu nehafu, saka mikana 49 yekuchinja inopa shanduko 24.5 paavhareji, kuwedzera kana kubvisa anenge 3.5. Makumi matatu neshanu inhanho tatu dzakadaro pamusoro peavhareji; vhiri rakaenzana rinogadzira shanduko dzakawanda kudaro kamwe chete pazvinyorwa zvinenge 500.
Mitsara inotaura nyaya imwe chete. Chinyorwa chechokwadi che50 chine mutsara wechina kana kupfuura anenge 98% enguva, uye mutsara wacho wakareba kwazvo unowanzova weshanu kana wetanhatu.
Vanhu vanokumbirwa kugadzira chinyorwa chisina hurongwa vanochinja kakawandisa, nekuti mutsara wechina kana wechishanu unoita kwavari sehurongwa. Taylor (2021) anoratidza chiratidzo ichocho muzvinyorwa zvekukanda mari zvakagadzirwa nevadzidzi: kusava nehurongwa kwechokwadi kune mitsara mirefu kupfuura zvinotarisirwa nevanhu.
Bhuku renyaya dzekasino rinotaura nezvemutambi ane nhamba yakabuda kashanu yakatevedzana uye rinoti iri rekodhi. Izvi zvinoshaya sei pavhiri reEurope? Uye zvinofanira kuitika kangani kumwe kunhu mukasino imwe ine matafura 20, imwe neimwe ichitenderera ka40 paawa, masikati neusiku?
Ratidza mhinduro
Mhinduro Nhamba yakadomwa kashanu yakatevedzana: 1 pa69 miriyoni. Chero nhamba ichibuda kana mamwe mana mushure mekunge yatanga kubuda: 1 pa1.87 miriyoni. Kasino iyoyo inotenderera kanenge 7 miriyoni pagore, saka inofanira kuona mutsara weshanu katatu kana kana pagore.
Nhamba yakadomwa inobuda nemukana we1/37 pakutenderera kumwe nekumwe, saka kashanu kakatevedzana kune mukana we(1/37)⁵ = 1 pa69,343,957. Asi hapana anodoma nhamba pachine nguva. Chero chinobuda pakutanga, kutenderera kuna kunotevera kunofanira kuchidzokorora: (1/37)⁴ = 1 pa1,874,161.
Matafura 20 × kutenderera 40 × maawa 24 × mazuva 365 = kutenderera 7,008,000 pagore. Kutenderera kwega kwega kunogona kutanga mutsara, saka kasino inotarisira 7,008,000/1,874,161 ≈ 3.7 mitsara yeshanu pagore.
Hapana rekodhi yepamutemo yemhando iyi iripo, uye hapana inodiwa: chiitiko chisingawanzoitika patafura imwe chinhu chakajairika mukasino yese, uye nyaya dzinotaurwa nezvetafura pazvakaitika. Nyaya iyi, muna Goldman (2007), inoitika pavhiri rine zero mbiri, pane nhamba dziri 1 pa79 miriyoni ne1 pa2.09 miriyoni.
Kuseka zvishoma
Mitsara mirefu ndiyo chimiro chekusava nehurongwa.
Zvinyorwa
- 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.