Misali: zaman wasa da Martingale
Dala goma a kan ja, ana ninka su bayan kowace asara, a tebur mai iyakar $500. Juyi bayan juyi, har da juyin da ya kawo ƙarshensa.
Zaman wasa na kwaikwayo da Martingale daga jarin caca na $1,000. Ƙananan nasarori arba'in da ɗaya, sannan asara shida a jere da caca ta bakwai da aka ƙi karɓa. Zaman wasan ya ƙare da asarar $220 bayan an kai riba ta $410, kuma abin da tsarin yake yi kenan.
Shirin
A sa $10 a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya →. Bayan asara, a ninka. Bayan nasara, a koma $10. Iyakar teburteburIyakar teburiMafi ƙanƙanta da mafi girman cacar da aka yarda da ita. Mafi girman ita ce ke dakatar da jerin ƙarin caca masu ninkawa.Karanta gaba ɗaya → $500 ce, don haka kuɗin caca su ne 10, 20, 40, 80, 160, 320 sannan caca ta $640 da tebur zai ƙi karɓa. Asara shida a jere suna karya tsarin; kowane ƙoƙari yana da yiwuwar (19/37)⁶ ≈ 1.8% ta yin haka, kuma zaman wasa mai juye-juye 100 yana ɗauke da kusan ƙoƙari 50. Abin da ake tsammani: kusan kashi 60% na yiwuwar karyewa cikin juye-juye 100, da asarar $630 idan hakan ya faru.
Juye-juye 1–30
MartingaledabaraMartingaleJerin ƙarin caca da ke ninka caca bayan kowace asara. Ku duba sashen “Dabarun caca na roulette” don ganin abin da yake yi da wanda ba ya yi.Karanta gaba ɗaya → na yau da kullum: jerin asara ɗaya zuwa uku, kowanne yana ƙarewa da nasarar da ke ba da +$10 tsaf. Zuwa juyi na 30 mun sami nasara 17, kowacce tana rufe zagaye, kuma muna da riba ta $170. Kuɗin caca mafi girma ya zuwa yanzu $80 ne bayan asara uku. Yana ji kamar na'urar buga takardun $10.
Juye-juye 31–60
Abu iri ɗaya, tare da zagaye ɗaya na asara huɗu (kuɗin caca ya kai $160, sannan nasara) wanda na ɗan lokaci ya sa $310 a kan tebur kuma ya ji kamar jarumta. Bayan juye-juye 60: zagaye 41 sun kammala, riba ta $410, kuma mafi ƙarancin jarin cacakuɗiJarin cacaJimillar kuɗin da aka ware don wasa. Sarrafa jarin caca shi ne yanke shawarar nawa za a sa a haɗari a kowace caca da kowane zaman wasa.Karanta gaba ɗaya → shi ne $1,040. Hoton kowane zaman wasa na Martingale yana kama da haka a mafi yawan tsawonsa.
Juye-juye 61–66
A A A A A A. Kuɗin caca 10, 20, 40, 80, 160, 320: an rasa $630. Caca ta gaba za ta zama $640; iyakar kuma $500 ce. Tsarin ya karye. Za mu iya sa $500 (kuma idan ya ci, har yanzu muna da asarar $130 a zagayen) ko mu koma $10 mu karɓi asarar. BaƙicacaBaƙiCacar ɗaya zuwa ɗaya (even-money) a kan lambobi baƙi 18. A Faransanci: noir.Karanta gaba ɗaya → ko sifilidabaranSifiliRamin kore guda ɗaya da babu cacar ɗaya zuwa ɗaya, ta dozin ko ta ginshiƙi da ke rufe shi; tushen fifikon gidan caca. Ana kuma kiransa: sifili ɗaya, 0.Karanta gaba ɗaya → shida a jere suna da yiwuwarlissafiYiwuwaDamar faruwar wani sakamako, daga 0 zuwa 1 ko daga 0% zuwa 100%. Lamba ɗaya: 1/37 = 2.70%.Karanta gaba ɗaya → 1.8% a kowane zagaye. Mun yi kusan zagaye 45. Yiwuwar kai wannan matsayi a wani wuri cikin zagaye 45 kusan 55% ce. Ba rashin sa'a ba ne; shi ne matsakaicin abin da ke faruwa.
- p10 −$1,000
- p25 −$1,000
- tsakiya −$1,000
- p75 +$790
- p90 +$1,690
Lissafin kuɗi
Riba ta $410 bayan juye-juye 60, asara ta $220 bayan 66. Jimillar caca: kusan $2,100 a juye-juye 66, idan aka kwatanta da $660 ga wanda ke caca daidai-wa-daida da $10. Asarar da ake tsammanilissafiAsarar da ake tsammaniƘimar da ake tsammani sau jimillar kuɗin da aka yi caca da su; matsakaicin adadin da ake rasawa a cikin zaman wasa ko wani lokaci.Karanta gaba ɗaya → a kan jimillar cacakuɗiJimillar cacaJimillar kuɗin da aka yi caca da su a cikin zaman wasa ko wani lokaci, har da kuɗin da aka ci aka sake sawa. Ana kuma kiranta: handle, action.Karanta gaba ɗaya → ta $2,100 ita ce $57; ainihin −$220 ɗinmu yana kusan sulusin standard deviationlissafiStandard deviationTushen murabba'i na bambancin sakamako; nisan da sakamako ke yawan yi daga ƙimar da ake tsammani.Karanta gaba ɗaya → ɗaya ƙasa da haka, wanda ba abin mamaki ba ne ga tsarin da rarrabuwar sakamakonsa take da dogon wutsiya a hagu. Da mun tsaya a juyi na 60 da iyakar ribadabaraIyakar ribaBurin riba da aka tsayar tun farko wanda idan aka kai shi ake ƙare zaman wasa.Karanta gaba ɗaya → ta $400, da mun tafi da riba ta $410, kuma zaman wasa na gaba zai ɗauki 1.8% ɗin nan a kowane zagaye.
Abin da zaman wasan ya nuna
Martingale yana mayar da caca ta 48.65% zuwa jerin da ke cin nasara a kashi 98% na zagayensa kuma yana rasa raka'akuɗiRaka'aKuɗin caca na tushe da tsari ko ɗan wasa ke aiki da shi. Ana bayyana jerin ƙarin caca a raka'a don su yi aiki a kowane tebur.Karanta gaba ɗaya → 63 a sauran kashi 2%. Ba ya canza asarar da ake tsammani a kowace dala; yana ninka yawan dalolin ne. Wanda ke caca daidai-wa-daida a gefenmu ya yi caca da sulusin abin da muka yi, kuma a matsakaici ya rasa sulusin abin da muka rasa. Ɗan wasan da ke amfani da wannan tsarin na shekara guda zai ci nasara a yawancin maraice amma ya yi asara a shekarar.
Sau nawa jerin asara ke zuwa
Cacar ɗaya zuwa ɗaya a kan dabaran mai sifili ɗaya tana yin asara a juyi 19 cikin 37. Kowane layi yana nuna yiwuwar cewa wasu juye-juye a jere duk za su yi asara, da abin da ɗan wasan Martingale, wanda ke ninka caca bayan kowace asara, ya rasa zuwa lokacin.
| asara a jere | yiwuwa | kusan 1 cikin | asara zuwa yanzu | caca ta gaba |
|---|---|---|---|---|
| 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 |
Yiwuwar ita ce 19/37 da aka ninka da kanta sau ɗaya a kowace asara, ana ƙirgawa daga juyi ɗaya ƙayyadadde. Zaman wasa mai tsawo yana da juye-juye da yawa inda irin wannan jeri zai iya farawa, don haka a cikin yamma guda ya fi yiwuwa nesa ba kusa ba fiye da yadda layi ɗaya ke nunawa.
Tambayoyi
Asara tara ne za su karya shi maimakon shida: 0.25% a kowane zagaye, da asarar $5,110 idan hakan ya faru. Faɗuwa da ba kasafai ba, faɗuwa mafi tsayi, amma −2.70% iri ɗaya.
Da ya ci a kashi 48.65% na lokaci kuma duk da haka ya bar zagayen a −$130. Babu kyakkyawan mataki bayan Martingale ya karye; akwai kuɗin cacar da kuka zaɓa a gaba kawai.
Eh, a wannan zaman wasan. Ba a matsakaicin dukan zaman wasa ba.
Nishaɗi da lissafi
Ku fara gwada waɗannan da kanku. Kowace mafita a naɗe take; ku buɗe ta idan kun shirya.
A teburin $1 zuwa $500, ɗan wasan MartingaledabaraMartingaleJerin ƙarin caca da ke ninka caca bayan kowace asara. Ku duba sashen “Dabarun caca na roulette” don ganin abin da yake yi da wanda ba ya yi.Karanta gaba ɗaya → yana farawa da $1 a kan jacacaJaCacar ɗaya zuwa ɗaya (even-money) a kan lambobi ja 18. A Faransanci: rouge.Karanta gaba ɗaya → a dabaran mai sifilidabaranSifiliRamin kore guda ɗaya da babu cacar ɗaya zuwa ɗaya, ta dozin ko ta ginshiƙi da ke rufe shi; tushen fifikon gidan caca. Ana kuma kiransa: sifili ɗaya, 0.Karanta gaba ɗaya → ɗaya. Asarori nawa a jere ne suke dakatar da ninkawa, nawa aka rasa zuwa lokacin, kuma sau nawa hakan yake faruwa?
Nuna mafita
Amsa Asarori tara: an rasa $511, kuma caca ta gaba za ta zama $512. Yana faruwa sau ɗaya cikin kusan jerika 403.
Kuɗin cacar su ne 1, 2, 4, 8, 16, 32, 64, 128 da 256: tare $511. Na goma zai zama $512, ya wuce iyaka. Cacar $500 da ta ci har yanzu tana barin ɗan wasa da asarar $11; wadda ta faɗi tana barinsa da asarar $1,011.
Ja yana faɗuwa da yiwuwar 19/37, don haka asarori tara a jere suna da yiwuwar (19/37)⁹ ≈ 0.25%, sau ɗaya cikin kusan jerika 403. Kowane jeri da aka kammala yana cin $1, don haka ɗan wasa yana iya tsammanin kusan $402 na ƙananan nasarori kafin wannan asarar $511 ɗaya, kuma har yanzu ana rasa 2.70% na duk abin da aka saka a matsakaici.
A dabaran mai sifili biyu yiwuwar ita ce (20/38)⁹, sau ɗaya cikin kusan 323. Bollman (2021) ya buga “kusan 1 cikin 833”, wato (18/38)⁹, yiwuwar nasarori tara a jere.
Ɗan barkwanci
Ƙananan nasarori arba'in da ɗaya da babbar asara ɗaya. Wannan shi ne dukan tsarin.
Majiyoyi
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”