Urugero: Umukino wa Martingale
Amadolari icumi ku mutuku, akubwa kabiri nyuma ya buri gihombo, ku meza y'imbibi za $500. Izunguruka ku rindi, harimo n'izunguruka riwurangiza.
Umukino wigana ukuri wa Martingale uhereye ku gishoro cyo gukina cya $1.000. Intsinzi nto mirongo ine n'imwe, hanyuma ibihombo bitandatu bikurikiranye n'itega rya karindwi ryanzwe. Umukino urangira uri munsi ya $220 nyuma yo kuba wari kuri +$410, kandi ibyo ni byo ubu buryo bukora.
Gahunda
Tega $10 ku mutukuitegaUmutukuItega ryishyura kimwe ku kindi ku mibare 18 y'umutuku. Mu Gifaransa: rouge.Soma byose →. Nyuma y'igihombo, kuba kabiri. Nyuma y'intsinzi, subira kuri $10. Imbibi z'amezaamezaImbibi z'amezaItega rito n'irinini byemewe. Imbibi zo hejuru ni zo zihagarika impererekane zikuba kabiri.Soma byose → ni $500, bityo amatega ni 10, 20, 40, 80, 160, 320 hanyuma itega rya $640 ameza azanga. Ibihombo bitandatu bikurikiranye bisenya ubu buryo; buri gerageza rifite (19/37)⁶ ≈ 1,8% byo kubigeraho, kandi umukino w'amazunguruka 100 urimo amagerageza nka 50. Ibiteganyijwe: amahirwe hafi 60% yo gusenyuka mu mazunguruka 100, n'igihombo cya $630 iyo bibaye.
Amazunguruka 1–30
MartingaleingambaMartingaleUruhererekane rw'amatega rukuba itega kabiri nyuma ya buri gutsindwa. Reba igice cy'Ingamba umenye icyo rukora n'icyo rudakora.Soma byose → isanzwe: impererekane z'ibihombo kimwe kugeza kuri bitatu, buri rumwe rurangizwa n'intsinzi yinjiza +$10. Ku izunguruka rya 30 tumaze kugira intsinzi 17, buri imwe isoza icyiciro, kandi twungutse $170. Itega rinini kugeza ubu ryari $80 nyuma y'ibihombo bitatu. Byiyumvamo nk'imashini icapa inoti za $10.
Amazunguruka 31–60
Ibisa n'ibyabanje, harimo icyiciro kimwe cy'ibihombo bine (amatega agera kuri $160, hanyuma intsinzi) cyashyize $310 ku meza akanya gato kandi cyiyumvagamo nk'ubutwari. Nyuma y'amazunguruka 60: ibyiciro 41 birangiye, twungutse $410, kandi aho igishoro cyo gukinaamafarangaIgishoro cyo gukinaAmafaranga yose yashyizwe ku ruhande yo gukina. Gucunga igishoro ni ukwemeza ingano yacyo uzashyira mu kaga kuri buri tega no kuri buri mukino.Soma byose → cyageze hasi ni $1.040. Igishushanyo cya buri mukino wa Martingale gisa gutya mu gihe kinini cyawo.
Amazunguruka 61–66
H H H H H H. Amatega 10, 20, 40, 80, 160, 320: $630 zirahomba. Itega rikurikiraho ryari kuba $640; imbibi ni $500. Uburyo burasenyutse. Dushobora gutega $500 (kandi niritsinda, tuzaba tukiri munsi ya $130 muri iki cyiciro) cyangwa gusubira kuri $10 tukemera igihombo. UmukaraitegaUmukaraItega ryishyura kimwe ku kindi ku mibare 18 y'umukara. Mu Gifaransa: noir.Soma byose → cyangwa zeruuruzigaZeruAkazu kamwe k'icyatsi katafatwa n'itega ryishyura kimwe ku kindi, irya dazeni cyangwa iry'inkingi; ni ho inyungu ya kazino ikomoka. Nanone: zeru imwe, 0.Soma byose → inshuro esheshatu zikurikiranye bifite amahirweimibareAmahirweAmahirwe y'igisubizo, kuva kuri 0 kugeza kuri 1 cyangwa kuva kuri 0% kugeza kuri 100%. Umubare umwe: 1/37 = 2,70%.Soma byose → ya 1,8% kuri buri cyiciro. Twari tumaze gukina ibyiciro nka 45. Amahirwe yo kugera aha ahantu runaka mu byiciro 45 yari nka 55%. Ntibyari amahirwe mabi; byari ibisanzwe byo hagati (median).
- p10 −$1.000
- p25 −$1.000
- mediane −$1.000
- p75 +$790
- p90 +$1.690
Ibaruramari
Twungutse $410 nyuma y'amazunguruka 60, turi munsi ya $220 nyuma ya 66. Amafaranga yose yategewe: nka $2.100 mu mazunguruka 66, mu gihe utega $10 ihoraho yari gutega $660. Igihombo giteganyijweimibareIgihombo giteganyijweAgaciro gateganyijwe gakubye amafaranga yose yategewe; igihombo mpuzandengo mu mukino umwe cyangwa mu gihe runaka.Soma byose → kuri $2.100 z'amafaranga yose yategeweamafarangaAmafaranga yose yategeweAmafaranga yose yategewe mu mukino umwe cyangwa mu gihe runaka, harimo n'intsinzi zongeye gutegwa. Nanone: handle, action.Soma byose → ni $57; igisubizo cyacu nyacyo −$220 kiri munsi yaho nka kimwe cya gatatu cy'ikinyuranyo gisanzweimibareIkinyuranyo gisanzweUmuzi wa kare w'ihindagurika; intera isanzwe y'igisubizo uvuye ku gaciro gateganyijwe.Soma byose →, ibyo bikaba bisanzwe ku buryo ifite umurizo muremure w'ibumoso. Iyo duhagarara ku izunguruka rya 60 dufite imbibi z'inyunguingambaImbibi z'inyunguIntego y'inyungu yemejwe mbere, iyo uyigezeho uhagarika umukino.Soma byose → za $400, twari kugenda twungutse $410, kandi umukino ukurikiyeho wari kugumana 1,8% imwe kuri buri cyiciro.
Icyo uyu mukino werekana
Martingale ihindura itega rya 48,65% ikaba uruhererekane rutsinda 98% by'ibyiciro byarwo kandi rugatakaza initeamafarangaIniteItega ry'ibanze uburyo cyangwa umukinnyi akoresha. Impererekane z'amatega zisobanurwa mu nite kugira ngo zikoreshwe ku meza ayo ari yo yose.Soma byose → 63 muri 2% bisigaye. Ntihindura igihombo giteganyijwe kuri buri dolari; ikuba amadolari. Utega itega rihoraho wari iruhande rwacu yateze kimwe cya gatatu cy'ayo twateze kandi atakaza, ku mpuzandengo, kimwe cya gatatu. Umukinnyi ukoresha ubu buryo umwaka wose azatsinda imigoroba myinshi ariko ahombe umwaka.
Uruhererekane rw'ibihombo ruza kangahe
Itega ryishyura kimwe ku kindi ku ruziga rufite zeru imwe ritsindwa amazunguruka 19 kuri 37. Buri murongo ni amahirwe y'uko amazunguruka runaka yose atsindwa, n'ibyo umukinnyi wa Martingale, ukuba kabiri itega nyuma ya buri gihombo, aba amaze guhomba icyo gihe.
| ibihombo bikurikirana | amahirwe | hafi 1 kuri | ibyahombwe kugeza ubu | itega rikurikira |
|---|---|---|---|---|
| 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 |
Amahirwe ni 19/37 akubwe ubwayo rimwe kuri buri gihombo, ubaze uhereye ku izunguruka runaka. Umukino muremure ugira amazunguruka menshi uruhererekane nk'urwo rushobora gutangiriraho, bityo mu mugoroba umwe birashoboka cyane kurusha uko umurongo umwe ubyerekana.
Ibibazo
Ibihombo icyenda ni byo byabusenya aho kuba bitandatu: 0,25% kuri buri cyiciro, na $5.110 zihomba iyo bibaye. Manga iba gake, manga ndende kurushaho, −2,70% imwe.
Ryari gutsinda 48,65% by'igihe kandi rigasiga icyiciro kuri −$130 uko byagenda kose. Nta cyemezo cyiza kibaho nyuma ya Martingale yasenyutse; hari gusa itega uhitamo gukurikizaho.
Yego, kuri uwo mukino. Si ku mpuzandengo y'imikino yose.
Kwishimisha n'Imibare
Banza ubigerageze ubwawe. Buri gisubizo kirapfunyitse; ugifungure igihe witeguye.
Ku meza ya $1 kugeza kuri $500, umukinnyi wa MartingaleingambaMartingaleUruhererekane rw'amatega rukuba itega kabiri nyuma ya buri gutsindwa. Reba igice cy'Ingamba umenye icyo rukora n'icyo rudakora.Soma byose → atangirira kuri $1 ku mutukuitegaUmutukuItega ryishyura kimwe ku kindi ku mibare 18 y'umutuku. Mu Gifaransa: rouge.Soma byose → ku ruziga rwa zeruuruzigaZeruAkazu kamwe k'icyatsi katafatwa n'itega ryishyura kimwe ku kindi, irya dazeni cyangwa iry'inkingi; ni ho inyungu ya kazino ikomoka. Nanone: zeru imwe, 0.Soma byose → imwe. Ni ibihombo bingahe bikurikiranye bihagarika gukuba kabiri, ni angahe yatakaje icyo gihe, kandi bibaho kangahe?
Erekana igisubizo
Igisubizo Ibihombo icyenda: $511 zatakajwe, kandi itega rikurikira ryaba $512. Bibaho rimwe mu ruhererekane 403.
Amatega ni 1, 2, 4, 8, 16, 32, 64, 128 na 256: hamwe $511. Irya cumi ryaba $512, rirenze imbibi. Itega rya $500 ritsinze riracyasiga umukinnyi ari munsi ho $11; iritsinzwe rimusiga ari munsi ho $1.011.
Umutuku utsindwa ku mahirwe ya 19/37, bityo ibihombo icyenda bikurikiranye bifite amahirwe ya (19/37)⁹ ≈ 0,25%, rimwe mu ruhererekane 403. Buri ruhererekane rurangiye rutsindira $1, bityo umukinnyi ateganya hafi $402 z'intsinzi nto mbere y'igihombo kimwe cya $511, kandi 2,70% by'ibyategewe byose biracyatakara ku mpuzandengo.
Ku ruziga rwa zeru ebyiri amahirwe ni (20/38)⁹, rimwe muri 323. Bollman (2021) yanditse “hafi 1 kuri 833”, ari (18/38)⁹, amahirwe y'intsinzi icyenda zikurikiranye.
Akanya k'urwenya
Intsinzi nto mirongo ine n'imwe n'igihombo kinini kimwe. Ubwo ni bwo buryo bwose.
Inkomoko
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”