Xikombiso: Sesheni ya Martingale
Tidolara ta khume eka yo tshuka, ti phindhiwa kambirhi endzhaku ka ku lahlekeriwa kun'wana na kun'wana, eka tafula ra $500. Rhendzeleko hi rhendzeleko, ku katsa ni rhendzeleko leri yi herisaka.

Sesheni ya simulexini ya Martingale hi mali ya ku tlanga ya $1,000. Ku hlula kutsongo ka makume mune n'we, kutani ku lahlekeriwa kutsevu hi ku landzelelana na xibejo xa vunkombo lexi aleriweke. Sesheni yi hela yi ri ehansi hi $220 endzhaku ka loko yi ri ehenhla hi $410, leswi ku nga leswi sisiteme yi swi endlaka.
Kungu
Bheja $10 eka yo tshukaxibejoYo tshukaXibejo xa mali yo ringana eka tinomboro ta 18 to tshuka. Hi Xifurwa: rouge.Hlaya hinkwaswo →. Endzhaku ka ku lahlekeriwa, phindha kambirhi. Endzhaku ka ku hlula, tlhelela eka $10. Ndzilakano wa tafulatafulaNdzilakano wa tafulaXibejo xa le hansi na xa le henhla lexi pfumeleriweke. Ndzilakano wa le henhla hi wona lowu yimisaka ntlhandlamano wa ku phindha kambirhi.Hlaya hinkwaswo → i $500, hikwalaho mali ya swibejo i 10, 20, 40, 80, 160, 320 kutani xibejo xa $640 lexi tafula ri nga ta xi ala. Ku lahlekeriwa kutsevu hi ku landzelelana ku tshova sisiteme; ku ringeta kun'wana na kun'wana ku na (19/37)⁶ ≈ 1.8% ya ku endla sweswo, naswona sesheni ya marhendzeleko ya 100 yi na ku ringeta ka kwalomu ka 50. Leswi languteriweke: kwalomu ka nkoteko wa 60% wa ku tshoka eka marhendzeleko ya 100, na ku lahlekeriwa ka $630 loko swi humelela.
Marhendzeleko 1–30
MartingaleqhingaMartingaleNtlhandlamano wa swibejo lowu phindhaka xibejo kambirhi endzhaku ka ku lahlekeriwa kun'wana na kun'wana. Languta xiyenge xa Maqhinga ku vona leswi wu swi endlaka na leswi wu nga swi endliki.Hlaya hinkwaswo → ya ntolovelo: ku lahlekeriwa kun'we ku ya eka kunharhu, kun'wana na kun'wana ku heteleriwa hi ku hlula loku nyikaka +$10. Hi rhendzeleko 30 hi hlurile ka 17, kun'wana na kun'wana ku pfala ntsendzeleko, naswona hi le henhla hi $170. Mali ya xibejo leyikulu ku fika sweswi a yi ri $80 endzhaku ka ku lahlekeriwa kunharhu. Swi twala onge i muchini wo kandziyisa mapapila ya $10.
Marhendzeleko 31–60
Swi ya emahlweni hi ndlela leyi fanaka, ku ri na ntsendzeleko wun'we wa ku lahlekeriwa kumune (mali ya swibejo ku fika eka $160, kutani ku hlula) lowu nkarhinyana wu vekeke $310 eka tafula naswona wu twaleke onge i vunhenha. Endzhaku ka marhendzeleko ya 60: mitsendzeleko ya 41 yi hetiwile, hi le henhla hi $410, naswona ndhawu ya le hansi ka mali ya ku tlangamaliMali ya ku tlangaMali hinkwayo leyi hlayiseriweke ku tlanga. Ku lawula mali ya ku tlanga i ku boha leswaku u ta yi veka engozini ku fika kwihi hi xibejo na hi sesheni.Hlaya hinkwaswo → ku sukela eka rhendzeleko 30 a ku ri $1,040. Histogiramu ya sesheni yin'wana na yin'wana ya Martingale yi languteka hi ndlela leyi eka xiphemu lexikulu xa ku leha ka yona.

Marhendzeleko 61–66
L L L L L L. Mali ya swibejo 10, 20, 40, 80, 160, 320: $630 yi lahlekile. Xibejo lexi landzelaka a xi ta va $640; ndzilakano i $500. Sisiteme yi tshovekile. Hi nga bheja $500 (naswona loko xi hlula, ha ha ta va ehansi hi $130 eka ntsendzeleko) kumbe ku sungula nakambe hi $10 hi amukela ku lahlekeriwa. Yo ntimaxibejoYo ntimaXibejo xa mali yo ringana eka tinomboro ta 18 to ntima. Hi Xifurwa: noir.Hlaya hinkwaswo → kumbe tizerovhilwaZeroKhamara yin'we ya rihlaza leyi ku nga riki na xibejo xa mali yo ringana, xa dazini kumbe xa kholomu lexi yi funengetaka; xihlovo xa vuyelo bya khasino. Nakambe: zero yin'we, 0.Hlaya hinkwaswo → ta tsevu hi ku landzelelana swi na nkotekotinhlayoNkotekoNkoteko wa mbuyelo, ku suka eka 0 ku ya eka 1 kumbe 0% ku ya eka 100%. Nomboro yin'we: 1/37 = 2.70%.Hlaya hinkwaswo → wa 1.8% eka ntsendzeleko wun'wana na wun'wana. A hi endlile mitsendzeleko ya kwalomu ka 45. Nkoteko wa ku fika eka ndhawu leyi kun'wana eka mitsendzeleko ya 45 a wu ri kwalomu ka 55%. A ku nga ri ku pfumaleka ka nkateko; a ku ri xiphemu xa le xikarhi (median).
- p10 −$1,000
- p25 −$1,000
- xikarhi (median) −$1,000
- p75 +$790
- p90 +$1,690
Tibuku ta mali
Ehenhla hi $410 endzhaku ka marhendzeleko ya 60, ehansi hi $220 endzhaku ka 66. Mali hinkwayo leyi bhejiweke: kwalomu ka $2,100 eka marhendzeleko ya 66, loko ku pimanisiwa na $660 eka mubheji wa $10 hi mpimo wun'we. Ku lahlekeriwa loku languteriweketinhlayoKu lahlekeriwa loku languteriwekeNtsengo lowu languteriweke wu andzisiwa hi mali hinkwayo leyi bhejiweke; mali ya xiringaniso leyi lahlekaka eka sesheni kumbe eka nkarhi wo karhi.Hlaya hinkwaswo → eka $2,100 ya mali hinkwayo leyi bhejiwekemaliMali hinkwayo leyi bhejiwekeMali hinkwayo leyi bhejiweke eka sesheni kumbe nkarhi wo karhi, ku katsa na mali leyi hluriweke leyi tlhela yi bhejiwa. Nakambe: handle, action.Hlaya hinkwaswo → i $57; −$220 ya hina ya xiviri yi le hansi ka sweswo hi kwalomu ka xiphemu xa vunharhu xa ku hambuka loku tolovelekeketinhlayoKu hambuka loku tolovelekekeRimitsu ra xikwere ra ku hambana-hambana; mpfhuka lowu tolovelekeke exikarhi ka mbuyelo na ntsengo lowu languteriweke.Hlaya hinkwaswo →, leswi nga hlamarisiki eka sisiteme leyi ku hangalaka ka yona ku nga na ncila wo leha eximatsini. Loko a hi yimile eka rhendzeleko 60 hi ndzilakano wa ku hlulaqhingaNdzilakano wa ku hlula (stop-win)Xikongomelo xa mpindzulo lexi vekiweke ka ha ri emahlweni lexi u hetaka sesheni loko u xi fikelela.Hlaya hinkwaswo → wa $400, a hi ta huma hi ri ehenhla hi $410, naswona sesheni leyi landzelaka a yi ta va na 1.8% leyi fanaka eka ntsendzeleko wun'wana na wun'wana.
Leswi sesheni yi swi kombaka
Martingale yi hundzula xibejo xa 48.65% xi va ntlhandlamano lowu hlulaka 98% ya mitsendzeleko ya wona naswona wu lahlekeriwa hi tiyunitimaliYunitiMali ya xibejo ya xisekelo leyi sisiteme kumbe mutlangi a tirhaka ha yona. Ntlhandlamano wa swibejo wu hlamuseriwa hi tiyuniti leswaku wu tirha eka tafula rin'wana na rin'wana.Hlaya hinkwaswo → ta 63 eka 2% leyi saleke. A yi cinci ku lahlekeriwa loku languteriweke eka dolara yin'wana na yin'wana; yi andzisa tidolara. Mubheji hi mpimo wun'we loyi a a ri etlhelweni ka hina u bheje xiphemu xa vunharhu xa mali leyi naswona u lahlekeriwe, hi xiringaniso, hi xiphemu xa vunharhu. Mutlangi loyi a tirhisaka sisiteme leyi lembe hinkwaro u ta hlula eka madyambu yo tala kambe a lahlekeriwa hi lembe.
Ndzandzelelano wa ku lahlekeriwa wu ta kangani
Xibejo xa mali yo ringana eka vhilwa ra zero yin'we xi lahlekeriwa eka marhendzeleko ya 19 eka 37. Mula wun'wana ni wun'wana i nkoteko wa leswaku marhendzeleko yo karhi hinkwawo ma lahlekeriwa, na leswi mutlangi wa Martingale, loyi a phindhaka kambirhi loko a lahlekeriwile, a lahlekeriweke swona hi nkarhi wolowo.
| ku lahlekeriwa hi ku landzelelana | nkoteko | kwalomu ka 1 eka | leswi lahlekeke sweswi | xibejo lexi landzelaka |
|---|---|---|---|---|
| 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 |
Nkoteko i 19/37 lowu andzisiwaka hi wona n'wexe kan'we eka ku lahlekeriwa kun'wana ni kun'wana, ku hlayiwa ku sukela eka rhendzeleko rin'we. Sesheni yo leha yi na marhendzeleko yo tala laha ndzandzelelano wo tano wu nga sungulaka kona, hikwalaho eka nimadyambu nkoteko wa wona wu kulu ngopfu ku tlula leswi mula wun'we wu swi kombaka.
Swivutiso
Ku lahlekeriwa kukaye ku yi tshova ematshan'weni ya kutsevu: 0.25% eka ntsendzeleko wun'wana na wun'wana, na $5,110 leyi lahlekaka loko swi humelela. Xidziva lexi nga talangiki, xidziva xo enta, −2.70% leyi fanaka.
A xi ta hlula 48.65% ya nkarhi naswona a xi ta siya ntsendzeleko eka −$130 hambiswiritano. A ku na goza lerinene endzhaku ka Martingale leyi tshovekeke; ku na mali ya xibejo ntsena leyi u yi hlawulaka endzhaku ka sweswo.
Ina, eka sesheni yoleyo. Ku nga ri eka xiringaniso xa tisesheni hinkwato.
Ku Tihungasa hi Tinhlayo
Ringeta leswi hi wexe ku sungula. Nhlamulo yin'wana na yin'wana yi pfariwile; yi pfula loko u lunghekile.
Eka tafula ra $1 ku ya eka $500, mutlangi wa MartingaleqhingaMartingaleNtlhandlamano wa swibejo lowu phindhaka xibejo kambirhi endzhaku ka ku lahlekeriwa kun'wana na kun'wana. Languta xiyenge xa Maqhinga ku vona leswi wu swi endlaka na leswi wu nga swi endliki.Hlaya hinkwaswo → u sungula hi $1 eka yo tshukaxibejoYo tshukaXibejo xa mali yo ringana eka tinomboro ta 18 to tshuka. Hi Xifurwa: rouge.Hlaya hinkwaswo → eka vhilwa ra zerovhilwaZeroKhamara yin'we ya rihlaza leyi ku nga riki na xibejo xa mali yo ringana, xa dazini kumbe xa kholomu lexi yi funengetaka; xihlovo xa vuyelo bya khasino. Nakambe: zero yin'we, 0.Hlaya hinkwaswo → yin'we. Xana ku lahlekeriwa kangani ku landzelana ku yimisa ku andzisa kambirhi, ku lahlekiwe swingani hi nkarhi wolowo, naswona swi humelela kangani?
Komba nhlamulo
Nhlamulo Ku lahlekeriwa ka nkaye: $511 yi lahlekile, naswona xibejo lexi landzelaka a xi ta va $512. Swi humelela kan'we eka kwalomu ka minhlandlamano ya 403.
Mali ya swibejo i 1, 2, 4, 8, 16, 32, 64, 128 na 256: hinkwayo $511. Ya vukhume a yi ta va $512, ku tlula ndzilakano. Xibejo xa $500 lexi hlulaka xa ha siya mutlangi a lahlekeriwile hi $11; lexi lahlekeriwaka xi n'wi siya a lahlekeriwile hi $1,011.
Yo tshuka yi lahlekeriwa hi nkoteko wa 19/37, hikwalaho ku lahlekeriwa ka nkaye ku landzelana ku na nkoteko wa (19/37)⁹ ≈ 0.25%, kan'we eka kwalomu ka minhlandlamano ya 403. Ntlhandlamano wun'wana na wun'wana lowu heleleke wu hlula $1, hikwalaho mutlangi u languta ku kuma kwalomu ka $402 ya ku hlula kutsongo ku nga si fika ku lahlekeriwa kun'we ka $511, naswona 2.70% ya hinkwaswo leswi bhejiweke ya ha lahleka hi xiringaniso.
Eka vhilwa ra zero mbirhi nkoteko i (20/38)⁹, kan'we eka kwalomu ka 323. Bollman (2021) u kandziyisa “kwalomu ka 1 eka 833”, leswi nga (18/38)⁹, nkoteko wa ku hlula ka nkaye ku landzelana.
Ku hlekisa katsongo

Ku hlula kutsongo ka makume mune n'we na ku lahlekeriwa kukulu kun'we. Hi yona sisiteme hinkwayo.
Swihlovo
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”