Afɔɖeɖe ɖeka ɖeka: Martingale fefeɣi
Dɔla ewo ɖe dzĩ dzi, si wodzina ɖe edzi zi eve le gabubu ɖe sia ɖe megbe, le kplɔ̃ $500 tɔ ŋu. Trɔtrɔ ɖeka ɖeka, kpe ɖe trɔtrɔ si wu enu ŋu.
Martingale fefeɣi si wowɔ kpɔɖeŋu na, tso gaƒoƒu $1,000 me. Dziɖuɖu suesue blaene vɔ ɖeka, emegbe gabubu ade ɖe wo nɔewo yome kple bɛt adrelia si wogbe. Fefeɣi la wu enu kple gabubu $220 le esime wòkpɔ $410 kpɔ, eye esiae ɖoɖo la wɔna.
Ɖoɖo la
Ɖo bɛt $10 ɖe dzĩbɛtDzĩBɛt sɔsɔe ɖe xexlẽdzesi dzĩ 18 la dzi. Le Frans gbe me: rouge.Xlẽe blibo → dzi. Le gabubu megbe la, dzii ɖe edzi zi eve. Le dziɖuɖu megbe la, gbugbɔ yi $10. Kplɔ̃ ƒe seɖoƒekplɔ̃Kplɔ̃ ƒe seɖoƒeBɛtga suetɔ kple gãtɔ si woɖe mɔ ɖo. Bɛtga gãtɔ lae xea mɔ na tɔtrɔ ɖoɖo siwo ƒoa bɛtga ɖe eve.Xlẽe blibo → nye $500, eya ta bɛtgawo nye 10, 20, 40, 80, 160, 320 eye emegbe bɛt $640 si kplɔ̃ la agbe. Gabubu ade siwo kplɔ wo nɔewo ɖo gbãa ɖoɖo la; agbagbadzedze ɖe sia ɖe ƒe mɔnukpɔkpɔ be wòawɔ esia nye (19/37)⁶ ≈ 1.8%, eye agbagbadzedze abe 50 ene le fefeɣi si me trɔtrɔ 100 le me. Nu si wokpɔ mɔ na: mɔnukpɔkpɔ abe 60% ene be wòagbã le trɔtrɔ 100 me, kple gabubu $630 ne egbã.
Trɔtrɔ 1–30
MartingaleaɖaŋuMartingaleTɔtrɔ ɖoɖo si tsɔa bɛtga ƒoa ɖe eve le gabubu ɖe sia ɖe megbe. Kpɔ Aɖaŋuwo ƒe akpa la be nànya nu si wòwɔna kple nu si mewɔna o.Xlẽe blibo → gbadza: gabubu ɖeka va ɖo etɔ̃ ɖe wo nɔewo yome, eye dziɖuɖu si naa +$10 wua wo dometɔ ɖe sia ɖe nu. Va se ɖe trɔtrɔ 30 la, míeɖu dzi zi 17, eye wo dometɔ ɖe sia ɖe wu ƒoƒo aɖe nu, eye míekpɔ $170. Bɛtga gãtɔ va se ɖe fifia nye $80 le gabubu etɔ̃ megbe. Edzena abe mɔ̃ si taa gagbalẽ $10 tɔwo ene.
Trɔtrɔ 31–60
Nu ɖeka ma ke geɖe wu, kple ƒoƒo ɖeka si me gabubu ene le (bɛtga va ɖo $160, emegbe dziɖuɖu) si tsɔ $310 de kplɔ̃ dzi hena ɣeyiɣi kpui aɖe eye wòdze abe dzinɔameƒo ene. Le trɔtrɔ 60 megbe: ƒoƒo 41 wu enu, míekpɔ $410, eye gaƒoƒugaGaƒoƒuGa katã si nèɖo ɖe vovo na fefe. Gaƒoƒu dzi kpɔkpɔ fia be nàɖo nya me be akpa ka nàtsɔ ade afɔku me le bɛt ɖe sia ɖe kple fefeɣi ɖe sia ɖe me.Xlẽe blibo → la ƒe teƒe si le ete wu tso trɔtrɔ 30 nye $1,040. Martingale fefeɣi ɖe sia ɖe ƒe histogram ɖenɔa alea le eƒe didime ƒe akpa gãtɔ me.
Trɔtrɔ 61–66
B B B B B B. Bɛtga 10, 20, 40, 80, 160, 320: míebu $630. Bɛt si kplɔe ɖo anye $640; seɖoƒe la nye $500. Ɖoɖo la gbã. Míate ŋu aɖo bɛt $500 (eye ne eɖu dzi hã la, míagakpɔtɔ abu $130 le ƒoƒo la me) alo míagbugbɔ ayi $10 eye míaxɔ gabubu la. MɔnukpɔkpɔakɔntabubuMɔnukpɔkpɔMɔnukpɔkpɔ be emetsonu aɖe nadzɔ, tso 0 va ɖo 1 alo tso 0% va ɖo 100%. Xexlẽdzesi ɖeka: 1/37 = 2.70%.Xlẽe blibo → be yibɔbɛtYibɔBɛt sɔsɔe ɖe xexlẽdzesi yibɔ 18 dzi. Frans gbe me: noir.Xlẽe blibo → alo zeroʋuafɔZeroDo gbemumu ɖeka si dzi bɛt sɔsɔe, wuieve alo sɔti ƒe bɛt aɖeke metsyɔna o; kasino ƒe viɖe ƒe dzɔtsoƒe. Woyɔnɛ hã be zero ɖeka, 0.Xlẽe blibo → ade nado ɖe wo nɔewo yome nye 1.8% le ƒoƒo ɖe sia ɖe me. Míewɔ ƒoƒo abe 45 ene. Mɔnukpɔkpɔ be míava ɖo afi sia le ƒoƒo 45 dometɔ aɖe me nye abe 55% ene. Menye dzɔgbevɔ̃ o; titinatɔ wònye.
- p10 −$1,000
- p25 −$1,000
- titinatɔ −$1,000
- p75 +$790
- p90 +$1,690
Akɔntawo
Míekpɔ $410 le trɔtrɔ 60 megbe, míebu $220 le 66 megbe. Bɛtga katã: abe $2,100 ene le trɔtrɔ 66 me, ne míetsɔe sɔ kple $660 na ame si ɖoa $10 ɖeka ɖaa. Gabubu si wokpɔ mɔ naakɔntabubuGabubu si wokpɔ mɔ naAsixɔxɔ si wokpɔ mɔ na tsɔ dzi ɖe bɛtga katã si woɖo dzi; ga si wobuna le titina me le fefeɣi alo ɣeyiɣi aɖe me.Xlẽe blibo → le bɛtga katãgaBɛtga katãGa si woɖo bɛt ɖo katã le fefeɣi alo ɣeyiɣi aɖe me, kple dziɖuga siwo wogbugbɔ ɖo bɛt. Woyɔnɛ hã be handle, action.Xlẽe blibo → $2,100 me nye $57; míaƒe −$220 si dzɔ ŋutɔ le ete na ema abe kakaɖe ƒe dzidzenuakɔntabubuKakaɖe ƒe dzidzenuKakaɖe ƒe ke; didime si emetsonu aɖe ɖona tso asixɔxɔ si wokpɔ mɔ na gbɔ zi geɖe.Xlẽe blibo → ɖeka ƒe akpa etɔ̃lia ene, si menye nukunu o na ɖoɖo si ƒe emetsonuwo ƒe mamamã ƒe asi miame didi ŋutɔ. Ne míetɔ te le trɔtrɔ 60 kple viɖe ƒe seɖoƒeaɖaŋuViɖe ƒe seɖoƒeViɖe ƒe taɖodzinu si nèɖo do ŋgɔ, eye ne èɖoe la, èɖe asi le fefeɣi la ŋu.Xlẽe blibo → $400 la, anɔ be míedzo kple viɖe $410, eye fefeɣi si kplɔe ɖo anɔ 1.8% ɖeka ma ke tsɔm le ƒoƒo ɖe sia ɖe me.
Nu si fefeɣi la ɖe fia
Martingale trɔa bɛt 48.65% tɔ wòzua ɖoɖo si ɖua dzi le eƒe ƒoƒowo ƒe 98% me eye wòbua dzidzenugaDzidzenuGɔmedzedze bɛtga si ŋu ɖoɖo alo fefewɔla aɖe wɔa dɔ ɖo. Woɖɔa tɔtrɔ ɖoɖowo ɖe dzidzenuwo me ale be woawɔ dɔ le kplɔ̃ ɖe sia ɖe dzi.Xlẽe blibo → 63 le 2% susɔeawo me. Metrɔa gabubu si wokpɔ mɔ na le dɔla ɖe sia ɖe me o; edzia dɔlawo ɖe edzi. Ame si ɖoa bɛtga ɖeka ɖaa le míaƒe xa la ɖo bɛt ƒe akpa etɔ̃lia ko eye wòbu ƒe akpa etɔ̃lia, le titina me. Fefewɔla si azã ɖoɖo sia ƒe ɖeka la aɖu dzi le fiẽ geɖe me eye wòabu ƒe la.
Zi nenie gabubu ɖe wo nɔewo yome vana
Bɛt sɔsɔe le ʋuafɔ zero ɖeka dzi bua trɔtrɔ 19 le 37 me. Fli ɖe sia ɖe fia mɔnukpɔkpɔ be trɔtrɔ aɖewo ɖe wo nɔewo yome nabu katã, kple ga si Martingale fefewɔla, si tsɔa bɛtga ɖoa zi eve le gabubu ɖe sia ɖe megbe, bu va ɖo ɣemaɣi.
| gabubu ɖe wo nɔewo yome | mɔnukpɔkpɔ | abe 1 le … me | gabubu va ɖo fifia | bɛt si kplɔe ɖo |
|---|---|---|---|---|
| 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 |
Mɔnukpɔkpɔ la nye 19/37 si wotsɔ dzi ɖe eɖokui dzi zi ɖeka le gabubu ɖe sia ɖe ta, tso trɔtrɔ ɖeka aɖe dzi. Trɔtrɔ geɖe le fefeɣi didi me, siwo dzi ɖoɖo sia tɔgbe ate ŋu adze egɔme le, eyata le fiẽ ɖeka me la, edzɔna zi geɖe wu ale si fli ɖeka fia.
Nyabiasewo
Gabubu asieke gbãnɛ ɖe ade teƒe: 0.25% le ƒoƒo ɖe sia ɖe me, eye wobua $5,110 ne edzɔ. To si medzɔna zi geɖe o, to si kɔ wu, −2.70% ɖeka ma ke.
Anɔ dzi ɖum le 48.65% me eye wòagakpɔtɔ agblẽ ƒoƒo la ɖe −$130. Nuwɔna nyui aɖeke meli le Martingale si gbã megbe o; bɛtga si nàtia emegbe koe li.
Ẽ, na fefeɣi ma. Menye na titina le fefeɣiwo katã me o.
Modzaka kple akɔntabubu
Te wo kpɔ le ɖokuiwò si gbã. Wobla ŋuɖoɖo ɖe sia ɖe ɖe go; ʋui ne èsɔ gbe.
Le kplɔ̃ $1 va ɖo $500 aɖe ŋu la, MartingaleaɖaŋuMartingaleTɔtrɔ ɖoɖo si tsɔa bɛtga ƒoa ɖe eve le gabubu ɖe sia ɖe megbe. Kpɔ Aɖaŋuwo ƒe akpa la be nànya nu si wòwɔna kple nu si mewɔna o.Xlẽe blibo → fefewɔla aɖe dze egɔme kple $1 ɖe dzĩbɛtDzĩBɛt sɔsɔe ɖe xexlẽdzesi dzĩ 18 la dzi. Le Frans gbe me: rouge.Xlẽe blibo → dzi le ʋuafɔ zeroʋuafɔZeroDo gbemumu ɖeka si dzi bɛt sɔsɔe, wuieve alo sɔti ƒe bɛt aɖeke metsyɔna o; kasino ƒe viɖe ƒe dzɔtsoƒe. Woyɔnɛ hã be zero ɖeka, 0.Xlẽe blibo → ɖeka dzi. Gabubu nenie ɖe wo nɔewo yome tɔa bɛtga gbɔgbɔ, nenie wòbu va ɖo ɣe ma ɣi, eye zi nenie esia dzɔna?
Fia ŋuɖoɖo la
Ŋuɖoɖo Gabubu asieke: wobu $511, eye bɛt si akplɔe ɖo anye $512. Edzɔna zi ɖeka le ƒoƒo abe 403 ene me.
Bɛtgawo nye 1, 2, 4, 8, 16, 32, 64, 128 kple 256: katã $511. Ewolia anye $512, si wu seɖoƒe la. Bɛt $500 si ɖu dzi gakpɔtɔ gblẽa fefewɔla la ɖi kple gabubu $11; esi bu gblẽnɛ ɖi kple gabubu $1,011.
Dzĩ bua kple mɔnukpɔkpɔ 19/37, eya ta gabubu asieke ɖe wo nɔewo yome ƒe mɔnukpɔkpɔ nye (19/37)⁹ ≈ 0.25%, zi ɖeka le ƒoƒo abe 403 ene me. Ƒoƒo blibo ɖe sia ɖe ɖua $1, eya ta fefewɔla la kpɔa mɔ na dziɖuɖu sue abe $402 ene hafi gabubu $511 ɖeka ma nava, eye le titina me la, wogakpɔtɔ bua ga siwo katã woɖo ƒe 2.70%.
Le ʋuafɔ zero eve dzi la, mɔnukpɔkpɔ nye (20/38)⁹, zi ɖeka le abe 323 ene me. Bollman (2021) ta “abe 1 le 833 me ene”, si nye (18/38)⁹, dziɖuɖu asieke ɖe wo nɔewo yome ƒe mɔnukpɔkpɔ.
Nukokoe sue
Dziɖuɖu suesue blaene vɔ ɖeka kple gabubu gã ɖeka. Esiae nye ɖoɖo la katã.
Nunyaƒewo
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”