Roulette ƒe kɔmpiutawo
Alesi kɔmpiuta dzidzea bɔl ƒe ɣeyiɣi, ame siwo wɔ gbãtɔwo, kple alesi wòle be wòanɔ pɛpɛpɛ.
Roulette kɔmpiuta dzidzea bɔl kple rotor ƒe ɣeyiɣi le trɔtrɔ ƒe sekend gbãtɔwo me eye wòyɔa ʋuafɔ ƒe akpa si me wòle be bɔl la nage ɖo. Edward Thorp kple Claude Shannon wɔ gbãtɔ le ƒe 1961 me, eye Eudaemons wɔ digital-tɔwo tso ƒe 1976 me. Mɔnu la bia be woaxɔ bɛtwo le bɔl ƒuƒu megbe: studio gbagbewo tua bɛtɖoɖo ne woƒu bɔl la egbea, eye Nevada xe mɔ ɖe mɔ̃ siawo nu tso ƒe 1985 me.
Alesi wowɔ roulette kɔmpiuta ƒe ɖoɖo gbãtɔ
Susu la va Edward Thorp ta me le ƒe 1955 ƒe keleŋɔli me, esime wònye ŋutinunya ƒe sukuvi kɔkɔ le UCLA: ʋuafɔ si wowɔ nyuie akpa be mate ŋu aɖe akpa o la, ele be wòaɖo bɔldɔwɔnuBɔlBɔl sue si wotsɔ ƒua du ɖe mɔ la me ɖe rotor la ƒe yiyi ŋu. Egbegbe bɔlwo nye ivorine alo Teflon, 18–21 mm.Xlẽe blibo → la ɖe mɔ dzi le mɔ si woate ŋu agblɔ ɖi abe ɣletinyigba ene. Exɔ ʋuafɔ bɔbɔe sue aɖe si ƒe lolome nye afã ƒe video kple gaƒoƒo-dzidzemɔ̃ le nɔnɔmetata la me, eye wòkpɔ be emeʋuʋu mele ɖeka o ale gbegbe be womate ŋu agblɔ nu ɖi tso eŋu o, eye mɔzɔzɔ aɖe ɖe Nevada le December 1958 me ɖe fia be kasino ʋuafɔwo tsana nyuie. Emegbe blackjack xɔ eƒe ɣeyiɣi. Le November 1960 me, le MIT la, ebia Claude Shannon be wòaɖo eƒe kaɖewo xexlẽ ŋuti agbalẽ ɖe National Academy of Sciences; le kpekpe la ƒe nuwuwu la, Shannon bia nu bubu si dzi wòle dɔ wɔm le, eye roulette dɔ la ʋu yi Shannon ƒe anyigbate xɔ me. Woƒle ʋuafɔ si sɔ kple sewo tso Reno $1,500, wotsɔe ɖo billiard-kplɔ̃ xoxo si wowɔ kple kpe ŋu, eye wodzidze bɔl ƒe ɣeyiɣi kple kekeli si dana kple gaƒoƒo si dzidzea sekend ƒe akpa alafalia. Esi wova bi la, woƒe ɣeyiɣi dzidzedze ƒe vodadawo ɖi tso abe sekend 0.03 ene va ɖo 0.01. Le June 1961 me la, transistor wuieve nɔ kɔmpiuta la me eye eƒe lolome sɔ kple sigaret ƒe aɖaka: tsyɔnu si le afɔkpa me, si wotsɔa afɔ ƒe asibide gã zãna, dzidzea rotordɔwɔnuRotorƲuafɔ la ƒe akpa si trɔna eye dowo le edzi.Xlẽe blibo → kple bɔl la ƒe ɣeyiɣi, eye gbeɖiɖi aɖe le to ɖeka me yɔa ʋuafɔ la ƒe akpaʋuafɔAkpaDowo ƒe akpa si kplɔ wo nɔewo ɖo le ʋuafɔ la dzi, si to vovo na xexlẽdzesi ƒe ha aɖe le kplɔ̃ ƒe ɖoɖo dzi.Xlẽe blibo → enyi dometɔ ɖeka. Le Las Vegas le dzomeŋɔli ma me la, Shannon dzidze ɣeyiɣi le ʋuafɔ la gbɔ eye wòŋlɔ xexlẽdzesiwo ɖi abe ɖoɖo ŋu fefewɔla bubu ɖe sia ɖe ene, esime Thorp ɖo bɛt sue siwo nye dime le kplɔ̃ la ƒe nuwuwu. Nyagblɔɖiwo nɔ te, gake ka siwo le lili abe ɖa ene si yi tomenu me la ŋena ɖaa, eye zi ɖeka nyɔnu aɖe si nɔ Thorp gbɔ la kpɔ nu si do go tso eƒe to me eye vɔvɔ̃ ɖoe. Womeɖo bɛt vavãwo kpɔ o. Thorp ɖe gbeƒã roulette kɔmpiuta ƒe ɖoɖo la le ƒe 1966 me eye wòɖe eƒe nyatakaka bliboawo ɖe go le ƒe 1979 kple 1984 me.
Digital kɔmpiuta gbãtɔwo
Thorp kple Shannon ƒe mɔ̃ la nye analog: eƒe kawo ƒe ɖoɖoe nye eƒe dɔwɔɖoɖo, eye mɔnu la trɔtrɔ bia be woagbugbɔ eƒe kawo aɖo. Microprocessor ɖe seɖoƒe ma ɖa. Alan Lewis, sukuvi aɖe le Caltech, tsɔ digital kɔmpiuta si wòwɔ le aƒeme de kamera ƒe aɖaka me yi Circus Circus le Las Vegas le ƒe 1972 me, dzidze ʋuafɔwo ƒe ɣeyiɣi tso balkɔn si le kplɔ̃wo tame dzi eye wòtsɔ radio ɖo nyagblɔɖiwo ɖe zɔhɛ si nɔ anyi. Ewɔ dɔ, gake mekpɔ ga aɖeke o; emegbe ese egɔme be yemetsɔ ʋuafɔ la ƒe tsɔtsɔ de eme o. Tso ƒe 1976 me la, ŋutinunya ƒe sukuvi aɖewo ƒe ha le Santa Cruz, Eudaemons, wɔ dɔ la blibo. Woƒle kasino ʋuafɔ, wodzidze bɔl, rotor, tsɔtsɔ kple tɔtɔ la, eye woŋlɔ akɔntabubu siwo me ɖoɖo atɔ̃ le, siwo fefewɔla la ɖɔna ɖo na ʋuafɔ ɖe sia ɖe to afɔ ƒe asibide ƒe tsyɔnuwo zizi me abe aɖabaƒoƒo blaeve ene hafi ɖoa bɛt. Woƒe kɔmpiuta yɔa akpa enyi dometɔ ɖeka le sekend ʋɛ aɖewo megbe le trɔtrɔ la me. Le kplɔ̃ ŋutɔŋutɔ dzi le January 1978 me la, ena viɖe si wogblɔ be enye 25%; mɔ̃wo, siwo wobla ɖe ŋutilã ŋu eye emegbe wotsɔ de afɔkpawo me la, gblẽna zi geɖe wu ŋutinunya la (kpɔ Eudaemons).
Nu ka tae bɛt ɖoɖo tsitsi nye nu vevi
Kasino ate ŋu atɔ te nyagblɔɖi keŋkeŋ to bɛtwo gbegbe me ne woƒu bɔl la. Thorp kpɔ be kloe aɖeke mewɔ nenema o: le Reno, Las Vegas, London, Monte Carlo, Nice, Venice kple Puerto Rico la, kɔnu si wowɔna enye be woagblɔ “bɛt bubu megali oɖoɖoBɛt bubu megali oDila ƒe gbeɖeɖe (alo nya si dzena le ekran dzi) si tua bɛtɖoɖo nu. Womate ŋu aɖo gakpewo ɖi, aʋã wo alo aɖe wo ɖa o.Xlẽe blibo →” le tsatsa ɖeka alo eve do ŋgɔ na bɔl la gege. Fesre ma koe nyagblɔɖi ƒe ɖoɖo ɖe sia ɖe si va tso ɣemaɣi dzi hiã, tso Eudaemons dzi va ɖo Ritz ƒe ha la ƒe bɛtyɔyɔ tsitsiwo le racetrackkplɔ̃RacetrackAkpa si le abe azi ene le kplɔ̃ ƒe ɖoɖo gbagbewo kple elektronik ɖoɖowo dzi si ɖea xexlẽdzesiwo fiana le alesi wole ʋuafɔ la dzi ene, eye wozãnɛ tsɔ ɖoa ŋutinɔlawo ƒe bɛt kple akpa ƒe bɛtwo kple asikaka ɖeka.Xlẽe blibo → (ʋuafɔ ƒe ɖoɖo le kplɔ̃ dzi) dzi. Nevada xe mɔ ɖe nyagblɔɖimɔ̃wo nu le May 1985 me, eye studio gbagbewo tua bɛtɖoɖo ne woƒu bɔl la egbea.
Alesi kasinowo wɔ nu ɖe eŋu
Le ƒe siwo me woxɔa bɛtwo kokoko le bɔl ƒuƒu megbe la, kasinowo wɔa nu ɖe fefewɔla siwo dzi wole ɖikeke le la ŋu to dila la dzi. Ŋutinya siwo ku ɖe Norman Leigh ƒe ɖoɖo ŋu fefewɔlawo le Nice le ƒe 1966 me kple nyagblɔɖi ƒe ha siwo va emegbe ŋu la ƒo nu tso croupieramewoCroupierDila si le roulette kplɔ̃ ŋu.Xlẽe blibo → yeye le trɔtrɔ ɖe sia ɖe me, bɔl si woɖɔli, trɔtrɔ siwo wowɔ kpuie alo kabakaba, kplɔ̃ si kasino la ŋutɔ ƒe amewo yɔ, kple le nuwuwu la kplɔ̃ si wotu ŋu. Ŋutinya siawo tso fefewɔlawo gbɔ eye esesẽ be woado wo kpɔ (Goldman, 2007). Mɔnu siawo sɔ kokoko: trɔtrɔ kpui alo kabakaba mate ŋu ana bɔl la nayi dodɔwɔnuDoDo 37 siwo dzi xexlẽdzesiwo le le rotor la dzi dometɔ ɖeka. Woyɔnɛ hã be slot, cup.Xlẽe blibo → aɖe me o, gake etɔtɔa ɣeyiɣi si nyagblɔɖila dzidzena la.
Ɖe roulette dilawo ate ŋu ada bɔl ɖe xexlẽdzesi aɖe dzi? Dzixɔse tovo la
Alesi wòle be nyagblɔɖi la nanyo
Thorp (1984) bu asixɔxɔ si le nyagblɔɖi ŋu ne eƒe vodada wɔ ɖe gakpo ƒe nɔnɔme (bell curve) dzi: le trɔtrɔ si wowɔna zi geɖe me la, do si wogblɔ ɖi la tra do σ ɖe akpa ɖeka alo bubu dzi. Ɖo bɛt ɖe xexlẽdzesi si wogblɔ ɖi ɖeka dzi, alo eya kple eƒe ŋutinɔlabɛtŊutinɔlawoXexlẽdzesi ɖeka kple do eve siwo le eƒe axa ɖe sia ɖe dzi le ʋuafɔ la dzi, xexlẽdzesi ɖeka ƒe gakpe atɔ̃.Xlẽe blibo → eve le akpa ɖe sia ɖe dzi, eye viɖe la ku ɖe σ ɖeka ko ŋu. Nyagblɔɖi si de blibo aɖu xexlẽdzesi ɖeka ƒe bɛtbɛtXexlẽdzesi ɖekaXexlẽdzesi ɖeka, fetu 35:1.Xlẽe blibo → ɖe sia ɖe dzi. Ne σ = do 10, si nye pɛpɛpɛnyenye si Thorp kple Shannon ɖo la, xexlẽdzesi ɖeka ƒe bɛt gbugbɔa abe +44% ene, xexlẽdzesi si Thorp na na woƒe mɔ̃ la; eƒe ŋutinya si wòŋlɔ le ƒe 1998 me tsɔe ɖe ʋuafɔ la ƒe akpa enyilia si dzi wode asi wu la dzi. Viɖe la ɖina kabakaba ne vodada la le dzidzim eye wòbuna le abe do 17 ene le Europa ʋuafɔ dzi kple 16 le Amerika ʋuafɔ dzi, esime nyagblɔɖi la tra kloe ʋuafɔ la ƒe afã. Thorp ŋutɔ ƒe vodadawo ƒe akɔntabubu ɖe nu si tae seɖoƒe ma te ɖe eŋu fia: vodada vovovo siwo nye do 1.4 kple 5.5 tso rotor kple bɔl ƒe ɣeyiɣi dzidzedze me, 7 tso bɔl ƒe gege to mɔxenuwodɔwɔnuMɔxenuGayibɔ ƒe mɔxenu siwo le anyiɖiƒe la dzi eye wokakaa bɔl si le gege ge la ɖe afi sia afi. Woyɔa wo hã be canoe, diamond, pin.Xlẽe blibo → dzi me kple 6 tso tɔtɔ le dowo me la ƒo ƒu zu abe 10.8 ene.
Nyabiasewo
Ao. Bɔl aɖeke meli o. Software la tsɔa xexlẽdzesi la hafi nɔnɔmetata si le ʋuʋum la dzea egɔme.
Ɣeyiɣi dzidzedze ate ŋu aɖu wo dzi, eya tae aɖeke mewɔa dɔ nenema o.
Modzaka kple akɔntabubu
Te wo kpɔ le ɖokuiwò si gbã. Wobla ŋuɖoɖo ɖe sia ɖe ɖe go; ʋui ne èsɔ gbe.
ŊutinɔlawobɛtŊutinɔlawoXexlẽdzesi ɖeka kple do eve siwo le eƒe axa ɖe sia ɖe dzi le ʋuafɔ la dzi, xexlẽdzesi ɖeka ƒe gakpe atɔ̃.Xlẽe blibo → ƒe nuƒoƒo-bɛt ɖoa gakpegaGakpeNu si tsi tre ɖi na ga aɖe si woɖo ɖi, si wotsɔa ɖoa kplɔ̃ ƒe ɖoɖo la dzi tsɔ ɖoa bɛt. Woyɔnɛ hã be check.Xlẽe blibo → ɖeka ɖe xexlẽdzesi aɖe dzi kple ɖe dodɔwɔnuDoDo 37 siwo dzi xexlẽdzesiwo le le rotor la dzi dometɔ ɖeka. Woyɔnɛ hã be slot, cup.Xlẽe blibo → eve siwo le eƒe axa ɖe sia ɖe dzi le ʋuafɔ la ŋu: gakpe atɔ̃. Zi nenie wòle be nyagblɔɖi naɖo do atɔ̃ mawo me hafi wòanye viɖe ɖekeo, eye viɖe kae wòhena vɛ ne enye nyateƒe zi ɖeka le zi atɔ̃ me?
Fia ŋuɖoɖo la
Ŋuɖoɖo Enye viɖe ɖekeo le 5 le 36 me, 13.9%, ne wotsɔe sɔ kple 13.5% to nudzɔdzɔ ɖeɖe ko me. Ne enye nyateƒe zi ɖeka le zi atɔ̃ me la, etrɔa 44% vɛ wu ga si woɖo.
Ne nuƒoƒo-bɛt la ɖu dzi la, gakpe ɖeka ɖua dzi 35 ɖe 1 ŋu eye wògbugbɔna kple eƒe dziɖuga, gakpe 36, eye ene bubuawo buna. Eya ta dziɖuɖu ɖeka trɔa 36 vɛ ɖe 5 si woɖo ta, eye nuƒoƒo-bɛt la nye viɖe ɖekeo ne eɖu dzi zi 5 le 36 me, 13.9%. To nudzɔdzɔ me la, eɖua dzi zi 5 le 37 me, 13.5%. Vovototo sue ma, si mede afã le alafa ɖeka me o, gbɔe 2.70% la katã tso.
Ne eɖu dzi zi ɖeka le zi atɔ̃ me la, gakpe 0.2 × 36 = 7.2 gbugbɔna vaa ɖe 5 ɖe sia ɖe si woɖo ta, +44%. Ne enye ɖeka le ene me la, +80%.
Eya tae nyagblɔɖi ƒe nyateƒenyenye ƒe dzidziɖedzi sue aɖe hã ƒe asixɔxɔ lolo alea gbegbe, eye eya tae kasinowo xea mɔ na nuƒoƒo-bɛtwokplɔ̃Nuƒoƒo-bɛtBɛt si wogblɔna na dila la ɖe esi teƒe be woatsɔ asi aɖoe, zi geɖe la, bɛt ɖe ʋuafɔ ƒe akpa dzi abe voisins alo tiers ene. Woyɔnɛ hã be “gbeƒãɖeɖe-bɛt”.Xlẽe blibo → kaba ne bɛtga le kɔkɔ: vovototo sue ma ye nye kasino la ƒe viɖe blibo. Wogblɔ be Ritz fefewɔla siwo nɔ anyi le ƒe 2004 me ɖo bɛt nenema.
Thorp ŋlɔ vodada ene siwo le wo ɖokui si le eƒe nyagblɔɖi me, le do ƒe xexlẽme me: 1.4 tso rotordɔwɔnuRotorƲuafɔ la ƒe akpa si trɔna eye dowo le edzi.Xlẽe blibo → ƒe ɣeyiɣidzidze me, 5.5 tso bɔldɔwɔnuBɔlBɔl sue si wotsɔ ƒua du ɖe mɔ la me ɖe rotor la ƒe yiyi ŋu. Egbegbe bɔlwo nye ivorine alo Teflon, 18–21 mm.Xlẽe blibo → ƒe ɣeyiɣidzidze me, 7 tso bɔl ƒe dzadza to mɔxenuwodɔwɔnuMɔxenuGayibɔ ƒe mɔxenu siwo le anyiɖiƒe la dzi eye wokakaa bɔl si le gege ge la ɖe afi sia afi. Woyɔa wo hã be canoe, diamond, pin.Xlẽe blibo → dzi me kple 6 tso tɔtɔtɔ le dowo me. Aleke gbegbe vodada blibo la lolo, eye nenie ɣeyiɣidzidze ƒe vodada eveawo tsɔ kpe ɖe eŋu?
Fia ŋuɖoɖo la
Ŋuɖoɖo Abe do 10.8 ene katã. Ne ɣeyiɣidzidze ƒe vodadawo meli o la, anye 9.2, eya ta ɣeyiɣidzidze eveawo tsɔ 1.6 ko kpe ɖe eŋu.
Vodada siwo le wo ɖokui si mekpena ɖe wo nɔewo ŋu tẽ o; woƒe dzidzi eve (squares) koe kpena ɖe wo nɔewo ŋu. Vodada blibo la ƒe lolome si dzɔna zi geɖe nye dzidzi eveawo ƒe nu ƒoƒu ƒe ke (square root): 1.4² + 5.5² + 7² + 6² = 1.96 + 30.25 + 49 + 36 = 117.2, eye √117.2 ≈ 10.8.
Ne ɣeyiɣidzidze ƒe vodada eveawo meli o: √(49 + 36) = √85 ≈ 9.2.
Vodada blibo si nye do 10.8 le do 17 ƒe seɖoƒe si le ɖoɖowɔɖi si le axa sia dzi me, eye eƒe asixɔxɔ nye abe +34% ene le xexlẽdzesi ɖeka dzi. Nusɔsrɔ̃ si Thorp ɖe tso eme: ne bɔl ƒe dzadza to mɔxenuwo dzi zu vodada gãtɔ la, ɣeyiɣidzidze nyui wu mehea viɖe gã aɖeke vɛ o.
Nukokoe sue
Ŋutinunya la wɔa dɔ. Bɛtɖoɣi la tu.
Nunyaƒewo
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”
- Bass, T. A. The Eudaemonic Pie.
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Goldman, N. Great Gambling Scams.
- Nevada Revised Statutes, chapter 465.