Gafefela ƒe susu me vodada
Dzixɔse be emetsonu aɖe ƒe ɣeyiɣi “de” elabena medze ɣeyiɣi aɖe o.
Le dzĩ ewo megbe la, yibɔ ƒe mɔnukpɔkpɔ gakpɔtɔ nye 18/37. Ʋuafɔ la meŋlɔa nu aɖeke da ɖi o eye nu aɖeke mele eŋu o.
Susu me vodada la
Ne dzĩbɛtDzĩBɛt sɔsɔe ɖe xexlẽdzesi dzĩ 18 la dzi. Le Frans gbe me: rouge.Xlẽe blibo → do zi ewo la, fefewɔla geɖe sena le wo ɖokui me be yibɔbɛtYibɔBɛt sɔsɔe ɖe xexlẽdzesi yibɔ 18 dzi. Frans gbe me: noir.Xlẽe blibo → ƒe ɣeyiɣi “de”, eye woɖoa bɛt ɖe edzi. Ame bubuwo sena be dzĩ “xɔ dzo”, eye woɖoa bɛt ɖe eya dzi. Wo eve siaa tsɔ ɖoɖo si wu enu xoxo la bua tame le trɔtrɔ si medzɔ haɖe o ŋu. 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 menya nu si trɔtrɔ ewo mamlɛtɔwo nye o; dowodɔwɔnuDoDo 37 siwo dzi xexlẽdzesiwo le le rotor la dzi dometɔ ɖeka. Woyɔnɛ hã be slot, cup.Xlẽe blibo → ƒe lolome nye ɖeka ma ke abe gaƒoƒoɖeka si va yi ene; yibɔ ƒe mɔnukpɔkpɔakɔntabubuMɔnukpɔkpɔMɔnukpɔkpɔ be emetsonu aɖe nadzɔ, tso 0 va ɖo 1 alo tso 0% va ɖo 100%. Xexlẽdzesi ɖeka: 1/37 = 2.70%.Xlẽe blibo → nye 18/37 abe ɣesiaɣi ene.
Nu si ta wòsena abe nyateƒe ene
Le ɣeyiɣi didi me la, dzĩ kple yibɔ ƒe akpawo gogona ɖe 18/37 ŋu ɖe sia ɖe vavã. Xexlẽdzesi gãwo ƒe seakɔntabubuXexlẽdzesi gãwo ƒe seEmetsonu siwo le wo ɖokui si ƒe titina gogona ɖe asixɔxɔ si wokpɔ mɔ na ŋu esime dodokpɔwo ƒe xexlẽme le dzidzim ɖe edzi.Xlẽe blibo → la ka ɖe edzi. Gake gogo sia vana to tsitsi me, menye to ɖɔɖɔɖo me o: le trɔtrɔ 1,000 bubu megbe la, dzĩ ewo siwo ʋu ɖe edzi la zu nu tsɛ aɖe le akpa la me, menye elabena yibɔ va ɖo wo nu o, ke boŋ elabena kpɔɖeŋu la tsi. Mɔ aɖeke meli si nana yibɔ nado bɔbɔe wu o, eye xexlẽdzesi gãwo ƒe se la mebia aɖeke o.
Monte Carlo, August ƒe ŋkeke 18, 1913
Yibɔ do zi 26 ɖe wo nɔewo yome le kplɔ̃ aɖe dzi le Casino de Monte-Carlo. Tso abe yibɔ wuiatɔ̃lia ene dzi la, fefewɔlawo ƒo zi ɖe dzĩ dzi, wodzi bɛtga ɖe edzi zi eve, eye wogadzii ake, eye trɔtrɔ ɖe sia ɖe “ka ɖe edzi wu” esi do ŋgɔ. Kasino la kpɔ franc miliɔn geɖe. Ɖoɖo la ƒe mɔnukpɔkpɔ nye 1 le miliɔn 137 me tso yibɔ gbãtɔ dzi, eye mɔnukpɔkpɔ be wòava dzɔ le afi aɖe le xexeame ƒe kasinowo me mlɔeba la kloe nye ɖeka. Esia ta woyɔa gafefela ƒe susu me vodada hã be Monte Carlo ƒe susu me vodada.
Menye nukunu o. Edzɔna zi ɖeka le 44 me.
Fefewɔlawo de dzesii. Dzĩ ƒe ɣeyiɣi “de”.
Amewo yɔ kplɔ̃ la dzi. Wodzia bɛtga le dzĩ dzi zi eve le gabubu ɖe sia ɖe megbe.
Ga gbogbo bu. Yibɔ yeye ɖe sia ɖe nana dzĩ sena abe ɖe wòka ɖe edzi wu ene.
Ɖoɖo la wu enu. Kasino la kpɔ franc miliɔn geɖe tso ame siwo ɖo bɛt tsi tre ɖe ɖoɖo aɖe si mate ŋu “anya” be ɖoɖoe yenye o ŋu.
Asi xɔdzo
Amadede aɖe dzi lele elabena edze ɖe wo nɔewo yome la nye vodada ma ke si wotrɔ: wokpɔa mɔ be ɖoɖo la ayi edzi, menye be awu enu o. Susumenunyalawo yɔnɛ be asi xɔdzodzixɔse tovoAsi xɔdzoDzixɔse be dziɖuɖu geɖe ɖe wo nɔewo yome, alo emetsonu ɖeka ma ke geɖe, naa mɔnukpɔkpɔ be bubu nava la sɔ gbɔ ɖe edzi. Le ʋuafɔ la gbɔ la, enye gafefela ƒe susu me vodada si wotrɔ.Xlẽe blibo →, le numekuku si Gilovich, Vallone kple Tversky wɔ le ƒe 1985 me megbe; wodi ɖoɖo ɖe wo nɔewo yome le basketball ƒe bɔlƒoƒo me, eye womekpɔ aɖeke wu dzɔdzɔme o. Le ƒe 2018 me la, Miller kple Sanjurjo ɖee fia be dodokpɔ la ŋutɔ tre ɖe akpa ɖeka: le nuŋlɔɖi kpui me la, bɔl siwo ge ɖe eme kpata le esi ge ɖe eme megbe ƒe akpa ɖina wu bɔlƒola la ƒe xexlẽ blibo le titina me, eya ta fefewɔla si si asi xɔdzo aɖeke mele o la dzena abe ɖe wòfa vie ene. Esi wodzra eɖo la, nyatakaka mawo ke ɖe asi xɔdzo sue aɖe fia. Ame ate ŋu axɔ dzo; ʋuafɔ ya mele nɔnɔme aɖeke me o. Fefewɔla aɖewo xɔ dzixɔse eve siaa ɖe si ɖekae: be ɖoɖo ayi edzi va se ɖe esime wòanye “didi akpa”, eye emegbe wòawu enu. Le ʋuafɔ dzɔdzɔe dzi la, wo dometɔ ɖe sia ɖe ƒe asixɔxɔ si wokpɔ mɔ naakɔntabubuAsixɔxɔ si wokpɔ mɔ naEmetsonu le titina me le bɛt ɖe sia ɖe me le ɣeyiɣi didi me. −1/37 le bɛtga me na Europa bɛt gbadza ɖe sia ɖe.Xlẽe blibo → sɔ kple amadede tiatia to gaku ƒoƒo me: bɛtga la ƒe −2.70%.
Le kplɔ̃ ŋutɔŋutɔ aɖe ŋu
Croson kple Sundali (2005) kpɔ dedienɔnɔ ƒe video gaƒoƒo 18 tso 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 → eve ƒe kplɔ̃ ɖeka dzi le kasino gã aɖe me le Reno: fefewɔla 139 siwo ɖo bɛt 24,131. Le bɛt sɔsɔewobɛtBɛt sɔsɔeDzĩ/yibɔ, madzemadze/dzedze, gã/sue. Xexlẽdzesi 18, fetu 1:1.Xlẽe blibo → dzi la, fefewɔlawo ma ɖe akpa eve kloe sɔsɔe: ame aɖewo dzea ɖoɖo kpuiwo yome eye bubuwo tsia tre ɖe wo ŋu. Le ƒomevi ɖeka atɔ̃ ɖe wo nɔewo yome megbe la, wotre ɖe ɖoɖo la ŋu, eye le ade alo wu megbe la, wo ƒe bɛtwo ƒe 85% nɔ akpa kemɛ dzi. Fefewɔla mawo ke ɖe asi xɔdzo fia le wo ɖokui ŋu: le dziɖuɖu le xexlẽdzesiwo dzi megbe la, woxɔ xexlẽdzesi 13.6 le trɔtrɔ si kplɔe ɖo me le titina me, tsɔ sɔ kple 9.2 le gabubu megbe. Wo ƒe ʋuafɔ la meɖe akpaɖeɖe ƒe dzesi aɖeke fia o, eya ta nu siawo dometɔ aɖeke metrɔ nu si wo dometɔ aɖeke ate ŋu akpɔ mɔ na o.
Le kasino godo
Hehe ma ke dzena le afi siwo woɖoa nyametso ŋutɔŋutɔwo le. Clotfelter kple Cook (1993) kpɔ Maryland ƒe gbe sia gbe xexlẽdzesifefe gbɔ: ga si woɖo bɛt ɖe xexlẽdzesi aɖe dzi ɖi kabakaba esi wòdo ko, eye wòxɔ ɣleti geɖe hafi wògbugbɔ ɖo eƒe teƒe, togbɔ be xexlẽdzesiɖeɖe la meɖoa ŋku nu aɖeke dzi o hã. Chen, Moskowitz kple Shue (2016) kpɔe le aɖaŋudɔwɔlawo gbɔ. Amerika ƒe sedrɔ̃la siwo drɔ̃a sitsoƒedidi ƒe nyawo ate ŋu agbe nya aɖe wu va se ɖe akpa 3.3 le alafa me ne wolɔ̃ ɖe esi do ŋgɔ la dzi. Baseball ƒe ʋɔnudrɔ̃lawo gbena strike yɔyɔ wu akpa 1.5 le alafa me le esi woyɔ ɖeka megbe, eye wòwu zi eve ema le bɔlƒoƒo siwo te ɖe nɔewo ŋu me. Le dodokpɔ aɖe si wowɔ le dɔwɔƒe le gadzidzidɔwɔla siwo woxe fe ɖeka ɖaa na me la, wotrɔ nyametsotsowo ƒe va se ɖe 9% le mɔ sia nu. Nyawo va le nudzɔdzɔ ƒe ɖoɖo nu, eya ta nyametsotso mamlɛtɔ megblɔ naneke tso esi kplɔe ɖo ŋu o, abe alesi trɔtrɔ mamlɛtɔ megblɔa naneke tso esi kplɔe ɖo ŋu o ene.
Gafefela ƒe susu me vodada tɔtrɔ
Nunyala Ian Hacking (1987) na ŋkɔ ƒomevi etɔ̃lia aɖe. Ame aɖe ge ɖe xɔ aɖe me, kpɔ be dice eve dze ade eve, eye wòbu be ele be woƒu wo zi geɖe xoxo. Ƒuƒu ɖe sia ɖe ƒe mɔnukpɔkpɔ be wòanye ade eve sɔ, eɖanye fiẽ ma ƒe gbãtɔ alo akpe ɖekelia o, eya ta nu si wòkpɔ la megblɔ alesi fefe la xɔ ɣeyiɣi ŋu naneke o. Le roulette me la, enye fefewɔla si va ɖaŋɖi aɖe si ɖe dzĩ enyi fia gbɔ eye wòbu be ele be wotrɔ kplɔ̃ la gaƒoƒo geɖe hafi wo dze. Susu me vodada si bɔ la tsɔa esi va yi xlẽna ɖe trɔtrɔ si kplɔe ɖo me; esia ya tsɔa nu si medzɔna zi geɖe o xlẽna ɖe esi va yi si ame aɖeke mekpɔ o me.
Susumenunyala aɖe si xɔe se
Nunyala aɖewo ʋli susu me vodada sia ta kpɔ. Germania susumenunyala Karl Marbe to vidzidziwo ƒe agbalẽ ene me, siwo dometɔ ɖe sia ɖe me vidzidzi 49,152 le, ekpɔ be ŋutsuvi alo nyɔnuvi ƒe ɖoɖo ɖe wo nɔewo yome si didi wu nye 17, eye wòbu be ɖoɖo didiwo medzɔna zi geɖe abe alesi dzɔdzɔme ɖe mɔ ɖo ene o, ale be ɖoɖo aɖe nana emetsonu kemɛ nadzɔ bɔbɔe wu. Dzɔdzɔme ko gblɔ nu bubu: le vidzidzi 196,608 me la, ɖoɖo 17 alo wu dzena abe zi ene le atɔ̃ me ene. Marbe kpɔ alesi nudzɔdzɔ ƒe ɖoɖo dzena pɛpɛpɛ. Epstein (2013) gagblɔ nya sia; “Ɖoɖo ɖe wo nɔewo yome ƒe mɔnukpɔkpɔ le roulette me” ɖe roulette tɔ fia.
Afi si susu me vodada la meku ɖo o
Ne ʋuafɔ la ɖea akpa le eƒe ŋutilã me la, trɔtrɔ siwo va yi aɖe nu fia, elabena woanye kpeɖodzi le dowo ŋu, menye le dzɔgbenyui ŋu o. Ema nye Numekuƒe la ƒe nyati, eye ehiã trɔtrɔ akpe geɖe tso ʋuafɔ ɖeka si wonya me hafi wòagblɔ nane. Na dzĩ ewo ɖe wo nɔewo yome le ʋuafɔ si womenya o dzi la, akpaɖeɖe ƒe gɔmeɖeɖe mate ŋu anye nyateƒe abe dzɔdzɔme tɔ ene kura o.
Nyabiasewo
Ao. Eku ɖe nudzɔdzɔ ɖe sia ɖe si le eɖokui si eye wògbugbɔna dzɔna ŋu: dice, gaku, lotto ƒe xexlẽdzesiwo.
Akpawo agogo ɖe wo nɔewo ŋu. Wò emetsonu agakpɔtɔ anye abe ga si nèɖo bɛt ɖo ƒe −2.70% ene.
Titina ƒe se aɖeke meli o. Xexlẽdzesi gãwo ƒe se ye li, eye ewɔa dɔ to tsitsi me.
Modzaka kple akɔntabubu
Te wo kpɔ le ɖokuiwò si gbã. Wobla ŋuɖoɖo ɖe sia ɖe ɖe go; ʋui ne èsɔ gbe.
Le ga dada zi 10 megbe la, ga la ɖe ta 7 kple megbe 3 fia. Le dada 1,000 megbe la, eɖe ta 517 kple megbe 483 fia. Ɖe megbewo ɖo ta ŋua?
Fia ŋuɖoɖo la
Ŋuɖoɖo Ao. Vovototo la dzi tso 4 va ɖo 34. Ta kple megbe ƒe sɔsɔme koe te ɖe sɔsɔenyenye ŋu wu.
Ta kple megbe ƒe sɔsɔme ɖi tso 7/3, abe 2.33 ene, va 517/483, abe 1.07 ene. Ema nye xexlẽdzesi gãwo ƒe seakɔntabubuXexlẽdzesi gãwo ƒe seEmetsonu siwo le wo ɖokui si ƒe titina gogona ɖe asixɔxɔ si wokpɔ mɔ na ŋu esime dodokpɔwo ƒe xexlẽme le dzidzim ɖe edzi.Xlẽe blibo → le dɔ wɔm.
Vovototo si le wo dome la dzi, tso 4 va ɖo 34. Le ga dzɔdzɔe me la, vovototo abe 30 ene le dada 1,000 megbe nye nu ɖaa: vovototo si dzɔna zi geɖe dzina ɖe edzi abe dada ƒe xexlẽme ƒe square root ene, gake sɔsɔme la tenɔa ɖe 1 ŋu.
Naneke mehe megbewo gbɔ o. Ta siwo sɔ gbɔ le gɔmedzedzea me la, dada 990 siwo kplɔe ɖo la fia wo ɖe eme; womeɖɔ wo ɖo o.
Da ga zi ene eye nàkpɔ dada siwo kplɔ ta ɖo enumake ko. Wo dometɔ ƒe akpa kae nye ta? Wɔe na ɖoɖo 16 siwo ate ŋu adzɔ dometɔ ɖe sia ɖe eye nàdi akpa mawo ƒe titina. Ɖe enye 50%a?
Fia ŋuɖoɖo la
Ŋuɖoɖo Ao. Enye 17/42, abe 40.5% ene. Ne èkpɔe le mɔ sia nu la, ga dzɔdzɔe dze abe ɖe wòfa le ta megbe ene.
Ŋlɔ ɖoɖo 16 la. Wo dometɔ eve, TTTT kple TTTH, me ta aɖeke mele le dada etɔ̃ gbãtɔwo me o, eya ta naneke mekplɔ ta ɖo o; esia gblẽ 14 ɖi.
Le wo dometɔ ɖe sia ɖe me la, tsɔ dada siwo kplɔ ta ɖo eye nàdi akpa si nye ta. HHHH naa 3 le 3 me. HHHT naa 2 le 3 me. HTHT naa 0 le 2 me. Ne èto 14awo katã me: ɖoɖo ade naa 0, ene naa 1/2, ɖeka naa 2/3 eye etɔ̃ naa 1 (HHHH, THHH kple TTHH).
Tsɔ akpaawo kpe ɖe wo nɔewo ŋu: 4 × 1/2 + 2/3 + 3 = 17/3. Ma ɖe 14 dzi: 17/42 ≈ 40.5%.
Dada aɖeke mekpɔa megbe o; wo dometɔ ɖe sia ɖe nye 50–50. Tɔtrɔ la tso titina didi ɖoɖo ɖeka ɖeka: ɖoɖo si me ta geɖe le la si dada geɖe le be nàkpɔ gake woxlẽnɛ zi ɖeka, abe ɖoɖo si me ta ɖeka ko le ene. Miller kple Sanjurjo (2018) ɖee fia be ƒe 1985 ƒe asi xɔdzo ŋuti numekuku la dzidze eƒe basketball fefewɔlawo le mɔ sia nu, eya ta fefewɔla siwo dze abe womeɖoa ɖe wo nɔewo yome wu nudzɔdzɔ o ene la ɖoa ɖe wo nɔewo yome wu vie le nyateƒe me.
Nukokoe sue
Tsitsi, menye ɖɔɖɔɖo o. Nu aɖeke mele ʋuafɔ la ŋu o.
Nunyaƒewo
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Croson, R. & Sundali, J. “The gambler’s fallacy and the hot hand: empirical data from casinos.”
- Chen, D. L., Moskowitz, T. J. & Shue, K. “Decision making under the gambler’s fallacy: evidence from asylum judges, loan officers, and baseball umpires.”
- Clotfelter, C. T. & Cook, P. J. “The ‘gambler’s fallacy’ in lottery play.”
- Gilovich, T., Vallone, R. & Tversky, A. “The hot hand in basketball: on the misperception of random sequences.”
- Miller, J. B. & Sanjurjo, A. “Surprised by the hot hand fallacy? A truth in the law of small numbers.”
- Hacking, I. “The inverse gambler’s fallacy: the argument from design. The anthropic principle applied to Wheeler universes.”