Kala-duwanaansho
Sababta hal lambar iyo sharad casaan ah oo leh isku khasaaraha la filayoxisaabKhasaaraha la filayoQiimaha la filayo oo lagu dhuftay wadarta lacagta la sharadsaday; celceliska lacagta lagu khasaaro fadhi ama muddo.Akhri dhammaan → ay u dareemaan sidii laba ciyaarood oo kala duwan.
Kala-duwanaanshuhu wuxuu cabbiraa inta ay natiijooyinku ku kala firdhaan qiimaha la filayo agtiisa. Unug kasta oo la sharadsado waa qiyaastii 34 hal lambar iyo qiyaastii 1 casaan.
Qaaciddada hal sharad
Sharad bixiya W ilaa 1 oo leh itimaalxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → p, natiijada unuglacagUnugSharadka saldhigga ah ee nidaam ama ciyaartoy ku shaqeeyo. Kordhinnada waxaa lagu sharxaa unugyo si ay ugu shaqeeyaan miis kasta.Akhri dhammaan → kasta waa +W itimaal p iyo −1 itimaal 1 − p. Qiimaha la filayoxisaabQiimaha la filayoCelceliska natiijada sharad kasta muddada dheer. −1/37 ee sharadka sharad kasta oo Yurub caadi ah.Akhri dhammaan → waa pW − (1 − p) = −1/37. Kala-duwanaanshuhuxisaabKala-duwanaanshoCabbir muujinaya sida ballaaran ee natiijooyinku ugu kala firdhsan yihiin qiimaha la filayo agtiisa. Sare hal lambar, hoose sharadyada lacag isle'eg.Akhri dhammaan → waa E[X²] − EV² = pW² + (1 − p) − (1/37)². Hal lambarsharadHal lambarHal lambar oo keliya, wuxuu bixiyaa 35:1.Akhri dhammaan →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. CasaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Waxa ay u tahay fadhi
Kala-duwanaanshuhu wuxuu isugu darmaa wareegyo madaxbannaanxisaabWareegyo madaxbannaanWareeg kastaa wuxuu leeyahay isla itimaallada iyada oo aan loo eegin taariikhda. Saldhigga xisaab kasta oo goobtan ku jirta.Akhri dhammaan →, sidaas darteed N wareeg oo sharad go'an ah kala-duwanaanshaha wadartu waa N × sharad² × σ², leexashada caadiga ahnaxisaabLeexashada caadiga ahXididka labajibbaarka ee kala-duwanaanshaha; masaafada caadiga ah ee natiijo ay u jirto qiimaha la filayo.Akhri dhammaan → waa σ × sharad × √N. 100 wareeg oo $10 ah: leexashada caadiga ahi waa qiyaastii $584 hal lambar iyo $100 casaan, iyadoo labadaba la filayo isla −$27. Hal ciyaartoy wuxuu arkaa natiijooyin boqollaal isku rogrogaya; kan kale wuxuu arkaa hoos-u-socod tartiib ah. Labaduba waxay bixinayaan isku qiimo.
Kala-duwanaanshaha iyo nidaamyada
KordhinistaraatiijiKordhinXeer kasta oo beddela sharadka iyadoo lagu salaynayo natiijooyinkii hore. Kordhinnada tabanka ah waxay kor u qaadaan khasaare kadib, kuwa togan guul kadib.Akhri dhammaan → ma beddesho EV-ga unug kasta oo la sharadsado laakiin waxay beddeshaa qadarka la sharadsado iyo qaabka qaybinta labadaba. MartingaleistaraatiijiMartingaleKordhin labanlaabta sharadka khasaare kasta kadib. Eeg qaybta Istaraatiijiyadda si aad u ogaato waxa ay qabato iyo waxa aysan qaban.Akhri dhammaan → wuxuu hoos u dhigaa kala-duwanaanshaha fadhiyada intooda badan (guulo yaryar oo badan) wuxuuna ku daraa dabo buuran (khasaaraha weyn ee dhif ah); kala-duwanaanshaha guud ee fadhiyada oo dhan wuu ka sarreeyaa kan sharadka joogtada ahistaraatiijiSharad joogto ahIsla qadarka la sharadsado wareeg kasta. Saldhigga kordhin kasta lala barbardhigo.Akhri dhammaan → dabadaas darteed. ParoliistaraatiijiParoliKordhin togan: labanlaab guul kadib, dib u bilow khasaare kadib ama saddex guulood oo isku xigta kadib. Sidoo kale: Martingale rogan.Akhri dhammaan → wuxuu sameeyaa liddiga. Dooridda nidaam waa dooridda qaab kala-duwanaansho; celceliska kuma jiro liiska.
- p10 −$500
- p25 −$500
- dhexdhexaad −$500
- p75 +$40
- p90 +$1,120
Istaraatiijiyadda Sharadka Joogtada ah ee RouletteIstaraatiijiyadda Paroli ee Roulette (Martingale Rogan)
Sababta ay ciyaartoyga muhiim ugu tahay
Kala-duwanaanshaha ayaa ka dhiga fadhiyada gaagaaban kuwo aan la saadaalin karin, kuwa dheerna kuwo la saadaalin karo. σ = $100 iyo EV = −$27 100 wareeg gudahood, faa'iidadu waa rubuc buuqa, fadhi faa'iido ku dhammaadaana waa caadi. 10,000 wareeg gudahood EV-gu waa −$2,700, σ-na waa $1,000; faa'iidadu hadda waa ku dhawaad saddex jeer buuqa, taxane guuleed-na waa dhacdo saddex-sigma ah. Kala-duwanaanshuhu waa saaxiibka ciyaartoyga muddada gaaban, kasiinadana muddada dheer.
Kala-duwanaanshaha isku-dhafka
Dhowr sharad oo isla wareeg ah, natiijooyinku way isku xiran yihiin (soo baxa 17 sidoo kale waa soo bax madowsharadMadowSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee madow. Faransiis: noir.Akhri dhammaan → iyo dersinkasharadDersin1–12, 13–24 ama 25–36, wuxuu bixiyaa 2:1.Akhri dhammaan → labaad), sidaas darteed kala-duwanaanshuhu si fudud isuma darmaan. Qalabka Dhisaha Sharadka wuxuu xisaabiyaa qaybinta saxda ah ee koox kasta oo chipslacagChipCalaamad u taagan qadar go'an, oo la dul dhigo shaxda sharadka si sharad loo sameeyo. Sidoo kale: check.Akhri dhammaan → ah isagoo tiriya dhammaan 37-ka natiijo, taas oo ah habka keliya ee saxda ah.
Qaacido
Su'aalo
Maya. Sharad kastaa wuxuu leeyahay isku qiimaha la filayo. Kala-duwanaansho sare wuxuu ka dhigan yahay isrogrog ballaaran oo agtiisa ah.
Sharadyada lacag isle'egsharadSharad lacag isle'eg ahCasaan/madow, kisi/dhaban, sare/hoose. 18 lambar, wuxuu bixiyaa 1:1.Akhri dhammaan →, σ ≈ 1 unug kasta. Ka sii hooseeya la partagexeerLa partageXeer Faransiis ah: marka eberku soo baxo, kala badh sharad lacag isle'eg ah ayaa la soo celiyaa. Wuxuu faa'iidada kasiinada sharadyadaas u dhimaa 1.35%.Akhri dhammaan →, taas oo sidoo kale hagaajisa celceliska.
Faa'iidada la filayo waa isku mid doollar kasta; kala-duwanaanshuhu wuxuu saameeyaa oo keliya inta dakhliga kasiinadu kala-jiiran yahay, kasiinaduna waxay leedahay kumanaan ciyaartoy oo siman.
Madadaalo Xisaabeed
Marka hore adigu isku day. Xal kasta waa qarsoon yahay; fur marka aad diyaar u tahay.
Laba ciyaartoy mid kastaa wuxuu sharadsadaa $1 wareeggiiba 100 wareeg giraangir Yurub ah, mid had iyo jeer casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan →, kan kalena had iyo jeer 17. Kee ayaa itimaal badan inuu faa'iido ku jiro dhammaadka?
Muuji xalka
Jawaab Ciyaartoyga 17: 50.9%, marka loo eego 35.5% casaanka. Labaduba waxay lumiyaan $2.70 celcelis ahaan.
Casaan: ciyaartoygu faa'iido ayuu ku jiraa 51 guul ama ka badan 100-kiiba, mid kastaa itimaalxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → 18/37 ah. Qaybinta binomial waxay bixisaa 35.5%, si sax ah 50 guul, oo ah isku-dheelli, waa 7.7% kale.
Lambarka 17: guul kastaa waxay soo celisaa $36, sidaa darteed laba guul (−$28) kuma filna, saddexna (+$8) way ku filan yihiin. Fursadda saddex ku dhac ama ka badan 100 wareeg oo 1/37 ah waa 50.9%.
Ciyaartoyga hal lambar ayaa inta badan faa'iido ku jira, laakiin natiijooyinku waa kuwo kala-gooni ah: hal ku dhac oo ka badan ama ka yar wuxuu natiijada dhaqaajiyaa $36, ciyaartoyda khasaaraha ku jirtana badanaa way ka sii fog yihiin. Bollman (2024) wuxuu bixiyaa tirooyinka Mareykanka, 26.5% iyo 49.2%.
Kaftan yar
Isku khasaaraha la filayo. Mid ka mid ah ayaa kuu sheegaya si qaylo leh.
Ilaha
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.