Xisaabta Roulette · La dabaqay · 13 daqiiqo

Khatarta Burburka

Q: Kordhin ma hoos u dhigtaa khatarta burburka?

Martingale wuu hoos u dhigaa fadhiyada gaagaaban wuxuuna si weyn u kordhiyaa kuwa dhaadheer. Sharad joogto ah oo unug ka weyn leh ayaa ah habka daacadda ah ee lagu hoos u dhigo.

Itimaalka inaad khasaarto raasamaalka ciyaartaada oo dhan ka hor inta aadan gaarin bartilmaameed.

Jawaab gaaban

Sharadyada lacag isle'eg, khatarta burburku waxay raacdaa qaaciddada gambler’s ruin. Raasamaal $500 ah, sharadyo $10 ah iyo bartilmaameed $600 ah, waxaad gaartaa bartilmaameedka qiyaastii 57% marka, inta kalena waad burburtaa.

qaacidda

gambler’s ruin

p (lacag isle'eg)

18/37

q/p

1.0556

natiijada ugu da'da weyn

Pascal–Fermat, 1656

Su'aasha

Waxaad haysataa a unuglacagUnugSharadka saldhigga ah ee nidaam ama ciyaartoy ku shaqeeyo. Kordhinnada waxaa lagu sharxaa unugyo si ay ugu shaqeeyaan miis kasta.Akhri dhammaan → oo raasamaalka ciyaartalacagRaasamaalka ciyaartaWadarta lacagta loo qoondeeyay ciyaarta. Maaraynta raasamaalka ciyaarta waa go'aaminta inta laga khatarinayo sharad kasta iyo fadhi kasta.Akhri dhammaan → ah waxaadna doonaysaa inaad gaarto a + b unug, adigoo sharadsanaya hal unug mar kasta sharad lacag isle'eg ahsharadSharad lacag isle'eg ahCasaan/madow, kisi/dhaban, sare/hoose. 18 lambar, wuxuu bixiyaa 1:1.Akhri dhammaan → oo leh itimaalxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → guul p = 18/37 iyo itimaal khasaare q = 19/37. Waa maxay fursadda aad bartilmaameedka ku gaarto ka hor inta aadan eber gaarin? Jawaabta waxaa xisaabiyay Pascal, Fermat iyo Huygens 1650-meeyadii, waana mid ka mid ah natiijooyinka ugu da'da weyn ee itimaalka.

Blaise Pascal: Sheekada Giraangirta Roulette

Qaaciddada gambler’s ruin

P(gaarid bartilmaameed) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ). Khatarta burburkuxisaabKhatarta burburkaItimaalka in la khasaaro raasamaalka ciyaarta oo dhan ka hor inta aan la gaarin bartilmaameed ama tiro wareeg.Akhri dhammaan → waa hal laga jaray taas. q/p = 19/18 ≈ 1.0556, saamigu wuxuu u koraa si jibbaar ah tirada unugyada, sidaas darteed qaaciddadu si xun bay u ciqaabtaa unugyada yaryar: inta sharad ee loo baahdo si bartilmaameedka loo gaaro ay bataan, ayaa inta jeer ee cashuurta 2.70% jidka lagu bixiyo bataan.

raasamaalunugbartilmaameedsharadyada ilaa bartilmaameedkap(gaarid bartilmaameed)khatarta burburka

$500$10$60010≈ 57%≈ 43%

$500$50$6002≈ 79%≈ 21%

$500$10$1,00050≈ 6%≈ 94%

$500$100$1,0005≈ 43%≈ 57%

$500$500$1,000148.6%51.4%

$100$10$20010≈ 37%≈ 63%

Sharadyo lacag isle'eg, sharad joogto ah, la partage la'aan. Xisaabiyaha Khatarta Burburka ayaa xisaabta u sameeya tirooyin kasta.

Akhriskeeda

Unugyada yaryar way dhibaan. Isku dayga in $500 la labanlaabo sharadyo $10 ah wuxuu guuleystaa 6% marka; hal sharad $500 ah wuxuu guuleystaa 48.6% marka. Ciyaarta geesinimada leh, sharadyo yar oo waaweyn, waxay kordhisaa fursadda gaaridda bartilmaameed ciyaar qiimaheeda la filayo taban yahay, sababtoo ah waxay yareysaa inta jeer ee faa'iidada kasiinada la dabaqo. Sidoo kale waxay kordhisaa kala-duwanaanshahaxisaabKala-duwanaanshoCabbir muujinaya sida ballaaran ee natiijooyinku ugu kala firdhsan yihiin qiimaha la filayo agtiisa. Sare hal lambar, hoose sharadyada lacag isle'eg.Akhri dhammaan → waxa kugu dhaca, fiidkana si dhakhso ah bay u dhammeysaa. Aragtidan waxaa loo yaqaan “bold play is optimal” (ciyaarta geesinimadu waa tan ugu fiican), waxaana caddeeyay Dubins iyo Savage 1965.

Fursadda in $500 loo beddelo $1,000 casaan%

hal sharad $500 ah

48.6%

sharadyo $100 ah

≈ 43%

sharadyo $50 ah

≈ 37%

sharadyo $20 ah

≈ 21%

sharadyo $10 ah

≈ 6%

sharadyo $5 ah

≈ 0.5%

024.3048.6%

Inta sharad ee loo baahdo ay bataan, ayaa inta jeer ee faa'iidada kasiinada la bixiyo bataan. Ciyaarta cabsida lehi waa qaali.

Meesha dhibaatadu ka bilaabatay

Su'aashu way ka da' weyn tahay roulette. 1656 Pascal wuxuu Fermat u dhigay hal-xiraale: laba ciyaartoy ayaa tuura saddex laadh, mid kastaa wuxuu ku bilaabaa 12 calaamadood; tuuris 11 ah waxay calaamad u dhaqaajisaa hal dhinac, tuuris 14 ahna dhinaca kale. Labaduba way xalliyeen, Huygens, oo ka maqlay warqad uu ka helay xisaabyahan Pierre de Carcavi, wuxuu daabacay 1657 isagoo ah masalada shanaad ee buuggii ugu horreeyay ee itimaalka, jawaabta la socoto caddeyn la'aan. Kow iyo toban waxaa lagu tuuri karaa 27 qaab, afar iyo tobanna 15 oo keliya, sidaas darteed calaamad kastaa waxay u dhaqaaqdaa dhinaca ciyaartoyga koowaad 9 jeer 14-kiiba, qaaciddada kore, oo leh 12 calaamadood mid kasta, waxay ka dhigtaa qiyaastii 1,157 jeer ka itimaal badan inuu wax walba ku guuleysto intii uu wax walba khasaari lahaa. Faa'iido 2.70% ah aad bay uga yar tahay, laakiin isla qaaciddadaas ayaa muujinaysa waxa ay samayso sharadyo badan gudahood.

Hal-xiraalaha Pascal, tuuris kasta oo saddex laadh ah waxay calaamad u dhaqaajisaa ciyaartoyda dhexdooda.

Sharad geesinimo leh oo dhab ah

Abriil 2004 Ashley Revell, nin dhallinyaro Ingiriis ah, wuxuu iibiyay ku dhawaad wax kasta oo uu lahaa, oo ay ku jiraan dharkiisa, wuxuuna $135,300 u qaatay Plaza ee Las Vegas. Sharadyo yaryar kadib qadarka oo dhan wuxuu dhigay casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan →, hal mar. KubbadduqalabKubbadKubbadda yar ee lagu tuuro jidka iyada oo ka soo horjeedda rotor-ka. Kubbadaha casriga ah waa ivorine ama Teflon, 18–21 mm.Akhri dhammaan → waxay ku dhacday casaan 7 wuxuuna kala baxay $270,600. Giraangir laba-ebergiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan → ah, wareeggaas keliya wuxuu ahaa fursad 47.37% ah wuxuuna celcelis ahaan ku kacay $7,121, faa'iidada 5.26% ee hal sharad. Haddii loo kala qaybin lahaa sharadyo $10 ah, isla bartilmaameedku wuxuu ahaan lahaa mid ku dhawaad rajo la'aan ah. Ciyaarta geesinimadu sharadka ma wanaajiso; waxay ka dhigtaa mid sida ugu gaaban.

Raasamaalka oo dhan ee Ashley Revell wuxuu saaran yahay hal wareeg oo giraangir laba-eber ah.

Khatarta burburka bartilmaameed la'aan

Haddii aad si fudud u ciyaarto ilaa aad burburto ama aad joojiso N wareeg kadib, su'aashu waxay noqonaysaa “waa maxay fursadda raasamaalkaygu eber taabto N wareeg gudahood?”. Ma jirto qaab xiran oo N guud ah laakiin jilayaasha goobtan ayaa xisaabiya: raasamaal $500 ah oo $10 casaan ah ku dhawaad weligiis ma burburo 100 wareeg (ka yar 1%), wuxuu burburaa qiyaastii 9% marka 500 wareeg, qiyaastii 95% markana 5,000. Xeer joojin la'aan itimaalku wuxuu u janjeeraa 100%, taas oo ah nooca muddada dheer ee faa'iidada kasiinadaxisaabFaa'iidada kasiinadaQaybta sharad kasta ee kasiinadu celcelis ahaan hayso: 2.70% roulette Yurub.Akhri dhammaan →.

Toban fadhi, raasamaal $500, $25 casaan, 200 wareegnatiijada iyo bilowga

1,000 fadhi × 500 wareeg · violet p10/p25/p75/p90, buluug khafiif ah dhexdhexaad, 81 muunadood oo khafiif ah · dul mari shaxda si aad u aragto qaybaha wareeg kasta

p10 −$500
p25 −$500
dhexdhexaad −$500
p75 +$0
p90 +$350

1,000 fadhi × 500 wareeg · dhidibka y waxaa lagu xaddiday boqolleyda 1aad–99aad (xaddadka −$500 ilaa +$1,500) · 500 wareeg · $25 aasaasi · lacag isle'eg

Xariiqyada taabta hoosta waa burbureen. Unug ka yar, way sii dheeraan lahaayeen waxayna ku dhammaan lahaayeen isla meeshaas.

Isku-soo-dhowaanshaha Muddada Dheer: Sharciga Tirooyinka Waaweyn ee Roulette

Intee le'eg, iyo intee horey

Laba natiijo oo kale oo qadiimi ah ayaa ka jawaaba su'aalo ay ciyaartoydu dhab ahaan weydiiyaan. Bartilmaameed la'aan, sharadyo joogto ah oo lacag isle'eg ahi waxay celcelis ahaan socdaan 37 wareeg unug kasta oo raasamaal ah giraangir Yurub ah iyo 19 mid Mareykan ah, sababtoo ah wareeg kastaa wuxuu celcelis ahaan qaataa 1/37 unug (1/19 giraangir Mareykan ah): 100 unug waxay celcelis ahaan socdaan 3,700 wareeg, inkastoo kala badh fadhiyada noocaas ahi ay ku dhammaadaan 3,134 gudahood (eeg Dhererka Fadhiga iyo Qiimihiisa). Raasamaalku ha le'ekaado inta uu le'ekaado, fursadda giraangir Yurub ah ee inaad weligaa k unug ka horreyso waa (18/19)ᵏ. Taasi waa 95% hal unug iyo 58% toban, laakiin ma jiro raasamaal, ha qoto dheeraado inta uu doono, oo siiya fursad siman inaad weligaa 13 unug ka sarreyso; giraangir Mareykan ah fursaddu waa (9/10)ᵏ waxayna ka hoos dhacdaa kala badh 7 unug.

unugyo horey, waqti kastaYurubMareykan

194.7%90.0%

576.3%59.0%

1058.2%34.9%

1349.5%25.4%

2033.9%12.2%

506.7%0.5%

1000.45%0.003%

Sharadyo lacag isle'eg, sharad joogto ah, raasamaal ku filan oo aan weligiis dhammaan. Fursaddu waa (18/19)ᵏ giraangir hal-eber ah iyo (9/10)ᵏ mid laba-eber ah.

Dhererka Fadhiga iyo Qiimihiisa Giraangirta iyo Xeerarka Roulette Mareykan

Raasamaal fursad konton-konton ah

Su'aasha rog: intee baad u baahan tahay inaad keento si aad ugu yaraan u hesho fursad konton-konton ah oo aad ku guuleysato qadar la cayimay ka hor inta aadan wax walba khasaarin? Guul yar, wax badan maya. Mid ka weyn, raasamaalka loo baahan yahay si xoog ah buu u koraa, bar kadibna raasamaal kasta kuma filna, sababtoo ah xitaa mid aan dhammaad lahayn wuxuu siiyaa fursad ka yar konton-konton inaad weligaa intaas horey u gaarto. Taylor (2021) si kale ayuu u dhigaa: giraangir Mareykan ah, si aad u hesho fursad konton-konton ah oo aad ku gaarto 100 unug waa inaad ku bilowdaa 94, adigoo khatar gelinaya 94 si aad u guuleysato 6. Giraangir Yurub ah waxaad u baahan lahayd 88.

si loogu guuleystoYurubMareykan

1 unug22

2 unug33

3 unug45

4 unug68

5 unug712

6 unug921

7 unug12raasamaal kasta kuma filna

8 unug15raasamaal kasta kuma filna

10 unug24raasamaal kasta kuma filna

12 unug46raasamaal kasta kuma filna

13 unug ama ka badanraasamaal kasta kuma filnaraasamaal kasta kuma filna

Raasamaalka ugu yar, unugyo ahaan, ee siiya ugu yaraan fursad konton-konton ah oo lagu guuleysto qadarka ka hor inta aan raasamaalka la khasaarin, sharadyo joogto ah oo lacag isle'eg ah. Xisaabtayada ka timid qaaciddada kore.

Casharka dhabta ah

Go'aanso waxa aad isku dayayso inaad samayso. Haddii hadafku yahay guul gaar ah, sharadso wax badan oo yar. Haddii hadafku yahay fiid dheer, sharadso wax yar oo aqbal in faa'iidada kasiinadu qaadan doonto 2.70%-keeda wadarta sharadyadalacagWadarta sharadyadaWadarta lacagta la sharadsaday fadhi ama muddo, oo lagu tiriyo guulaha dib loo sharadsaday. Sidoo kale: handle, action.Akhri dhammaan → ee weyn. Haddii hadafku labadaba yahay, wax baa ka tanaasulaya, badanaana waa bartilmaameedka.

Qaacido

P(bartilmaameed) = (1 − (q/p)ᵃ) / (1 − (q/p)ᵃ⁺ᵇ)

khatarta burburka = 1 − P(bartilmaameed)

q/p = 19/18 lacag isle'eg

celceliska wareegyada ilaa burbur, bartilmaameed la'aan = 37 × unugyo

P(weligaa k unug horey) = (18/19)ᵏ

Su'aalo

Kordhin ma hoos u dhigtaa khatarta burburka?

MartingaleistaraatiijiMartingaleKordhin labanlaabta sharadka khasaare kasta kadib. Eeg qaybta Istaraatiijiyadda si aad u ogaato waxa ay qabato iyo waxa aysan qaban.Akhri dhammaan → wuu hoos u dhigaa fadhiyada gaagaaban wuxuuna si weyn u kordhiyaa kuwa dhaadheer. Sharad joogto ahistaraatiijiSharad joogto ahIsla qadarka la sharadsado wareeg kasta. Saldhigga kordhin kasta lala barbardhigo.Akhri dhammaan → oo unug ka weyn leh ayaa ah habka daacadda ah ee lagu hoos u dhigo.

Ka warran sharadyada hal lambar?

Qaaciddada kore waa lacag isle'eg. Sharadyada kala-duwanaanshaha sare leh burburku wuu ka itimaal badan yahay sharadyada yaryar, bartilmaameedkana waxaa lagu gaaraa si kala-jiiran; isticmaal xisaabiyaha.

Maxay q/p u tahay tirada ugu muhiimsan?

Tallaabo kasta oo xagga bartilmaameedka ah waa xoogaa ka itimaal yar tallaabo kasta oo xagga burburka ah; saamigu wuxuu isku dhufmaa tirada tallaabooyinka.

Madadaalo Xisaabeed

Marka hore adigu isku day. Xal kasta waa qarsoon yahay; fur marka aad diyaar u tahay.

Waxaad haysataa $100 waxaadna rabtaa $1,000, adigoo ku sharadsanaya casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → oo keliya. Qorshe kowaad: sharadso $1 markiiba. Qorshe labaad: sharadso wax kasta oo aad haysato ilaa aad dhaafto $500, kadibna inta ku filan oo keliya inaad gaarto $1,000. Qorshahee baa ka wanaagsan, oo intee le'eg?
Muuji xalka
Jawaab Qorshe labaad, si fog. Wuxuu gaaraa $1,000 qiyaastii 9.0% waqtiga, oo u dhow 10%-ka caddaaladda ah. Qorshe kowaad wuxuu guulaystaa qiyaastii 7 jeer 10²².
Ciyaar caddaalad ahxisaabCiyaar caddaalad ahCiyaar aan dhinacna faa'iido lahayn: sharad kastaa wuxuu leeyahay qiime la filayo oo eber ah.Akhri dhammaan → waxaad $1,000 ka gaari lahayd $100 hal mar tobankii wax kasta oo aad samayso, sababtoo ah qiimaha celceliska ee lacagtaadu wuxuu ku sii jiraa $100.
Faa'iidada kasiinadu waxay qaadataa 2.70% sharad kasta, sidaa darteed inta yar ee aad guud ahaan sharadsato, ayaad u sii dhowaanaysaa hal tobankii. Qorshe labaad arrinta wuxuu ku go'aamiyaa dhowr sharad: $100 waxay noqotaa $200, $400, $800, kadibna $200 ayaa ku filan. Wuxuu guulaystaa qiyaastii 9.0% waqtiga. Qorshe kowaad wuxuu qaataa kumanaan sharad ka hor inta aan socodku dhammaan, faa'iidada kasiinaduna, oo ku yar mid kasta, waxay isu geysaa burbur ku dhow hubaal.
Tani waa natiijada Dubins–Savage qaabkeeda ugu fudud (Epstein, 2013): ciyaar u roon kasiinada, sharadso inta aad u baahan tahay, jeerar intii suurtagal ah u yar.
Waxaad haysataa $500 waxaadna rabtaa $1,000, adigoo joojinaya isla markaad hesho. Waxaad dooranaysaa hal nooc oo sharad ah waxaadna ku celcelinaysaa ilaa uu hal mar guulaysto ama lacagtu dhammaato. Noocee baa siiya fursadda ugu fiican?
Muuji xalka
Jawaab Hal sharad $500 ah oo casaan ah: 48.6%. Qorshe kasta oo lacagta ku kala fidiya sharadyo yaryar wuu ka liitaa.
Dooro sharad kasta si hal guul ay ku filnaato: $30 hal lambarsharadHal lambarHal lambar oo keliya, wuxuu bixiyaa 35:1.Akhri dhammaan → ah wuxuu helaa $1,050, $60 splitsharadSplitLaba lambar oo isku xiga, wuxuu bixiyaa 17:1.Akhri dhammaan → ah wuxuu helaa $1,020, iyo wixii la mid ah. Kadib tiri fursadda in ugu yaraan hal sharad guulaysto ka hor inta aan lacagtu dhammaan. Lix iyo toban sharad oo $30 ah oo hal lambar ah dhammaan way seegaan fursad (36/37)¹⁶ = 64.5%, sidaa darteed waxay gaaraan $1,000 35.5% waqtiga.
Shaxdu waxay muujinaysaa sharad kasta. Casaanku ayaa ugu fiican sababtoo ah wuxuu ku gaaraa hal sharad, sidaa darteed faa'iidada kasiinada hal mar ayaa la bixiyaa, $500. Six linesharadSix lineLix lambar oo ku jira laba saf oo isku xiga, wuxuu bixiyaa 5:1. Faransiis: sixain.Akhri dhammaan →-ku waa labaad sababtoo ah wuxuu u baahan yahay saddex oo keliya. Hal sharad dersinsharadDersin1–12, 13–24 ama 25–36, wuxuu bixiyaa 2:1.Akhri dhammaan → ah ayaa ugu liita, fursad 12/37 ah; xitaa haddii lagu ciyaaro unugyolacagUnugSharadka saldhigga ah ee nidaam ama ciyaartoy ku shaqeeyo. Kordhinnada waxaa lagu sharxaa unugyo si ay ugu shaqeeyaan miis kasta.Akhri dhammaan → $250 ah ilaa aad haysato $1,000 ama ka badan, dersinku wuxuu gaaraa 46.4% waqtiga oo keliya.
Bollman (2024) wuxuu isla shaxdaas u dhisaa giraangir Mareykan ah. Safka dersinka ee uu qoray wuxuu leeyahay qalad: waa inuu ahaadaa 12/38 = 31.6%.
sharadqadarka sharadka × tirada sharadyadafursadda gaaridda $1,000
Hal lambar$30 × 1635.5%
Split$60 × 835.9%
Street$90 × 534.5%
Corner$125 × 436.7%
Six line$166, $166, $16841.2%
Dersin$500 × 132.4%
Casaan$500 × 148.6%
Waxaad sharadsataa hal unug casaan, wareeg kadib wareeg, adigoo leh raasamaal ciyaareedlacagRaasamaalka ciyaartaWadarta lacagta loo qoondeeyay ciyaarta. Maaraynta raasamaalka ciyaarta waa go'aaminta inta laga khatarinayo sharad kasta iyo fadhi kasta.Akhri dhammaan → aan weligiis dhammaanayn. Wareegga ugu horreeya kadib waxaad tahay hal unug faa'iido ah ama hal unug khasaare ah. Waa maxay fursadda inaad mar uun si sax ah ugu soo laabato barta bilowga?
Muuji xalka
Jawaab 36 ka mid ah 37, 97.3%. Giraangir Mareykan ah waa 36 ka mid ah 38, 94.7%.
Haddii wareegga ugu horreeya guulaysto (18 jeer 37-kii), waxaad tahay hal unug faa'iido ah, faa'iidada kasiinaduna waxay hoos u jiidaa fadhi kasta oo aan dhammaad lahayn, sidaa darteed goor dhow ama goor dambe waxaad dib uga gudbaysaa barta bilowga: taasi waa hubaal. Haddii uu lumo (19 jeer 37-kii), waa inaad kor u fuushaa hal unug, fursadda inaad mar uun hal unug ka sarreysana waa 18/19 (eeg shaxda kore).
Wada jir: 18/37 + 19/37 × 18/19 = 18/37 + 18/37 = 36/37.
Guud ahaan fursaddu waa 1 laga jaray farqiga u dhexeeya fursadaha guusha iyo khasaaraha wareegga: 1 − 1/37 giraangir Yurub ah, 1 − 2/38 mid Mareykan ah. Ciyaar aan lahayn ebergiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan → farqigu waa waxba, fursaduna waa 1: dhibcuhu had iyo jeer waxay ku soo noqdaan barta bilowga. Epstein (2013) wuxuu bixiyaa xeerka guud.
Xujada Pascal ee 1656: laba ciyaartoy waxay tuuraan saddex laadhuu, mid kastaa wuxuu ku bilaabaa 12 xabbo. 11 kastaa xabbad u wareejisaa ciyaartoyga kowaad, 14 kastaa mid u wareejisaa kan labaad; tuurisyada kale lama tiriyo. Intee in le'eg ayaa ciyaartoyga kowaad uu ku guulaysan karaa dhammaan 24? Oo haddii aad taa beddelkeeda sharadsato 1 unug casaan wareeg kasta saaxiib u dhaqmaya sidii bangiga, 12 unug midkiiba, intee in le'eg ayaad ku guulaysan kartaa dhammaan 24?
Muuji xalka
Jawaab Ciyaartoyga kowaad wuxuu guulaystaa qiyaastii 1,157 jeer 1,158-kii. Adiga, casaanka, waxaad ku guulaysataa dhammaan 24-ka unug qiyaastii 34% waqtiga oo keliya.
Saddex laadhuu waxay sameeyaan 11 27 hab, 14-na 15 hab, sidaa darteed xabbad kasta oo dhaqaaqda waxay u tagtaa ciyaartoyga kowaad 27 jeer 42-kii, 9 jeer 14-kii. Dhinac kastaa markuu ku bilaabo 12, fursadda wax walba la qaato waa 1/(1 + r¹²), halkaas oo r ay tahay saamiga fursadda dhinaca kale iyo taada.
Ciyaartoyga kowaad r = 5/9, (5/9)¹² ≈ 0.00086, sidaa darteed fursaddu waa qiyaastii 0.99914: odds 9¹² ilaa 5¹², ama 282,429,536,481 ilaa 244,140,625, qiyaastii 1,157 ilaa 1. Huygens wuxuu daabacay isla tirooyinkaas 1657.
Casaanka, r = 19/18 eberka awgiis, (19/18)¹² ≈ 1.913: fursaddaadu waa 1/2.913 ≈ 34.3%. Lacag bir ah waxay siin lahayd 50%. Faa'iidada kasiinada ee 2.70% ee sharad kasta waxay isu geysaa, sharadyada badan ee ay qaadato, farqi 16 dhibcood ah.

Kaftan yar

$Ciyaarta geesinimadu waa tan ugu fiican. Sidoo kale si dhakhso ah bay u dhammaataa.$

Ciyaarta geesinimadu waa tan ugu fiican. Sidoo kale si dhakhso ah bay u dhammaataa.

Ilaha

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, daabacaadda 3aad, 1968. Gambler’s ruin, cutubka XIV.
Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
Carcavi, P. de. Warqad uu u qoray Huygens, 28 Sebtembar 1656, oo ku saabsan masaladii Pascal u dhigay Fermat. Œuvres complètes de Christiaan Huygens, vol. 1, 1888, bogagga 492–494.
Huygens, C. De Ratiociniis in Ludo Aleae. 1657. Daaweyntii ugu horreysay ee la daabacay ee qiimaha la filayo.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Cutubka 13, roulette.
Reuters. “Briton bets it all on roulette spin, and wins.” Abriil 2004.
Las Vegas Sun. “Man wagers life’s worth.” 12 Abriil 2004.

la eegay 2026-09-28model: Yurub, hal eberhabka shaqada ↗ilaha ↗