Itimaalka Taxanayaasha ee Roulette
Taxanayaasha dhaadheer ee hal midab waa caadi. Sidoo kale macno uma laha wareegga xiga.
Shan casaan oo isku xiga: 2.7%. Toban: 0.074%. Fadhi 200 wareeg ah, taxane lix ah oo hal midab ah wuxuu soo baxaa marar ka badan inta uusan soo bixin.
Inta jeer ee taxane khasaare yimaado
Sharad lacag isle'eg ah oo giraangir hal-eber ah wuxuu khasaaraa 19 wareeg 37-kiiba. Saf kasta waa fursadda in taxane wareegyo ah oo go'an dhammaantood khasaaraan, iyo inta uu ciyaartoy Martingale ah, oo labanlaaba khasaare kasta kadib, ilaa markaas khasaaray.
| khasaarooyin isku xiga | fursad | qiyaastii 1 ee | khasaaraha ilaa hadda | sharadka xiga |
|---|---|---|---|---|
| 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 |
Fursaddu waa 19/37 oo lagu dhuftay naftiisa hal mar khasaare kasta, laga tiriyo hal wareeg oo go'an. Fadhi dheer wuxuu leeyahay wareegyo badan oo taxane noocaas ahi ka bilaabmi karo, sidaa darteed fiid dhan way ka suurtagalsan tahay inta hal saf tilmaamayo.
Hal taxane
ItimaalkaxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → in k wareeg ee xiga ay dhammaantood casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → noqdaan waa (18/37)ᵏ. Laba: 23.7%. Shan: 2.7%. Toban: 0.074%, qiyaastii 1 ka mid ah 1,350. Labaatan: 1 ka mid ah 1.8 milyan. Lix iyo labaatan, rikoorka Monte Carlo: 1 ka mid ah 137 milyan. Kuwani waa itimaallada taxane gaar ah oo ka bilaabma wareeg gaar ah, taas oo ah su'aal ku dhawaad qofna dhab ahaan weydiinayn.
Fadhi gudihiis
Su'aasha dadku ula jeedaan waa “taxane k ah ma ka soo muuqan doonaa meel uun fadhigayga?”, jawaabtuna aad bay uga weyn tahay (18/37)ᵏ sababtoo ah fadhi 200 wareeg ah wuxuu bixiyaa ku dhawaad 200 meelood oo taxane ka bilaabmi karo. Taxane lix ama ka badan oo isku midab ah, casaan ama madowsharadMadowSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee madow. Faransiis: noir.Akhri dhammaan →, wuxuu ka soo muuqdaa fadhi 200 wareeg ah qiyaastii 94% marka; siddeed ama ka badan qiyaastii 47%; toban ama ka badan qiyaastii 14%. Haddii midabka hore loo magacaabo fursaduhu way yaraadaan, ilaa qiyaastii 75%, 27% iyo 7%. Ciyaartoy fiid oo dhan fadhiista wuxuu arki doonaa taxanayaal dhaadheer fiid kasta.
Sababta Martingale u daneeyo
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 → taban kastaa waxay leedahay dherer taxane oo jebiya: lix khasaare oo ka bilaabma sal $10 ah xad $500 ah, toban FibonacciistaraatiijiFibonacciKordhin raacda taxanaha 1, 1, 2, 3, 5, 8, 13…: hal tallaabo hore khasaare kadib, laba tallaabo dib guul kadib.Akhri dhammaan →, shan saddex-laabidda dersinnadasharadDersin1–12, 13–24 ama 25–36, wuxuu bixiyaa 2:1.Akhri dhammaan →. Itimaalka taxane khasaare oo lix ah lacag isle'eg waa (19/37)⁶ ≈ 1.8% isku day kasta, fadhi 200 wareeg ahna wuxuu ka kooban yahay laga yaabee 100 isku day, sidaas darteed jebintu waxay timaaddaa qiyaastii afar fadhi shantiiba oo dhererkaas ah. Itimaalka taxanayaasha roulette-ka ayaa ah sababta dhaadhacu aanu dhif u ahayn.
Lambarrada kulul iyo kuwa qabow
Isla xisaabtaas ayaa khuseysa hal lambarkasharadHal lambarHal lambar oo keliya, wuxuu bixiyaa 35:1.Akhri dhammaan →. 300 wareeg gudahood tirada la filayo lambar kasta waa 8.1; leexashada caadiga ahixisaabLeexashada caadiga ahXididka labajibbaarka ee kala-duwanaanshaha; masaafada caadiga ah ee natiijo ay u jirto qiimaha la filayo.Akhri dhammaan → waa qiyaastii 2.8. Lambar uun wuxuu muujin doonaa 15 soo bax, mid kalena 2, nasiib keliya, mar kasta. Looxa natiijooyinka ee iftiiminaya lambarrada “kulul” wuxuu iftiiminayaa dusha sare ee qaybin caadi ah. Shaybaarka Roulette wuxuu sharxayaa inta wareeg ee loo baahan yahay ka hor inta aanu lambar kululkhuraafaadLambar kululLambar dhowaan soo baxay in ka badan intii la filayay. Giraangir caddaalad ah waxba ma saadaaliyo.Akhri dhammaan → macno yeelan (kumanaan, hal giraangir oo la aqoonsaday).
Madaxbannaanidu waa ujeeddada oo dhan
Taxane toban casaan ah kama dhigo madow mid ka itimaal badan, sidoo kale kama dhigo casaan mid ka itimaal badan. Labaduba waa 18/37. Taxanayaashu waa sifo ka mid ah taxanayaasha nasiibka ah, waxayna noqon lahaayeen kuwo shaki leh haddii ay maqnaan lahaayeen: taxane 200 wareeg ah oo aan lahayn taxane ka dheer afar wuxuu noqon lahaa caddeyn aad uga xoog badan farageliin marka loo eego mid leh taxane laba iyo toban ah.
Qaacido
Su'aalo
26 madow oo Monte Carlo ka dhacay 18 Agoosto 1913 waa kan caanka ah. 32 casaan oo isku xiga ayaa laga soo sheegay kasiino Mareykan ah 1943. Labaduba way waafaqsan yihiin nasiib marka la eego inta wareeg ee kasiinooyinku sameeyaan.
Waa 18/37 si kasta ha ahaatee. Ku sharadso waxa qorshahaagu sheegayo, ama waxba.
Maya. Eexdu waxay u muuqataa godadqalabGodMid ka mid ah 37-ka qol ee lambarrada leh ee rotor-ka. Sidoo kale: slot, cup.Akhri dhammaan → qaarkood oo marar badan soo baxa kumanaan wareeg gudahood, ma aha taxanayaal midab ah.
Madadaalo Xisaabeed
Marka hore adigu isku day. Xal kasta waa qarsoon yahay; fur marka aad diyaar u tahay.
Imisa wareeg oo giraangir Yurub ah ayay qaadataa, celcelis ahaan, ka hor inta aan mid kasta oo ka mid ah 37-ka lambar soo bixin ugu yaraan hal mar?
Muuji xalka
Jawaab Qiyaastii 155 wareeg celcelis ahaan; dhexdhexaadku (median) waa 147.
Sugitaanka u tiri hal lambar cusub markiiba. Wareegga ugu horreeya had iyo jeer wuxuu muujiyaa lambar cusub. Markaad aragto 1 lambar, 36 ka mid ah 37-ka godqalabGodMid ka mid ah 37-ka qol ee lambarrada leh ee rotor-ka. Sidoo kale: slot, cup.Akhri dhammaan → waa cusub, sidaa darteed lambarka cusub ee xiga wuxuu qaataa 37/36 wareeg celcelis ahaan. Markaad aragto k lambar, wuxuu qaataa 37/(37 − k).
Isku dar sugitaannada: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = 155.5 wareeg.
Inta badan taasi waa dhammaadka. Lambarka ugu dambeeya keligiis wuxuu qaataa 37 wareeg celcelis ahaan, shanta ugu dambeysana qiyaastii 85. Giraangir Mareykan ah isla wadartaasi waxay bixisaa qiyaastii 161. Tani waa dhibaatada ururiyaha kuubannada (coupon collector’s problem); isla celceliskaas wuxuu ka soo baxaa xisaabinta caadiga ah.
37 wareeg oo giraangir Yurub ah, hal wareeg god kasta, imisa lambar oo kala duwan ayaad filan kartaa inaad aragto?
Muuji xalka
Jawaab Qiyaastii 23.6. Ku dhawaad saddex meelood meel lambarrada, qiyaastii 13, gabi ahaanba ma soo baxaan.
Qaado hal lambar, tusaale ahaan 17. Wareeg kasta wuxuu seegaa inuu soo baxo fursad 36/37 ah, sidaa darteed wuxuu seegaa dhammaan 37-ka wareeg fursad (36/37)³⁷ ≈ 0.363.
Lambar kastaa wuxuu leeyahay isla fursaddaas, sidaa darteed celcelis ahaan 37 × 0.363 ≈ 13.4 lambar ayaa maqan, 37 − 13.4 ≈ 23.6-na waa soo baxaan, qaar badan oo ka mid ah laba jeer ama ka badan.
Ciyaartoyda roulette waxay tan ugu yeeraan sharciga saddex meelood meelaha. Sharci maaha, waa xisaabta soo noqnoqoshada oo keliya: socod u dheer sida giraangirta, qiyaastii saddex meelood meel lambarrada way maqnaadaan, giraangir caddaalad ah iyo mid kaleba. 38 god, saamigu waa (37/38)³⁸ ≈ 0.363 sidoo kale; giraangir weyn wuxuu u dego meel u dhow 1/e ≈ 0.368.
Saaxiib ayaa ku tusaya laba liis oo 50 midab ah, casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → ama madowsharadMadowSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee madow. Faransiis: noir.Akhri dhammaan →, mid kasta oo la sheegay inuu ka yimid giraangir eberradagiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan → laga reebay. Mid wuxuu beddelaa midabka 25 jeer, socodkiisa ugu dheerna waa lix. Kan kale wuxuu beddelaa 35 jeer, weligiisna kama gudbo saddex. Kee baa la been-abuuray?
Muuji xalka
Jawaab Kan labaad. Liis dhab ah wuxuu beddelaa qiyaastii 24 ama 25 jeer. Mid leh 35 beddelaad wuxuu soo baxaa qiyaastii hal mar 500-kii liis, mid aan lahayn socod ka dheer saddexna qiyaastii laba jeer 100-kii liis.
Midab cusub kastaa ama wuxuu ku celiyaa kii ugu dambeeyay ama wuu beddelaa, kala badh iyo kala badh, sidaa darteed 49 fursadood oo beddelaad ah waxay bixiyaan 24.5 beddelaad celcelis ahaan, qiyaastii 3.5 kor ama hoos. Soddon iyo shan waa saddex tallaabo oo kuwaas ah oo ka sarreeya celceliska; giraangir caddaalad ah waxay soo saartaa intaas oo beddelaad ah qiyaastii hal mar 500-kii liis.
Socodyaduna isla sheekadaas ayay sheegaan. Liis dhab ah oo 50 ah wuxuu leeyahay socod afar ama ka badan qiyaastii 98% waqtiga, socodkiisa ugu dheerna inta badan waa shan ama lix.
Dadka la weydiiyo inay hindisaan liis nasiib ah aad bay u beddelaan, sababtoo ah socod afar ama shan ah wuxuu iyaga u muuqdaa qaab. Taylor (2021) wuxuu isla calaamaddaas ku muujiyaa liisaska tuurista lacagta birta ah ee ardaydu hindiseen: nasiibka dhabta ahi wuxuu leeyahay socodyo ka badan inta dadku filayaan.
Buug sheekooyin kasiino ah ayaa ka sheekeeya ciyaartoy lambarkiisu soo baxay shan jeer oo isku xigta, wuxuuna ugu yeeraa rikoor. Intee in le'eg ayay dhif ku tahay giraangir Yurub ah? Oo intee jeer ayay tahay inay ka dhacdo meel ka mid ah hal kasiino oo leh 20 miis, mid kastaa 40 jeer saacaddii wareejiyo, habeen iyo maalin?
Muuji xalka
Jawaab Lambar la magacaabay oo shan jeer oo isku xigta ah: 1 ka mid ah 69 milyan. Lambar kasta oo afar jeer oo kale soo baxa kadib markuu markii ugu horreysay soo baxo: 1 ka mid ah 1.87 milyan. Kasiinadaasi waxay wareejisaa qiyaastii 7 milyan jeer sannadkii, sidaa darteed waa inay aragtaa socod shan ah saddex ama afar jeer sannadkii.
Lambar la magacaabay wuxuu soo baxaa fursad 1/37 ah wareeg kasta, sidaa darteed shan isku xigta waxay leeyihiin fursad (1/37)⁵ = 1 ka mid ah 69,343,957. Laakiin cidna lambarka hore uma magacaabto. Wax kasta oo marka hore soo baxa, afarta wareeg ee xiga waa inay ku celiyaan: (1/37)⁴ = 1 ka mid ah 1,874,161.
20 miis × 40 wareeg × 24 saacadood × 365 maalmood = 7,008,000 wareeg sannadkii. Wareeg kastaa wuxuu bilaabi karaa socod, sidaa darteed kasiinadu waxay filaysaa 7,008,000/1,874,161 ≈ 3.7 socod oo shan ah sannadkii.
Rikoor rasmi ah oo noocan ah ma jiro, midna looma baahna: dhacdo dhif ah oo hal miis ka dhacda waa mid caadi ah kasiino oo dhan, sheekooyinkana waxaa laga sheekeeyaa miiska ay ka dhacday. Sheekada, ee Goldman (2007), waxay ka dhacdaa giraangir laba-eber leh, halkaas oo tirooyinku yihiin 1 ka mid ah 79 milyan iyo 1 ka mid ah 2.09 milyan.
Kaftan yar
Taxanayaasha dhaadheer waa sida nasiibku u eg yahay.
Ilaha
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.