Leexashada Caadiga ah ee Roulette
Leexashada caadiga ah ee roulette, xididka labajibbaarka ee 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 →, waa masaafada caadiga ah ee u dhexeysa natiijo iyo waxa laga filayo.
$1 kasta oo la sharadsado, σ waa 5.84 hal lambar iyo 1.00 casaan. Ku dhufo qadarka sharadka iyo xididka labajibbaarka tirada wareegyada si aad u hesho fadhi.
Xeer fudud
Qiyaastii saddex meelood laba meel fadhiyada waxay ku dhacaan hal σ gudaheed waxa la filayo, 95%-na laba gudahood. 100 wareeg oo casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → ah oo $10 ah (la filayo −$27, σ = $100) fadhiyada intooda badan waxay u dhexeeyaan −$127 iyo +$73, ku dhawaad dhammaantoodna −$227 iyo +$173. Natiijo ka baxsan xadkaas caddeyn uma aha wax kale marka laga reebo in hal fadhi labaatankiiba uu sidaas sameeyo.
Maxay u tahay √N
Khasaaraha la filayoxisaabKhasaaraha la filayoQiimaha la filayo oo lagu dhuftay wadarta lacagta la sharadsaday; celceliska lacagta lagu khasaaro fadhi ama muddo.Akhri dhammaan → wuxuu u koraa si u dhigma N; kala-firdhiddu waxay u kortaa si u dhigma √N. N yar, kala-firdhidda ayaa xukunta, fadhiyaduna waa sida qadaadiic tuuris oo xoogaa janjeera. N weyn, khasaaruhu wuxuu ka dheereeyaa kala-firdhidda. Barta isweydaarsiga, halka khasaaraha la filayo uu la mid yahay hal leexasho caadi ahxisaabLeexashada caadiga ahXididka labajibbaarka ee kala-duwanaanshaha; masaafada caadiga ah ee natiijo ay u jirto qiimaha la filayo.Akhri dhammaan →, waa N = (σ/faa'iido)² = (1/0.027)² ≈ 1,370 wareeg lacag isle'eg iyo (5.84/0.027)² ≈ 46,800 hal lambarsharadHal lambarHal lambar oo keliya, wuxuu bixiyaa 35:1.Akhri dhammaan →. Tirooyinkaas hoostooda, nasiibka ayaa go'aamiya; korkooda, faa'iidada kasiinada ayaa go'aamisa.
Isticmaalkeeda
Si aad u qiimeyso in fadhi uu ahaa mid aan caadi ahayn, xisaabi (natiijo − EV)/σ. Ciyaartoy $10 casaan ku sharadsada oo 100 wareeg ku dhammeeya +$150 wuxuu joogaa (150 + 27)/100 = 1.77σ, natiijo hal mar 25-kiiba dhacda: nasiib, ma aha wax la yaab leh. Ciyaartoy hal lambar ku sharadsada oo isla +$150 jooga wuxuu joogaa 0.3σ: habeen caadi ah. Isla natiijada doollarka ah macno kala duwan bay ku leedahay sharadyo kala duwan.
Khaladka caadiga ah ee saami
Isla xisaabtaas ayaa kuu sheegaysa inta wareeg ee loo baahan yahay si faa'iidada kasiinada looga arko xogta. Khaladka caadiga ah ee saamiga guusha la arkay waa √(p(1 − p)/N). Casaan N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Farqiga u dhexeeya qadaadiic caddaalad ah iyo casaan waa 1.35%, sidaas darteed 1,000 wareeg kadib weli si kalsooni leh uma kala sooci kartid. 10,000 kadib khaladka caadiga ahi waa 0.5% waadna kala sooci kartaa. Tani sidoo kale waa sababta ogaanshaha eexda giraangirta ay ugu baahan tahay wareegyo aad u badan.
Digniin ku saabsan janjeerka
Natiijooyinka hal lambar aad bay uga fog yihiin qaybin caadi ah fadhi gaaban: fadhiyada intooda badan waa −$10 joogto ah wareeg kasta oo leh boodboodyo +$350 ah mararka qaarkood. Xeerka ±1σ wuxuu si sax ah u sharxaa kala-firdhidda laakiin si liidata qaabka ilaa N uu boqollaal gaaro. Sharadyada lacag isle'egsharadSharad lacag isle'eg ahCasaan/madow, kisi/dhaban, sare/hoose. 18 lambar, wuxuu bixiyaa 1:1.Akhri dhammaan → qiyaasta caadiga ahi way wanaagsan tahay laga bilaabo qiyaastii 30 wareeg.
Qaacido
Su'aalo
Waa caddeyn inaad ciyaartay qiyaastii 40 fadhi, ama aad ahayd kan nasiibka leh ee afartankiiba mid. Ku celi.
Wuu sii yaraanayaa isrogroggiisu: khaladka caadiga ah ee celceliska waa σ/√N. Marka N = 10,000 waa 1% qadarka sharadka.
Madadaalo Xisaabeed
Marka hore adigu isku day. Xal kasta waa qarsoon yahay; fur marka aad diyaar u tahay.
100 wareeg oo giraangir Yurub ah, hal unuglacagUnugSharadka saldhigga ah ee nidaam ama ciyaartoy ku shaqeeyo. Kordhinnada waxaa lagu sharxaa unugyo si ay ugu shaqeeyaan miis kasta.Akhri dhammaan → oo casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → ah wuxuu faa'iido ku jiraa ugu yaraan 51 guul, hal unug oo hal lambarsharadHal lambarHal lambar oo keliya, wuxuu bixiyaa 35:1.Akhri dhammaan → ahna wuxuu faa'iido ku jiraa haddii lambarkiisu ku dhaco ugu yaraan 3 jeer. Isticmaal qalooca koorta si aad u qiyaasto labada fursadood, kadib is barbar dhig jawaabaha saxda ah.
Muuji xalka
Jawaab Casaan: qalooca koorta wuxuu bixiyaa 35.6% jawaabta saxda ahina waa 35.5%. Hal lambar: qalooca koorta wuxuu bixiyaa 55.0% jawaabta saxda ahina waa 50.9%. Habka gaaban wuu u shaqeeyaa casaanka wuuna u seegaa lambarka keliya.
Casaan: guulaha celceliskoodu waa 100 × 18/37 = 48.6, kala-fidsanaan √(100 × 18/37 × 19/37) = 5.0 ah. Faa'iido macnaheedu waa 51 ama ka badan; calaamadda badhtamaha, 50.5, waa 0.37 kala-fidsanaan oo ka sarreysa celceliska, qalooca koortuna wuxuu dhigaa 35.6% ka sarreeya taas. Isku-darka fursadaha saxda ah ee 51, 52 … 100 guul wuxuu bixiyaa 35.5%.
Hal lambar: ku dhacyada celceliskoodu waa 100/37 = 2.70, kala-fidsanaan √(100 × 1/37 × 36/37) = 1.62 ah. Saddex ku dhac ama ka badan macnaheedu waa ka sarreeya 2.5, 0.12 kala-fidsanaan oo ka hooseeya celceliska: 55.0% qalooca koorta. Si sax ah, waa 1 laga jaray fursadaha 0, 1 iyo 2 ku dhac, 6.5% + 17.9% + 24.7%, taas oo ka tagta 50.9%.
Qalooca koortu wuxuu u baahan yahay natiijooyin badan oo labada dhinac ee celceliska ah. Casaanku wuu haystaa 100 wareeg kadib; lambar ku dhaca wax ka yar saddex jeer celcelis ahaan ma haysto. Qalooccu xitaa wuxuu siiyaa 8.7% “ku dhac la'aan”, halkaas oo fursadda dhabta ahi tahay 6.5%. Taylor (2021) wuxuu binomial-ka iyo qalooca koorta isku barbar dhigaa si la mid ah.
Kaftan yar
Hal fadhi labaatankiiba wuxuu ka baxsan yahay laba sigma. Qof baa had iyo jeer dabada ku jira.
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.