Tinhlayo ta Roulette · Mianakanyo wa xisekelo · timinete 7

Ku Hambuka loku Tolovelekeke eka Roulette

Ku hambuka loku tolovelekeke eka roulette, ku nga rimitsu ra xikwere ra ku hambana-hambanatinhlayoKu Hambana-hambana (Variance)Mpimo wa leswaku mimbuyelo yi hangalaka ku fikela kwihi ku rhendzela ntsengo lowu languteriweke. Wu tlakukile eka straight up, wu le hansi eka swibejo swa mali yo ringana.Hlaya hinkwaswo →, i mpfhuka lowu tolovelekeke exikarhi ka mbuyelo na leswi wu languteriweke swona.

Nhlamulo yo koma

Eka $1 ya xibejo, σ i 5.84 eka straight up naswona i 1.00 eka yo tshuka. Eka sesheni, andzisa hi mali ya xibejo na hi rimitsu ra xikwere ra nhlayo ya marhendzeleko.

straight up
σ = 5.84
yo tshuka
σ = 1.00
ku kula
√N
±1σ
≈ 68% wa tisesheni

Nawu wo olova

Kwalomu ka swiphemu swimbirhi eka swinharhu swa tisesheni ti hela endzeni ka σ yin'we ya leswi languteriweke naswona 95% ti hela endzeni ka timbirhi. Eka marhendzeleko ya 100 ya yo tshukaxibejoYo tshukaXibejo xa mali yo ringana eka tinomboro ta 18 to tshuka. Hi Xifurwa: rouge.Hlaya hinkwaswo → hi $10 (leswi languteriweke −$27, σ = $100) tisesheni to tala ti wela exikarhi ka −$127 na +$73, naswona kwalomu ka hinkwato ti wela exikarhi ka −$227 na +$173. Mbuyelo lowu nga ehandle ka mpimo wolowo a hi vumbhoni bya nchumu, ku nga ri leswaku sesheni yin'we eka makume mambirhi yi endla tano.

marhendzeleko ya 100 hi $10 eka yo tshukampimoxiphemu xa tisesheni
endzeni ka 1σ−$127 ku ya eka +$73≈ 68%
endzeni ka 2σ−$227 ku ya eka +$173≈ 95%
endzeni ka 3σ−$327 ku ya eka +$273≈ 99.7%
u le ka mpindzuloehenhla ka $0≈ 42%
u tlakukile hi $100 kumbe ku tlulaehenhla ka +$100≈ 10%
Ku ringanyeta hi ku hangalaka ka normal. Ku hangalaka ka xiviri ku tshekile switsongo hikwalaho ka zero.

Hikokwalaho ka yini √N

Ku lahlekeriwa loku languteriweketinhlayoKu lahlekeriwa loku languteriwekeNtsengo lowu languteriweke wu andzisiwa hi mali hinkwayo leyi bhejiweke; mali ya xiringaniso leyi lahlekaka eka sesheni kumbe eka nkarhi wo karhi.Hlaya hinkwaswo → ku kula hi ku ya hi N; ku hangalaka ku kula hi ku ya hi √N. Loko N yi ri yitsongo, ku hangalaka hi kona ku fumaka naswona tisesheni ti fana na ku hoxa mali hi ku tshekela switsongo. Loko N yi ri yikulu, ku lahlekeriwa ku hundza ku hangalaka. Ndhawu leyi swi tsemakanaka eka yona, laha ku lahlekeriwa loku languteriweke ku ringanaka na ku hambuka loku tolovelekeketinhlayoKu hambuka loku tolovelekekeRimitsu ra xikwere ra ku hambana-hambana; mpfhuka lowu tolovelekeke exikarhi ka mbuyelo na ntsengo lowu languteriweke.Hlaya hinkwaswo → kun'we, i eka N = (σ/vuyelo)² = (1/0.027)² ≈ marhendzeleko ya 1,370 eka mali yo ringana na (5.84/0.027)² ≈ 46,800 eka ti straight upxibejoStraight upNomboro yin'we, yi hakela 35:1.Hlaya hinkwaswo →. Ehansi ka tinhlayo leti, nkateko hi wona wu tsemaka; ehenhla ka tona, i vuyelo.

Ku lahlekeriwa loku languteriweke tanihi ku andza ka σ, $10 eka yo tshukaEV / σ
marhendzeleko ya 10
0.09
marhendzeleko ya 100
0.27
marhendzeleko ya 1,000
0.85
marhendzeleko ya 1,370
1.00
marhendzeleko ya 10,000
2.70
marhendzeleko ya 100,000
8.54
EV / σ
04.258.54
Loko mpimanyiso wu hundza kwalomu ka 2, nkarhi wo hlula i xiendlakalo xo ka xi nga talangi. Leswi hi swona hinkwaswo leswi vuriwaka hi “khasino yi tshama yi hlula”.

Ku ku tirhisa

Ku vona loko sesheni a yi nga tolovelekangi, hlayela (mbuyelo − EV)/σ. Mutlangi wa $10 eka yo tshuka loyi a hetaka marhendzeleko ya 100 hi +$150 u le ka (150 + 27)/100 = 1.77σ, mbuyelo wa kan'we eka 25: nkateko, a hi nchumu wo hlamarisa. Mutlangi wa straight up eka +$150 leyi fanaka u le ka 0.3σ: vusiku bya ntolovelo. Mbuyelo wa tidolara lowu fanaka wu vula swilo swo hambana eka swibejo swo hambana.

Xihoxo xa ntolovelo xa xiphemu

Tinhlayo leti fanaka ti ku byela leswaku swi lava marhendzeleko mangani ku vona vuyelo eka data. Xihoxo xa ntolovelo xa xiphemu xa ku hlula lexi xiyiweke i √(p(1 − p)/N). Eka yo tshuka loko N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Ku hambana exikarhi ka mali leyi lulameke leyi hoxiwaka na yo tshuka i 1.35%, hikwalaho endzhaku ka marhendzeleko ya 1,000 a wu si kota ku swi hambanisa hi ku tiyiseka. Endzhaku ka 10,000 xihoxo xa ntolovelo i 0.5% naswona wa swi kota. Leswi hi swona swi endlaka leswaku ku kuma vhilwa leri tshekeke swi lava marhendzeleko yo tala ngopfu.

Xitsundzuxo hi ku tsheka

Mimbuyelo ya straight up a yi hangalaki hi ndlela ya normal eka sesheni yo koma: tisesheni to tala i −$10 leyi nga cinciki eka rhendzeleko yin'wana na yin'wana, na ku tlula ka +$350 nkarhi na nkarhi. Nawu wa ±1σ wu hlamusela ku hangalaka kahle kambe wu hlamusela xivumbeko hi ndlela yo biha ku fikela N yi ri emadzaneni. Eka swibejo swa mali yo ringanaxibejoXibejo xa mali yo ringanaYo tshuka/yo ntima, leyi nga ringaniki/leyi ringanaka, ehansi/ehenhla. Tinomboro ta 18, xi hakela 1:1.Hlaya hinkwaswo → ku ringanyeta ka normal ku lulamile ku sukela kwalomu ka marhendzeleko ya 30.

Fomula

σ = √Var
σ_sesheni = σ · mali ya xibejo · √N
z = (mbuyelo − EV) / σ_sesheni

Swivutiso

Xana sesheni yo hlula ya 2σ i vumbhoni bya sisiteme leyinene?

I vumbhoni bya leswaku u tlangile kwalomu ka tisesheni ta 40, kumbe a wu ri eka yin'we ya nkateko eka makume mune. Swi endle nakambe.

Hikokwalaho ka yini xiringaniso xa mina xa nkarhi wo leha xa ha tsutsuma?

Xi tsutsuma ku ya ehansi: xihoxo xa ntolovelo xa xiringaniso i σ/√N. Loko N = 10,000 i 1% wa mali ya xibejo.

Ku Tihungasa hi Tinhlayo

Ringeta leswi hi wexe ku sungula. Nhlamulo yin'wana na yin'wana yi pfariwile; yi pfula loko u lunghekile.

  1. Eka marhendzeleko ya 100 ya vhilwa ra le Yuropa, yunitimaliYunitiMali ya xibejo ya xisekelo leyi sisiteme kumbe mutlangi a tirhaka ha yona. Ntlhandlamano wa swibejo wu hlamuseriwa hi tiyuniti leswaku wu tirha eka tafula rin'wana na rin'wana.Hlaya hinkwaswo → yin'we eka yo tshukaxibejoYo tshukaXibejo xa mali yo ringana eka tinomboro ta 18 to tshuka. Hi Xifurwa: rouge.Hlaya hinkwaswo → yi le mahlweni hi ku hlula ka 51 kumbe ku tlula, naswona yuniti yin'we eka straight upxibejoStraight upNomboro yin'we, yi hakela 35:1.Hlaya hinkwaswo → yi le mahlweni loko nomboro ya yona yi huma minkarhi ya 3 kumbe ku tlula. Tirhisa khevha ya bell (bell curve) ku ringanyeta minkoteko hinkwayo yimbirhi, kutani u yi pimanisa na tinhlamulo ta kahle.

    Komba nhlamulo

    Nhlamulo Yo tshuka: khevha yi nyika 35.6% naswona nhlamulo ya kahle i 35.5%. Straight up: khevha yi nyika 55.0% naswona nhlamulo ya kahle i 50.9%. Ndlela leyi yo koma yi tirha eka yo tshuka kambe yi hoxeka eka nomboro yin'we.

    Yo tshuka: ku hlula ka xiringaniso i 100 × 18/37 = 48.6, hi ku hangalaka ka √(100 × 18/37 × 19/37) = 5.0. Ku va emahlweni swi vula 51 kumbe ku tlula; mfungho wa le xikarhi, 50.5, wu le henhla ka xiringaniso hi 0.37 wa ku hangalaka, naswona khevha yi veka 35.6% ehenhla ka kona. Ku hlanganisa minkoteko ya kahle ya ku hlula ka 51, 52 … 100 swi nyika 35.5%.

    Straight up: ku huma ka xiringaniso i 100/37 = 2.70, hi ku hangalaka ka √(100 × 1/37 × 36/37) = 1.62. Ku huma kunharhu kumbe ku tlula swi vula ehenhla ka 2.5, 0.12 wa ku hangalaka ehansi ka xiringaniso: 55.0% hi khevha. Hi ku kongoma, i 1 ku susa minkoteko ya ku huma ka 0, 1 na 2, 6.5% + 17.9% + 24.7%, leswi siyaka 50.9%.

    Khevha yi lava mimbuyelo yo tala hi matlhelo hamambirhi ya xiringaniso. Yo tshuka yi na yona endzhaku ka marhendzeleko ya 100; nomboro leyi humaka ehansi ka kanharhu hi xiringaniso a yi na yona. Khevha yi tlhela yi nyika 8.7% eka “ku nga humi”, laha nkoteko wa xiviri wu nga 6.5%. Taylor (2021) u veka binomial na khevha etlhelo-tlhelo hi ndlela leyi fanaka.

Ku hlekisa katsongo

Sesheni yin'we eka makume mambirhi yi le handle ka sigma timbirhi. Minkarhi hinkwayo ku na un'wana eka ncila.

Sesheni yin'we eka makume mambirhi yi le handle ka sigma timbirhi. Minkarhi hinkwayo ku na un'wana eka ncila.

Swihlovo

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, nkandziyiso wa vu-3, 1968. Gambler’s ruin, ndzima ya XIV.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Ndzima 13, roulette.
  3. Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
Tinhlayo ta RouletteKu Hambana-hambana (Variance)Tinhlayo ta RouletteKu Tshinelela hi Nkarhi wo Leha: Nawu wa Tinomboro Letikulu eka Roulette
ku kamberiwile 2026-09-28modlolo: wa le Yuropa, zero yin'wemaendlelo ya ntirho ↗swihlovo ↗