Nkoteko wa Tindzandzelelano eka Roulette
Tindzandzelelano to leha ta muhlovo wun'we ti tolovelekile. Naswona a ti vuli nchumu eka rhendzeleko leri landzelaka.
To tshuka ta ntlhanu hi ku landzelelana: 2.7%. Ta khume: 0.074%. Eka sesheni ya marhendzeleko ya 200, ndzandzelelano wa tsevu wa muhlovo wun'we wu humelela ku tlula hafu ya minkarhi.
Ndzandzelelano wa ku lahlekeriwa wu ta kangani
Xibejo xa mali yo ringana eka vhilwa ra zero yin'we xi lahlekeriwa eka marhendzeleko ya 19 eka 37. Mula wun'wana ni wun'wana i nkoteko wa leswaku marhendzeleko yo karhi hinkwawo ma lahlekeriwa, na leswi mutlangi wa Martingale, loyi a phindhaka kambirhi loko a lahlekeriwile, a lahlekeriweke swona hi nkarhi wolowo.
| ku lahlekeriwa hi ku landzelelana | nkoteko | kwalomu ka 1 eka | leswi lahlekeke sweswi | xibejo lexi landzelaka |
|---|---|---|---|---|
| 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 |
Nkoteko i 19/37 lowu andzisiwaka hi wona n'wexe kan'we eka ku lahlekeriwa kun'wana ni kun'wana, ku hlayiwa ku sukela eka rhendzeleko rin'we. Sesheni yo leha yi na marhendzeleko yo tala laha ndzandzelelano wo tano wu nga sungulaka kona, hikwalaho eka nimadyambu nkoteko wa wona wu kulu ngopfu ku tlula leswi mula wun'we wu swi kombaka.
Ndzandzelelano wun'we
NkotekotinhlayoNkotekoNkoteko wa mbuyelo, ku suka eka 0 ku ya eka 1 kumbe 0% ku ya eka 100%. Nomboro yin'we: 1/37 = 2.70%.Hlaya hinkwaswo → wa leswaku marhendzeleko ya k lama landzelaka hinkwawo ma va yo tshukaxibejoYo tshukaXibejo xa mali yo ringana eka tinomboro ta 18 to tshuka. Hi Xifurwa: rouge.Hlaya hinkwaswo → i (18/37)ᵏ. Mambirhi: 23.7%. Ntlhanu: 2.7%. Khume: 0.074%, kwalomu ka 1 eka 1,350. Makume mambirhi: 1 eka 1.8 wa timiliyoni. Makume mambirhi na tsevu, rekhodo ya Monte Carlo: 1 eka 137 wa timiliyoni. Leyi i minkoteko ya ndzandzelelano wo karhi lowu sungulaka eka rhendzeleko wo karhi, xivutiso lexi kwalomu ka ku hava munhu a xi vutisaka hakunene.
Eka sesheni
Xivutiso lexi vanhu va xi vulaka i “xana ndzandzelelano wa k wu ta humelela kun'wana eka sesheni ya mina?”, naswona nhlamulo yi kulu ngopfu ku tlula (18/37)ᵏ hikuva sesheni ya marhendzeleko ya 200 yi nyika kwalomu ka tindhawu ta 200 laha ndzandzelelano wu nga sungulaka kona. Ndzandzelelano wa tsevu kumbe ku tlula wa muhlovo lowu fanaka, yo tshuka kumbe yo ntimaxibejoYo ntimaXibejo xa mali yo ringana eka tinomboro ta 18 to ntima. Hi Xifurwa: noir.Hlaya hinkwaswo →, wu humelela eka sesheni ya marhendzeleko ya 200 kwalomu ka 94% wa minkarhi; wa nhungu kumbe ku tlula kwalomu ka 47%; wa khume kumbe ku tlula kwalomu ka 14%. Vula muhlovo ka ha ri emahlweni kutani minkoteko yi wela ehansi, ku ya eka kwalomu ka 75%, 27% na 7%. Mutlangi loyi a tshamaka madyambu hinkwawo u ta vona tindzandzelelano to leha madyambu man'wana na man'wana.
Hikokwalaho ka yini Martingale yi swi khathala
Ntlhandlamano wa swibejoqhingaNtlhandlamano wa swibejoNawu wun'wana na wun'wana lowu cincaka mali ya xibejo hi ku ya hi mimbuyelo leyi hundzeke. Ntlhandlamano wo lahlekisa wu yi tlakusa endzhaku ko lahlekeriwa, lowu nga wa ku hlula wu yi tlakusa endzhaku ko hlula.Hlaya hinkwaswo → wun'wana na wun'wana lowu engetelaka endzhaku ka ku lahlekeriwa wu na ku leha ka ndzandzelelano lowu wu wu tshovaka: ku lahlekeriwa kasevu ku sukela eka $10 ya xisekelo loko ndzilakano wu ri $500, kakhume eka FibonacciqhingaFibonacciNtlhandlamano wa swibejo lowu landzelaka nxaxamelo 1, 1, 2, 3, 5, 8, 13…: goza rin'we emahlweni endzhaku ko lahlekeriwa, magoza mambirhi endzhaku endzhaku ko hlula.Hlaya hinkwaswo →, kantlhanu loko u andzisa kanharhu eka tidazinixibejoDazini1–12, 13–24 kumbe 25–36, yi hakela 2:1.Hlaya hinkwaswo →. Nkoteko wa ndzandzelelano wa tsevu wo lahlekeriwa eka mali yo ringana i (19/37)⁶ ≈ 1.8% eka ringeto rin'wana na rin'wana, naswona sesheni ya marhendzeleko ya 200 yi nga va na kwalomu ka maringeto ya 100, hikwalaho ku tshoveka ku fika kwalomu ka tisesheni ta mune eka ntlhanu ta ku leha koloko. Nkoteko wa tindzandzelelano eka roulette hi wona xivangelo xa leswaku ku wela ka mali a ku talangi ku tsana.
Tinomboro to hisa na to titimela
Tinhlayo leti fanaka ti tirha eka ti straight upxibejoStraight upNomboro yin'we, yi hakela 35:1.Hlaya hinkwaswo →. Eka marhendzeleko ya 300, nhlayo leyi languteriweke eka nomboro yin'wana na yin'wana i 8.1; 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 → i kwalomu ka 2.8. Nomboro yin'wana yi ta humelela ka 15 naswona yin'wana ka 2 hi xitshuketa ntsena, minkarhi hinkwayo. Bodo ya mimbuyelo leyi kombisaka tinomboro “to hisa” yi kombisa nhloko ya ku hangalaka ka normal. Laborotari ya Roulette yi hlamusela leswaku swi lava marhendzeleko mangani leswaku nomboro yo hisantsheketoNomboro yo hisaNomboro leyi humeleleke ku tlula leswi languteriweke eku hetelelaka. Eka vhilwa leri nga tshekiki a yi vhumbi nchumu.Hlaya hinkwaswo → yi vula nchumu (magidi, eka vhilwa rin'we leri tiviwaka).
Ku tiyimela hi swona swa nkoka hinkwaswo
Ndzandzelelano wa to tshuka ta khume a wu endli leswaku yo ntima yi va na nkoteko lowukulu, naswona a wu endli leswaku yo tshuka yi va na nkoteko lowukulu. Hinkwato i 18/37. Tindzandzelelano i ntumbuluko wa tindzandzelelano ta xitshuketa naswona ku pfumaleka ka tona a ku ta tsakisa ku kanakana: ndzandzelelano wa marhendzeleko ya 200 lowu nga riki na ndzandzelelano wo leha ku tlula mune a wu ta va vumbhoni byo tiya ngopfu bya ku hlangahlanganisiwa ku tlula lowu nga na ndzandzelelano wa khume-mbirhi.
Fomula
Swivutiso
To ntima ta 26 e Monte Carlo hi 18 Mhawuri 1913 hi wona lowu dumeke. To tshuka ta 32 hi ku landzelelana ti vikiwile eka khasino ya le Amerika hi 1943. Hinkwato ti twanana na xitshuketa loko ku languteriwa nhlayo ya marhendzeleko lama tikhasino ti ma tirhisaka.
I 18/37 hi ndlela yihi na yihi. Bheja leswi pulani ya wena yi swi vulaka, kumbe u nga bheji nchumu.
E-e. Ku tsheka ku vonaka loko tikhamaraswitirhisiwaKhamaraYin'we ya tikhamara ta 37 leti nga na tinomboro eka rotor. Nakambe: slot, cup.Hlaya hinkwaswo → tin'wana ti huma ngopfu eka magidi ya marhendzeleko, ku nga ri hi tindzandzelelano ta muhlovo.
Ku Tihungasa hi Tinhlayo
Ringeta leswi hi wexe ku sungula. Nhlamulo yin'wana na yin'wana yi pfariwile; yi pfula loko u lunghekile.
Swi lava marhendzeleko mangani ya vhilwa ra le Yuropa, hi xiringaniso, leswaku tinomboro hinkwato ta 37 ti huma kan'we kumbe ku tlula?
Komba nhlamulo
Nhlamulo Kwalomu ka marhendzeleko ya 155 hi xiringaniso; xiphemu xa le xikarhi (median) i 147.
Hlayela ku rindza nomboro yin'we leyintshwa hi nkarhi. Rhendzeleko ro sungula ri tshama ri kombisa nomboro leyintshwa. Loko u vonile nomboro ya 1, tikhamaraswitirhisiwaKhamaraYin'we ya tikhamara ta 37 leti nga na tinomboro eka rotor. Nakambe: slot, cup.Hlaya hinkwaswo → ta 36 eka 37 i letintshwa, hikwalaho nomboro leyintshwa leyi landzelaka yi teka marhendzeleko ya 37/36 hi xiringaniso. Loko u vonile tinomboro ta k, swi teka 37/(37 − k).
Hlanganisa ku rindza hinkwako: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = marhendzeleko ya 155.5.
Xiphemu lexikulu xa sweswo xi le makumu. Nomboro yo hetelela yi ri yoxe yi teka marhendzeleko ya 37 hi xiringaniso, naswona to hetelela ta ntlhanu ti teka kwalomu ka 85. Eka vhilwa ra le Amerika, ku hlanganisa loku fanaka ku nyika kwalomu ka 161. Lexi i xiphiqo xa muhlengeleti wa tikhuphoni (coupon collector’s problem); xiringaniso lexi fanaka xi huma eka xibalo xa ntolovelo.
Eka marhendzeleko ya 37 ya vhilwa ra le Yuropa, rhendzeleko rin'we eka khamara yin'wana na yin'wana, u fanele ku langutela ku vona tinomboro to hambana tingani?
Komba nhlamulo
Nhlamulo Kwalomu ka 23.6. Kwalomu ka xiphemu xin'we xa vunharhu xa tinomboro, kwalomu ka 13, a ti humi nikatsongo.
Teka nomboro yin'we, a hi nge 17. Eka rhendzeleko rin'wana na rin'wana a yi humi hi nkoteko wa 36/37, hikwalaho a yi humi eka marhendzeleko hinkwawo ya 37 hi nkoteko wa (36/37)³⁷ ≈ 0.363.
Nomboro yin'wana na yin'wana yi na nkoteko lowu fanaka, hikwalaho hi xiringaniso tinomboro ta 37 × 0.363 ≈ 13.4 a ti humi naswona 37 − 13.4 ≈ 23.6 ta huma, to tala ta tona kambirhi kumbe ku tlula.
Vatlangi va roulette va swi vitana nawu wa swiphemu swinharhu (law of thirds). A hi nawu, i tinhlayo ta ku phindha ntsena: eka nxaxamelo wa marhendzeleko lowu lehaka ku fana na vhilwa, kwalomu ka xiphemu xin'we xa vunharhu xa tinomboro a ti humi, eka vhilwa leri nga tshekiki ku fana na eka rin'wana. Eka tikhamara ta 38 xiphemu lexi i (37/38)³⁸ ≈ 0.363 na xona; eka vhilwa lerikulu xi tshama kusuhi na 1/e ≈ 0.368.
Munghana u ku komba swinxaxamelo swimbirhi swa mihlovo ya 50, yo tshukaxibejoYo tshukaXibejo xa mali yo ringana eka tinomboro ta 18 to tshuka. Hi Xifurwa: rouge.Hlaya hinkwaswo → kumbe yo ntimaxibejoYo ntimaXibejo xa mali yo ringana eka tinomboro ta 18 to ntima. Hi Xifurwa: noir.Hlaya hinkwaswo →, xin'wana na xin'wana ku vuriwa xi huma eka vhilwa leri tizerovhilwaZeroKhamara yin'we ya rihlaza leyi ku nga riki na xibejo xa mali yo ringana, xa dazini kumbe xa kholomu lexi yi funengetaka; xihlovo xa vuyelo bya khasino. Nakambe: zero yin'we, 0.Hlaya hinkwaswo → ti susiweke. Xin'wana xi cinca muhlovo minkarhi ya 25 naswona ndzandzelelano wa xona wo leha ku tlula hinkwawo i wa tsevu. Lexin'wana xi cinca minkarhi ya 35 naswona a xi tluli nharhu. Hi xihi lexi vumbiweke hi munhu?
Komba nhlamulo
Nhlamulo Xa vumbirhi. Nxaxamelo wa xiviri wu cinca kwalomu ka minkarhi ya 24 kumbe 25. Lowu nga ni ku cinca ka 35 wu humelela kwalomu ka kan'we eka swinxaxamelo swa 500, naswona lowu nga riki na ndzandzelelano wo leha ku tlula nharhu kwalomu ka kambirhi eka 100.
Muhlovo wun'wana na wun'wana lowuntshwa wu phindha lowu hundzeke kumbe wu cinca, hafu na hafu, hikwalaho minkoteko ya 49 ya ku cinca yi nyika ku cinca ka 24.5 hi xiringaniso, ku engetela kumbe ku hunguta kwalomu ka 3.5. Makume manharhu na ntlhanu i magoza manharhu ya kona ehenhla ka xiringaniso; vhilwa leri nga tshekiki ri humesa ku cinca ko tala hivolaho kwalomu ka kan'we eka swinxaxamelo swa 500.
Tindzandzelelano ti vula mhaka leyi fanaka. Nxaxamelo wa xiviri wa 50 wu na ndzandzelelano wa mune kumbe ku tlula kwalomu ka 98% wa nkarhi, naswona ndzandzelelano wa wona wo leha ku tlula hinkwawo hi ntolovelo i wa ntlhanu kumbe tsevu.
Vanhu lava kombeliwaka ku vumba nxaxamelo wa xitshuketa va cinca ngopfu, hikuva ndzandzelelano wa mune kumbe ntlhanu wu va languteka ku fana na xivumbeko. Taylor (2021) u kombisa xikombiso lexi fanaka eka swinxaxamelo swa ku hoxa mali leswi vumbiweke hi swichudeni: xitshuketa xa xiviri xi na tindzandzelelano to tala ku tlula leswi vanhu va swi langutelaka.
Buku ya swihungwana swa khasino yi hlamusela hi mutlangi loyi nomboro ya yena yi humeke minkarhi ya ntlhanu yi landzelelana, kutani yi swi vitana rekhodo. Swi humelela hi nkoteko wo tani hi kwihi eka vhilwa ra le Yuropa? Naswona swi fanele ku humelela kangani endhawini yin'wana eka khasino yin'we leyi nga ni matafula ya 20, rin'wana na rin'wana ri rhendzelekisa minkarhi ya 40 hi awara, vusiku na nhlikanhi?
Komba nhlamulo
Nhlamulo Nomboro leyi vuriweke yi huma minkarhi ya ntlhanu yi landzelelana: 1 eka timiliyoni ta 69. Nomboro yin'wana na yin'wana yi huma minkarhi yin'wana ya mune endzhaku ka loko yi sungula ku humelela: 1 eka timiliyoni ta 1.87. Khasino yoleyo yi rhendzelekisa kwalomu ka timiliyoni ta 7 hi lembe, hikwalaho yi fanele ku vona ndzandzelelano wa ntlhanu minkarhi minharhu kumbe mune hi lembe.
Nomboro leyi vuriweke yi huma hi nkoteko wa 1/37 eka rhendzeleko rin'wana na rin'wana, hikwalaho ku huma ka ntlhanu ku landzelelana ku na nkoteko wa (1/37)⁵ = 1 eka 69,343,957. Kambe a nga kona loyi a vulaka nomboro ka ha ri emahlweni. Xin'wana na xin'wana lexi humaka ku sungula, marhendzeleko ya mune lama landzelaka ma fanele ku xi phindha: (1/37)⁴ = 1 eka 1,874,161.
Matafula ya 20 × marhendzeleko ya 40 × tiawara ta 24 × masiku ya 365 = marhendzeleko ya 7,008,000 hi lembe. Rhendzeleko rin'wana na rin'wana ri nga sungula ndzandzelelano, hikwalaho khasino yi langutela 7,008,000/1,874,161 ≈ 3.7 wa tindzandzelelano ta ntlhanu hi lembe.
A ku na rekhodo ya ximfumo ya muxaka lowu, naswona a yi lavekeki: xiendlakalo lexi nga talangiki eka tafula rin'we i xa ntolovelo eka khasino hinkwayo, naswona swihungwana swi hlamuseriwa hi tafula laha swi humeleleke kona. Xihungwana lexi, eka Goldman (2007), xi endleka eka vhilwa ra zero mbirhi, laha tinhlayo ti nga 1 eka timiliyoni ta 79 na 1 eka timiliyoni ta 2.09.
Ku hlekisa katsongo
Tindzandzelelano to leha hi ku languteka ka xitshuketa.
Swihlovo
- 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.