Lej roulette · Lub tswv yim tseem ceeb · 8 feeb

Feem tshwm sim hauv roulette

Txhua feem tshwm sim hauv roulette yog tus naj npawb qhov muab faib rau 37.

Lus teb luv

p = cov lej uas twv rau / 37. Ib tus lej: 2.70%. Kaum yim tus: 48.65%. Feem tshwm sim ntawm ib kab ke tshwj xeeb yog muab cov feem tshwm sim ntawm txhua zaus kiv sib khoo.

twv ib tus lej

1/37 · 2.70%

pawg kaum ob

12/37 · 32.43%

them sib npaug

18/37 · 48.65%

liab ob zaug

23.67%

Ib zaus kiv

Txhua lub ntawm 37 lub qhovkhoom sivLub qhovIb ntawm 37 lub qhov muaj lej saum lub log kiv. Kuj hu ua: slot, khob.Nyeem tag nrho → muaj feem tshwm sim sib npaug, yog li feem yeej ntawm roulette hauv ib zaus kiv tsuas yog kev suav xwb. Ib qho twv rau plaub tus lej yeej 4/37 ntawm cov zaus kiv, kwv yees li 10.8%. Ib zaus kiv tus feem tshwm simlejFeem tshwm simFeem uas ib qhov tshwm sim yuav muaj, txij 0 txog 1 los yog 0% txog 100%. Ib tus lej: 1/37 = 2.70%.Nyeem tag nrho → tsis muaj dab tsi ntxiv tshaj qhov ntawd, thiaj ua rau tag nrho kev ua si no suav tau rau ntawm ib daim ntawv so ncauj.

Feem yeej, raws hom kev twv% ntawm cov zaus kiv

Twv ib tus lej (1)

2.70%

Twv ob tus lej (2)

5.41%

Twv ib kab (3)

8.11%

Twv plaub ces kaum (4)

10.81%

Twv ob kab (6)

16.22%

Pawg kaum ob / kab ntsug (12)

32.43%

Them sib npaug (18)

48.65%

% ntawm cov zaus kiv

024.3248.65%

Txhua qhov twv yog cov lej uas twv rau muab faib rau 37. Nyiaj them txo qis thaum twv ntau tus lej ntxiv, kom nqi xav tias yuav tau yog tib yam −2.70% rau txhua kab.

Ntau zaus kiv

Cov zaus kiv tsis cuam tshuam ib leeg, yog li feem tshwm sim ntawm ib kab ke yog muab sib khoo. Liabkev twvLiabKev twv them sib npaug rau 18 tus lej liab. Lus Fabkis: rouge.Nyeem tag nrho → ob zaug sib law liag: (18/37)² = 23.7%. Liab ces xoomlub logXoomTib lub qhov ntsuab uas tsis muaj kev twv them sib npaug, pawg kaum ob los yog kab ntsug twg npog; yog qhov uas feem tsev twv txiaj los ntawm. Kuj hu ua: ib lub xoom, 0.Nyeem tag nrho →: (18/37)(1/37) = 1.3%. Kaum xya ob zaug sib law liag: (1/37)² = 0.073%, kwv yees li ib zaug hauv 1,369. Kev ua ntej ua tom qab tseem ceeb rau ib kab ke tshwj xeeb tab sis tsis tseem ceeb rau kev suav xwb: “liab ces dubkev twvDubKev twv them sib npaug rau 18 tus lej dub. Lus Fabkis: noir.Nyeem tag nrho →” yog 25.0% tab sis “ib liab thiab ib dub hauv ob zaus kiv, twg ua ntej los tau” yog 50.0%.

Cov zaus kiv roulette tsis cuam tshuam

Tsawg kawg ib zaug

Siv qhov seem. Feem uas twv ib tus lejkev twvTwv ib tus lejIb tus lej xwb, them 35:1.Nyeem tag nrho → tsis raug li hauv 37 zaus kiv yog (36/37)³⁷ = 36.3%, yog li feem uas raug tsawg kawg ib zaug yog 63.7%, tsis yog qhov “paub tseeb” uas ntau tus neeg ua si xav tias yuav tau los ntawm 37 zaug uas txhua zaug muaj 1 hauv 37. Tib qho kev suav no qhia tias ib tus lej muaj kwv yees li 1 hauv 3 feem uas tsis tawm kiag li hauv 37 zaus kiv, thiaj ua rau daim npav qhia qhov tshwm sim ib txwm muaj ob peb tus lej “txias”.

zaus kivp(tsis raug, twv ib tus lej)p(raug tsawg kawg ib zaug)

1076.0%24.0%

3736.3%63.7%

7413.2%86.8%

1006.5%93.5%

1501.7%98.3%

2000.4%99.6%

(36/37)ⁿ thiab 1 − (36/37)ⁿ. Txawm tias tom qab 100 zaus kiv, ib tus lej hauv kaum tsib tus tseem tsis tau tawm.

Qhov tshwm sim hauv roulette: nyeem daim npav

Lub sij hawm tos raws nruab nrab

Raws qhov nruab nrab, ib tus lej twv ib tus lej tawm ib zaug hauv txhua 37 zaus kiv, tab sis lub sij hawm tos hloov pauv heev: qhov tos nruab nrab (median) yog kwv yees li 25 zaus kiv (ib nrab ntawm cov zaug nws tawm ua ntej ntawd) thiab ib zaug tos hauv nees nkaum zaug ntev tshaj 110 zaus kiv. Lub sij hawm tos ntawm ib qho txheej txheem geometric muaj tus tw ntev, thiab ib tus neeg ua si uas “paub” tias ib tus lej yuav tsum tawm lawm tom qab 60 zaus kiv tab tom piav txog ib yam uas tshwm sim ib zaug hauv tsib zaug.

Kev ntseeg yuam kev: cov lej txog sij hawm tawm

Kev yuam kev uas pom ntau

Muab feem tshwm sim ntxiv ua ke rau cov xwm txheej uas tuaj yeem tshwm sim ua ke (liab lossis khib tsis yog 36/37; nws yog 26/37, vim kaum tus lej yog ob yam). Muab sib khoo rau cov xwm txheej hauv tib zaus kiv (liab thiab khib hauv ib zaus kiv yog 10/37, tsis yog 18/37 × 18/37). Muab cov zaus kiv dhau los suav ua ib feem ntawm kab ke uas koj tab tom twv: tom qab liab kaum zaug, feem tshwm sim ntawm liab zaum kaum ib yog 18/37, tsis yog (18/37)¹¹.

Feem hauv roulette yog dab tsi, thiab txawv li cas ntawm feem tshwm sim?

Cov tsev twv txiaj hais nyiaj themnyiajNyiaj themQhov uas ib qho kev twv yeej them rov qab, hais ua “X rau 1” ntxiv rau nyiaj twv uas xa rov qab.Nyeem tag nrho → ua feem (odds). Ib tus lej yeej nrog feem tshwm sim 1/37, yog li feem yeej ntawm roulette rau ib tus lej yog 36 rau 1 tawm tsam. Nyiaj them 35 rau 1 yog li ntawd tsis txaus ib chav twvnyiajChav twvNyiaj twv pib uas ib txheej txheem los yog ib tus neeg ua si siv. Kev nce nyiaj twv raug piav ua chav twv kom siv tau ntawm txhua lub rooj.Nyeem tag nrho →, thiab qhov ntawd yog feem tsev twv txiajlejFeem tsev twv txiajFeem ntawm txhua qhov nyiaj twv uas tsev twv txiaj khaws raws qhov nruab nrab: 2.70% hauv roulette Europe.Nyeem tag nrho → raws nws daim ntawv qub. Kev hloov: feem tawm tsam = (1 − p)/p; feem tshwm sim = 1/(feem + 1).

Qauv lej

p(kev twv) = n / 37

p(A ces B) = p(A) · p(B)

p(tsawg kawg ib zaug hauv k) = 1 − (1 − p)ᵏ

feem tawm tsam = (1 − p) / p

Cov lus nug

Feem tshwm sim uas xoom tawm ob zaug sib law liag yog npaum li cas?

(1/37)² = 1/1369 ≈ 0.073%.

Feem tshwm sim uas tawm liab lossis dub yog npaum li cas?

36/37 = 97.3%. Xoom yog qhov seem.

17 puas yog tus lej tawm ntau tshaj?

Tag nrho 37 tus yog 1/37. Kaum xya yog tus lej uas neeg twv ntau tshaj, thiab qhov ntawd yog ib qho tseeb txog tib neeg.

Lom zem nrog lej

Sim ua koj tus kheej ua ntej. Txhua lo lus teb raug quav cia; qhib nws thaum koj npaj txhij.

Koj twv rau liabkev twvLiabKev twv them sib npaug rau 18 tus lej liab. Lus Fabkis: rouge.Nyeem tag nrho →, zaus kiv dhau zaus kiv. Feem tshwm sim uas koj zaug yeej thib tsib los tseeb ntawm zaus kiv thib yim yog npaum li cas? Thiab uas koj muaj tsib zaug yeej hauv thawj yim zaus kiv?
Qhia lus teb
Lus teb 12.9%, kwv yees li 1 hauv 8, rau zaug yeej thib tsib ntawm zaus kiv thib yim. 33.4% rau tsib zaug yeej txog thaum ntawd.
Zaug yeej thib tsib ntawm zaus kiv thib yim txhais tau ob yam: zaus kiv thib yim yeej, thiab thawj xya zaus kiv muaj tseeb plaub zaug yeej thiab peb zaug poob, txawm sib law li cas los xij. Muaj 35 txoj kev muab plaub zaug yeej tso rau hauv xya zaus kiv.
Yog li feem tshwm sim yog 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9%.
Rau tsib zaug yeej txog zaus kiv thib yim, ntxiv tib hom ntawm rau zaug yeej thib tsib ntawm zaus kiv thib tsib, thib rau thiab thib xya: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%. Cov kws suav lej hu qhov no ua kev faib tawm negative binomial: yuav siv pes tsawg zaug sim kom tau ib tus naj npawb zaug ua tiav uas teem tseg. Taylor (2021) suav tib lo lus nug ntawm lub log roulette Asmeskas, 12.2%.

Lus lom zem

$Suav cov qhov. Faib rau 37. Sib khoo rau kab ke. Tiav lawm.$

Suav cov qhov. Faib rau 37. Sib khoo rau kab ke. Tiav lawm.

Qhov chaw los

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, tsab 3, 1968. Gambler’s ruin, tshooj XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Tshooj 13, roulette.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.

kuaj xyuas 2026-09-28qauv: roulette Europe, ib lub xoomtxoj kev ua haujlwm ↗qhov chaw los ↗