Lej roulette · Ntaub ntawv siv · 5 feeb

Daim ntawv feem thiab feem tshwm sim hauv roulette

Txhua yam kev twv txheem nrog nws feem tshwm sim, nyiaj them, nqi xav tias yuav taulejNqi xav tias yuav tauQhov tshwm sim nruab nrab ntawm ib qho kev twv thaum mus ntev. −1/37 ntawm cov nyiaj twv rau txhua qhov kev twv Europe ib txwm.Nyeem tag nrho → thiab qhov sib txawv txheem.

Lus teb luv

Txhua yam kev twv muaj tib tus nqi xav tias yuav tau, −2.70% ntawm nyiaj twv. Lawv txawv tsuas yog feem tshwm sim thiab qhov kis tawm xwb.

kev twv hauv daim ntawv
9
EV, txhua yam kev twv
−2.70%
σ txij
1.00 txog 5.84
kev twv hais lus
kuj yog 2.70%

Nyeem daim ntawv feem roulette no li cas

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 → qhia koj tias koj yeej ntau npaum li cas zaus; 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 →, uas hu ua feem roulette, qhia koj tias yeej tau pes tsawg; σ qhia koj tias txoj kev yuav ntxhov npaum li cas. Kab EV zoo tib yam rau txhua kab vim nws tsim li ntawd, yog li daim ntawv no tiag tiag yog ib daim ntawv xaiv kev hloov pauvlejKev hloov pauv (variance)Ib qho kev ntsuas tias cov qhov tshwm sim tawg dav npaum li cas ncig tus nqi xav tias yuav tau. Siab rau twv ib tus lej, qis rau kev twv them sib npaug.Nyeem tag nrho → ntawm ib tus nqi ruaj.

kev twvnpogp(yeej)themσ rau $1
Twv ib tus lej1/372.70%35:15.84
Twv ob tus lej2/375.41%17:14.09
Twv ib kab3/378.11%11:13.28
Twv plaub ces kaum4/3710.81%8:12.84
Twv ob kab6/3716.22%5:12.23
Pawg kaum ob12/3732.43%2:11.39
Kab ntsug12/3732.43%2:11.39
Them sib npaug18/3748.65%1:11.00
EV yog −$0.027 rau $1 ntawm txhua kab.

Kev twv hais lus

Cov kev twv thaj loglub logThaj logIb txoj kab qhov uas nyob sib txuas saum lub log, txawv ntawm ib pawg lej saum daim duab rooj twv.Nyeem tag nrho → yog kev muab cov kev twv txheem los ua ke thiab tau txais lawv feem tsev twv txiaj. Txhua yam muaj nws tus qauv nyiaj them vim cov npibnyiajNpibIb lub cim uas sawv cev rau ib tus nqi ruaj, muab tso rau saum daim duab rooj twv kom twv. Kuj hu ua: check.Nyeem tag nrho → tso tsis sib npaug.

kev twv hais lusnpibnpogp(raug ib qho)nyiaj tau thaum raug (chav twv)EV rau ib chav twv
Cov lej ze (5)55/3713.51%+31−2.70%
Jeu zéro47/3718.92%+14 lossis +32−2.70%
Orphelins58/3721.62%+13 lossis +31−2.70%
Tiers du cylindre612/3732.43%+12−2.70%
Voisins du zéro917/3745.95%+9 lossis +15−2.70%

Nqi xav tias yuav tau ntawm kev twv hais lus

Hla ntau zaus kiv

Feem tshwm sim tias yuav raug tsawg kawg ib zaug hauv k zaus kiv, rau ob peb lo lus nug uas neeg nquag nug.

kev twvhauv 10 zaus kivhauv 37 zaus kivhauv 100 zaus kiv
Twv ib tus lej24.0%63.7%93.5%
Twv ob tus lej42.6%87.1%99.6%
Twv plaub ces kaum68.1%98.6%> 99.9%
Pawg kaum ob98.0%> 99.9%> 99.9%
Xoom (tshwj xeeb)24.0%63.7%93.5%
1 − (1 − p)ᵏ.

Qhov kis tawm ntawm ib zaus ua si

Qhov sib txawv txheemlejQhov sib txawv txheemCag plaub fab ntawm kev hloov pauv (variance); qhov deb ib txwm ntawm ib qhov tshwm sim ntawm tus nqi xav tias yuav tau.Nyeem tag nrho → ntawm ib zaus ua si 100 zaus kiv, twv tib yam nyiaj $10, raws txhua yam kev twv, nrog tib qhov tshwm sim xav tias yuav tau yog −$27.

σ ntawm 100 zaus kiv, txhua zaus $10$
Twv ib tus lej
$584
Twv ob tus lej
$409
Twv ib kab
$328
Twv plaub ces kaum
$284
Twv ob kab
$223
Pawg kaum ob / kab ntsug
$139
Them sib npaug
$100
$
0292$584

Cov lus nug

Vim li cas EV thiaj zoo tib yam ntawm txhua kab?

Vim txhua yam nyiaj them yog 36/n − 1 piv rau qhov ncaj ncees 37/n − 1. Saib nplooj 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 →.

La partage nyob qhov twg?

Kev twv them sib npaugkev twvKev twv them sib npaugLiab/dub, khib/txawm, siab/qis. 18 tus lej, them 1:1.Nyeem tag nrho → ntawm lub rooj Fabkis: p thiab nyiaj them tsis hloov, EV −1.35%, σ ≈ 0.99.

Puas muaj daim ntawv rau lub log Asmeskas?

Muab faib rau 38 es tsis yog 37 ces kab EV dhau los ua −5.26% ntawm txhua kab, thiab −7.89% rau kev twv tsib tus lej.

Lus lom zem

Cuaj yam kev twv, ib tus nqi xav tias yuav tau, tsis nco qab dab tsi li.

Cuaj yam kev twv, ib tus nqi xav tias yuav tau, tsis nco qab dab tsi li.

Qhov chaw los

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Tshooj 13, roulette.
Lej rouletteFeem tshwm sim hauv rouletteLej rouletteKev hloov pauv (variance)Kawm rouletteNyiaj them hauv rouletteCuab yeej rouletteCuab yeej suav feem roulette
kuaj xyuas 2026-09-28qauv: roulette Europe, ib lub xoomtxoj kev ua haujlwm ↗qhov chaw los ↗