Lej roulette · Teeb meem lej · 7 feeb

Lo lus nug: ob pawg kaum ob thiab ib lub npib

Ob pawg kaum ob npog 24 tus lej. Ntxiv ib lub npib rau xoom ces koj npog 25. Qhov kev tiv thaiv no puas them tau?

Lus teb luv

Tsis them. Txhua feem yog −2.70% ntawm nws nyiaj twv, yog li tag nrho ua ke yog −2.70% ntawm tag nrho. Teeb meem no piav tias vim li cas, suav kev faib tawm tseeb, thiab qhia tias yam twg hloov (tus qauv) thiab yam twg tsis hloov (tus nqi).

ob pawg kaum ob
24/37 · tau +1 lossis −2
ntxiv xoom
npog 25/37
EV rau ib chav twv
−1/37 txawm li cas los xij
zaj lus qhia
cov EV sib ntxiv

Teeb meem

Koj twv $10 rau pawg kaum obkev twvPawg kaum ob1–12, 13–24 lossis 25–36, them 2:1.Nyeem tag nrho → thib ib, $10 rau pawg kaum ob thib ob thiab $1 rau 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 →. (a) Muaj cov qhov tshwm sim twg thiab lawv feem tshwm sim yog pes tsawg? (b) 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 → yog pes tsawg? (c) Lub 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 → xoom puas ua rau qhov twv zoo dua?

Kev daws (a) thiab (b)

Cov qhov tshwm sim: lub pobkhoom sivLub pobLub pob me me uas raug tso khiav raws txoj kev mus rov qab rau lub log kiv. Cov pob niaj hnub no ua los ntawm ivorine lossis Teflon, 18–21 mm.Nyeem tag nrho → poob rau 1–24 (24 lub qhovkhoom sivLub qhovIb ntawm 37 lub qhov muaj lej saum lub log kiv. Kuj hu ua: slot, khob.Nyeem tag nrho →): ib pawg kaum ob them $20, pawg tod poob $10, xoom poob $1: tau +$9. Lub pob poob rau 25–36 (12 lub qhov): ob pawg kaum ob poob, xoom poob: −$21. Lub pob poob rau xoom (1 lub qhov): cov pawg kaum ob poob $20, xoom them $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57 ib zaus kiv rau $21 nyiaj twv: 2.70%.

qhov tshwm simqhovfeem tshwm simqhov tshwm sim
1–242464.9%+$9
25–361232.4%−$21
012.7%+$15
xav tias yuav tau−$0.57 = 2.70% ntawm $21

Kev daws (c)

Yog tsis muaj lub npib xoom: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54 rau $20 nyiaj twv, kuj yog 2.70%. Lub npib xoom tau hloov qhov tshwm sim xoom −$20 mus ua +$15 (zoo dua $35 ib zaug hauv 37, muaj nqis $0.95 ib zaus kiv) thiab raug nqi $1 rau 36 zaus kiv tod (muaj nqis $0.97 ib zaus kiv). Qhov hloov tag nrho: −$0.03 ib zaus kiv, uas yog 2.70% ntawm ib duas las ntxiv ntawd. Qhov kev tiv thaiv no raug nqi ib yam li txhua yam.

Vim li cas qhov no siv tau rau txhua yam

Cov nqi xav tias yuav tau sib ntxiv. Txhua pawg kev twv ua ib zaug ua ke muaj EV sib npaug rau qhov sib ntxiv ntawm cov EV ntawm txhua feem, uas txhua feem yog −1/37 ntawm nws nyiaj twv. Yog li txhua yam muab ua ke yog −1/37 ntawm tag nrho nyiaj twv. Tsis muaj ib txoj kev tso npib rau ntawm daim duab rooj twvkhoom sivDaim duab rooj twvDaim duab twv uas luam rau saum lub rooj. Kuj hu ua: rooj, ntaub ntsuab, ntaub.Nyeem tag nrho →, txawm ntau npaum li cas, uas dim tau qhov no; lub cuab yeej Tsim Kev Twv yuav qhia tib yam rau txhua pawg uas koj tso tau. Qhov uas kev muab ua ke hloov yog kev faib tawm: koj yeej ntau zaus npaum li cas, yeej tau pes tsawg, thiab qhov phem tshaj phem npaum li cas.

Tib $21 peb txoj kev: feem yeej thiab qhov phem tshaj
$21 rau liab: p(yeej)
48.6% · phem tshaj −$21
ob pawg kaum ob + xoom: p(yeej)
67.6% · phem tshaj −$21
$21 rau 17: p(yeej)
2.7% · phem tshaj −$21
033.8067.6% · phem tshaj −$21
Tag nrho peb yam muaj EV −$0.57 ib zaus kiv. Lawv txawv tsuas yog tus qauv xwb.

Teeb meem tom ntej uas nyuaj dua

Nrhiav ib pawg kev twv txheem uas npog tag nrho 37 tus lej. Peb pawg kaum ob ($10 txhua pawg) ntxiv $1 rau xoom: ib tus twg ntawm 1–36 tau −$1 (ib pawg kaum ob them $20, ob pawg tod poob $20, xoom poob $1), thiab xoom tau +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 rau $31 nyiaj twv: 2.70%. Koj lav tau tias koj yeej tsis xav tsis thoob li, thiab koj tseem them tib tus nqi rau txoj cai ntawd.

Qauv lej

EV(muab ua ke) = Σ EV(cov feem) = −(tag nrho nyiaj twv)/37

Cov lus nug

Puas muaj ib pawg kev twv twg uas muaj feem tsev twv txiaj qis dua?

Tsis muaj, ntawm lub rooj Europe. Ntawm lub rooj Fabkis, tsuas yog kev twv them sib npaugkev twvKev twv them sib npaugLiab/dub, khib/txawm, siab/qis. 18 tus lej, them 1:1.Nyeem tag nrho → xwb yog 1.35%; ntxiv lwm yam twg los kuj tsa feem tsev twv txiaj ua ke.

Ua li cas yog twv ob qho liab thiab dub?

Poob $1 rau txhua $1 thaum xoom xwb, lwm zaus tsis tau dab tsi li. EV −2.70% tsis muaj qhov zoo li: tib pawg uas tsis muaj qab hau kiag li.

Yog li ntawd vim li cas thiaj muab kev twv los ua ke?

Kom xaiv tau tus qauv zaus ua si uas koj nyiam. Qhov ntawd yog ib qho laj thawj tseeb thiab yog tib qho xwb.

Lus lom zem

Kev tiv thaiv ntawm lub rooj roulette raug nqi npaum li nws txuag tau tseeb.

Kev tiv thaiv ntawm lub rooj roulette raug nqi npaum li nws txuag tau tseeb.

Qhov chaw los

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Tshooj 13, roulette.
kuaj xyuas 2026-09-28qauv: roulette Europe, ib lub xoomtxoj kev ua haujlwm ↗qhov chaw los ↗