Piv txwv: tswv yim ob pawg kaum ob hauv roulette
Kaum duas las rau txhua ob pawg kaum ob, npog 24 tus lej, rau tsib caug zaus kiv. Tswv yim roulette ob pawg kaum ob yog kev twv npog uas yeej ob zaus kiv hauv peb thiab tseem raug nqi 2.70%.
Ib zaug ua si sim 50 zaus kiv, $10 rau pawg kaum ob thib ib thiab thib ob. Peb caug ib zaug yeej $10, kaum cuaj zaug poob $20 (pawg kaum ob thib peb lossis xoom). Tag nrho −$70, tom qab tau nce $90. Qhov twv uas hnov zoo li nyab xeeb vim nws yeej ntau zaus thiab raug nqi raws nkaus li txhua lwm qhov.
Txoj kev npaj: tswv yim roulette ob pawg kaum ob
$10 rau pawg kaum obkev twvPawg kaum ob1–12, 13–24 lossis 25–36, them 2:1.Nyeem tag nrho → thib ib thiab $10 rau thib ob. Ib tus lej ntawm 1 txog 24 them ib pawg $20 thiab poob lwm pawg $10: +$10. Ib tus lej ntawm 25 txog 36, lossis 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 →, poob ob pawg: −$20. 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 →: (24 × 10 − 13 × 20)/37 = −20/37 = −$0.54 ib zaus kiv, uas yog 2.70% ntawm $20. Feem yeej 64.9%, uas yog tus lej uas muag qhov twv no.
Zaus kiv 1–25
Kaum yim zaug yeej, xya zaug poob: +$180 − $140 = +$40. Xya zaug poob suav nrog xoom ib zaug thiab peb tus lej pawg kaum ob thib peb sib law liag ntawm zaus kiv 11–13 uas raug nqi $60 ua ke thiab hnov zoo li yog qhov tsis tshua muaj. Nws yog 35.1% tuaj ua ib pawg, ib yam li cov pawg feem ntau ua.
Zaus kiv 26–50
Kaum peb zaug yeej, kaum ob zaug poob: +$130 − $240 = −$110. Kaum ob zaug poob hauv 25 zaus kiv yog ib qho 20% uas tshwm sim, tsis yog qhov tsis tshua muaj. Thaum kawg −$70; siab tshaj +$90 ntawm zaus kiv 31. Qhov twv no yeej tsis tau nce nqis loj rau sab twg li, vim yeej yog $10 thiab poob yog $20; nws tsuas maj mam zom mus xwb.
- p10 −$500
- p25 −$500
- median −$280
- p75 −$40
- p90 +$170
Kev suav nyiaj
Tag nrho twv $1,000 rau 50 zaus kiv. Nyiaj yuav poob raws nruab nrablejNyiaj yuav poob raws nruab nrabNqi xav tias yuav tau muab sib npaug rau tag nrho cov nyiaj twv; cov nyiaj nruab nrab uas poob hauv ib zaug ua si lossis ib lub sij hawm.Nyeem tag nrho → $27; tiag tiag −$70, kwv yees li ib 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 → qis dua (σ ib zaus kiv kwv yees li $14, yog li kwv yees li $100 rau 50 zaus kiv). Tib $20 rau liabkev twvLiabKev twv them sib npaug rau 18 tus lej liab. Lus Fabkis: rouge.Nyeem tag nrho → yuav muaj tib qhov xav tias yuav muaj thiab σ loj dua, kwv yees li $140 rau tag zaug ua si: ob pawg kaum ob yog ib txoj kev 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 → qis dua los poob tib tus nqi.
Zaug ua si no qhia dab tsi
Npog 24 tus lej ua rau roulette hnov zoo li ib qho kev ua si uas feem ntau koj yeej, thiab koj yeej tiag: 64.9% ntawm cov zaus kiv. 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 → teeb kom 35.1% uas koj poob raug nqi ob npaug ntawm qhov yeej them, thiab qhov piv no 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 → kho kom tau −1/37 ntawm tag nrho nyiaj twv. Ntxiv ib 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 → rau xoom ua “kev pov hwm” thiab feem tsev twv txiaj sib xyaw tseem yog 2.70%, vim kev pov hwm kuj raug nqi 2.70% thiab. Nplooj ntawv Teeb meem: Ob Pawg Kaum Ob thiab Ib Lub Npib suav nws kom ntxaws.
Cov lus nug
Tib yam lej: 24 tus lej, +1 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 → thaum tawm, −2 thaum tsis tawm. Kab ntsugkev twvKab ntsugKaum ob tus lej nyob hauv ib kab ntsug ntawm daim duab rooj twv, them 2:1.Nyeem tag nrho → faib cov lej uas npog thoob plaws lub log; pawg kaum ob sau lawv ua ib pawg ntawm daim duab rooj twv. Ob qho tsis tseem ceeb.
Npog 25 tus lej; tam sim no xoom tau +$15 es tsis yog −$20, raug nqi $1 ib zaus kiv. Nqi xav tias yuav tau yog −$0.57 rau $21, tseem yog 2.70%.
Nws yog, thiab nyiaj them teeb raws li ntawd. Feem ntau ntawm lub sij hawm koj yeej $10. Qee lub sij hawm koj poob $20. Qhov nruab nrab 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 →.
Lus lom zem
Yeej ob zaus kiv hauv peb. Poob ob npaug ntawm zaus thib peb. Qhov tshwm sim yog 2.70%.
Qhov chaw los
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.