Tswv yim · Kev nce nyiaj twv tom qab poob · 9 feeb

Tswv yim Martingale hauv roulette

Tswv yim Martingale hauv roulette muab nyiaj twv ntxiv ob npaug tom qab txhua zaus poob thiab rov qab mus rau nyiaj twv pib tom qab yeej. Txhua zaus yeej rov qab tau tag nrho cov nyiaj poob ua ntej ntxiv rau ib chav twv pib. Nplooj ntawv hauv qab no qhia tias qhov ntawd ua li cas rau nyiaj peev twv, thiab vim li cas nws hloov tsis tau nyiaj yuav poob raws nruab nrab.

Lus teb luvNws yeej tsis tau lub log. Ua ib txoj tswv yim muab ob npaug hauv roulette, Martingale ua rau yeej me me ntau zaus thiab qee zaus poob loj. Txawm kiv pes tsawg zaus los xij, nyiaj yuav poob raws nruab nrab tseem yog 2.70% ntawm tag nrho nyiaj twv, thiab vim kev nce nyiaj twv twv ntau, nyiaj yuav poob raws nruab nrab hauv ib zaug ua si loj dua li twv tib yam nyiaj, tsis yog me dua.

Txheej txheem twv Martingale hauv roulette ua hauj lwm li cas?

Poob, ces muab ob npaug. Yeej, ces rov qab mus rau nyiaj twv pib. Ntawd yog tag nrho txheej txheem twv. Nrog nyiaj twv pib $10 thiab ciam twv ntawm lub rooj $500, kab ke tag tom qab rau zaus poob. Kab kawg yog feem tshwm sim uas yuav mus txog kauj ruam ntawd rau kev twv them sib npaug, uas txhua zaus poob muaj feem tshwm sim 19/37.

poob #nyiaj twv tom ntejtag nrho nyiaj pheej hmoop(mus txog)

0$10$10100.00%

1$20$3051.35%

2$40$7026.37%

3$80$15013.54%

4$160$3106.95%

5$320$6303.57%

6$640$1,2701.83%

7$1,280$2,5500.94%

Nyiaj twv pib $10, ciam twv ntawm lub rooj $500. Tom qab rau zaus poob, nyiaj twv tom ntej yog $640, siab dua ciam: kev nce nyiaj twv tawg thiab poob $630. Feem tshwm sim uas yuav poob rau zaus sib law liag rau liab yog (19/37)^6 = 1.83%, kwv yees li ib zaug hauv txhua 55 zaus sim.

Taug txheej txheem

Poob ces muab nyiaj twv ntxiv ob npaug. Yeej ces rov qab mus rau thaum pib.

nyiaj twv tom ntej1qhov tshwm sim txog tam sim no0zaus kiv0

Nyiaj twv thiab qhov tshwm sim yog suav ua chav twv ntawm nyiaj twv pib.

Ib zaug ua si zoo li cas?

Nce me me ib kauj ruam zuj zus, ces muaj ib lub qhov ntxiab. Hauv Martingale roulette, txhua ncig muab ob npaug uas ua tiav ntxiv ib qho nyiaj twv pib, yog li kab nce zuj zus. Ncig uas tsoo ciam $500 nqa $630 rov qab ib zaug: 63 ntawm cov kauj ruam ntawd.

Kaum zaug ua si Martingale, pib $10, ciam $500qhov tshwm sim piv rau thaum pib

1,000 zaus ua si × 500 zaus kiv · ntshav p10/p25/p75/p90, xiav dawb median, 83 kab piv txwv tsaus · txav hla daim duab kom pom quantile ntawm ib zaus kiv

p10 −$1,000
p25 −$1,000
median −$1,000
p75 +$930
p90 +$1,830

1,000 zaus ua si × 500 zaus kiv · kab y txiav rau feem pua thib 1–99 (ntug −$1,000 txog +$2,640) · 500 zaus kiv · pib $10 · them sib npaug

Txhua kab yog ib zaug ua si kev twv them sib npaug pib ntawm nyiaj peev twv $1,000. Nce ntev, poob sai.

Nce me me ib kauj ruam zuj zus, ces muaj ib lub qhov ntxiab uas nqa tag nrho rov qab ib zaug.

Cuab yeej sim

Txhua qhov teeb tseg khiav 2,000 zaus ua si kev twv them sib npaug pib ntawm nyiaj peev twv $1,000. Cov qhov tshwm sim hloov tshiab tam sim ntawd.

Nyiaj twv pib

Ciam twv ntawm lub rooj

Zaus kiv rau ib zaus ua si

Qhov tshwm sim zaus ua si · 2,000 zaus ua si · 100 zaus kiv · pib $10 · ciam $500poob ← | → tau

−$1,000$0+$650

taw rau ib tug kem · kem liab yog zaus ua si poob, ntsuab yog yeej, kem daj ntseg hla $0

zaus ua si tau nyiaj

40.8%

qhov tshwm sim median

−$130

qhov tshwm sim nruab nrab

−$66.44

kev nce nyiaj twv tawg

59.3% ntawm cov zaus ua si

feem pua thib 5

−$1,000

nyiaj peev txo qis tshaj (median)

−$650

Feem ntau cov zaus ua si xaus nrog tau me ntsis (40.8%), qhov no yog vim li cas neeg thiaj nyiam. Qhov nruab nrab yog tsis zoo (−$66.44) vim cov zaus ua si poob loj heev: kev nce nyiaj twv ntsib ciam twv ntawm lub rooj hauv 59.3% ntawm cov zaus ua si. Tus neeg twv tib yam nyiaj $10 hauv tib cov zaus kiv xav tias yuav poob kwv yees li $27.

Kev poob sib law liag tuaj ntau npaum li cas

Ib qho kev twv them sib npaug ntawm lub log ib lub xoom poob 19 zaus kiv hauv 37. Txhua kab yog feem tshwm sim uas ib txheej zaus kiv poob tag nrho, thiab tus neeg ua si Martingale, uas muab nyiaj twv ntxiv ob npaug tom qab txhua zaus poob, twb poob pes tsawg lawm thaum ntawd.

Nyiaj twv pib

poob sib law liag	feem tshwm sim	kwv yees li 1 hauv	poob txog tam sim no	qhov twv tom ntej
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

Feem tshwm sim yog 19/37 muab sib khoo nws tus kheej ib zaug rau txhua zaus poob, suav pib ntawm ib zaus kiv uas teem tseg. Ib zaus ua si ntev muaj ntau zaus kiv uas txheej poob zoo li no pib tau, yog li hauv ib hmo nws yuav tshwm sim ntau dua li ib kab qhia.

Kaum tsib zaus poob sib law liag tshwm sim kwv yees li ib zaug hauv 22,000 zaus sim. Hnov zoo li muaj kev nyab xeeb. Tsis yog li, vim ob qho laj thawj. Txhua zaus kiv pib ib zaus sim tshiab, thiab ib hmo muaj ntau pua zaus kiv. Thiab tsis muaj leej twg mus txog kaum tsib: pib ntawm $10, ciam $500 nres kev muab ob npaug tom qab rau zaus poob, uas tshwm sim kwv yees li ib zaug hauv 55 zaus sim.

Vim li cas nws hloov tsis tau feem?

Nqi xav tias yuav tau ntxiv tau ua ke. Yog txhua qhov twv muaj qhov xav tias yuav tau −2.70% ntawm nws cov nyiaj twv, ces txhua kab ke kev twv, txawm xaiv nyiaj twv li cas los xij, muaj qhov xav tias yuav tau −2.70% ntawm tag nrho nyiaj twv. Kev xaiv nyiaj twv nyob ntawm cov qhov tshwm sim dhau los tau; nws nyob ntawm qhov tom ntej tsis tau.

E[Σ bᵢ·Xᵢ] = Σ bᵢ·E[Xᵢ] = −(1/37)·Σ bᵢ
bᵢ xaiv ua ntej zaus kiv i; Xᵢ = ±1 tsis cuam tshuam rau bᵢ

Cov kev nkag siab yuam kev uas muaj ntau

“Koj tsuas yuav tsum yeej ib zaug xwb los rov qab tau txhua yam.”

Muaj tseeb hauv ib ncig nce nyiaj twv uas ua tiav. Ncig uas ua tsis tiav, vim ciam twv ntawm lub rooj los sis koj cov nyiaj peev twv, poob tag nrho kab ke, thiab kab ke ntawd loj vim nws tsim li ntawd.

“Yog nyiaj peev twv loj txaus nws yuav tsis tawg.”

Ciam twv ntawm lub rooj nres kev muab ob npaug ua ntej feem ntau cov nyiaj peev twv tag ntev. Yog tsis muaj ciam, cov nyiaj peev twv uas xav tau loj tuaj sai heev (exponential) thaum nyiaj tau ib ncig tseem yog ib chav twv pib xwb.

“Poob rau zaus sib law liag yuav luag tsis muaj peev xwm tshwm sim.”

Rau liab nws tshwm sim hauv 1.83% ntawm cov qhov rais rau zaus kiv. Hauv ib zaug ua si 200 zaus kiv, feem ntau koj yuav pom tsawg kawg ib qho poob rau zaus sib law liag.

Lus lom zem

Yeej me me ntau zaus, poob loj ib zaug tsawg tsawg. Thiab koj them qhov poob ntawd koj tus kheej.

Qhov xaus raws lejTxheej txheem twv Martingale hauv roulette pauv feem tshwm sim siab uas yuav yeej me ntsis rau feem tshwm sim tsawg uas yuav poob ntau. Nws zoo li kev pov hwm uas muag rov qab: feem ntau hmo koj sau tau nyiaj me me thiab qee zaus tsawg tsawg koj them qhov poob loj koj tus kheej. Nws ua rau nyiaj twv nce hauv ib zaug ua si, yog li nws ua rau nyiaj yuav poob raws nruab nrab hauv ib zaug ua si nce. Nws tsis txo thiab txo tsis tau feem tsev twv txiaj. Yog koj tseem siv tswv yim Martingale hauv roulette, paub koj qhov tawg ua ntej: nrog nyiaj twv pib $10 thiab ciam $500, ntawd yog rau zaus poob sib law liag, ib qho uas tshwm sim 1.8% rau txhua zaus sim. Saib Kev tswj nyiaj peev twv thiab Ciam poob / ciam yeej.