Nkọwa Nzọụkwụ: Oge Egwuregwu Martingale
Dollar iri na uhie, a na-eme ya okpukpu abụọ mgbe mfu ọ bụla gachara, na tebụl $500. Ntụgharị na ntụgharị, gụnyere ntụgharị na-akwụsị ya.
Oge egwuregwu Martingale e mere ka ọ dị site n’ego egwuregwu $1,000. Obere mmeri iri anọ na otu, mgbe ahụ mfu isii n’usoro na nzọ nke asaa a jụrụ. Oge egwuregwu ahụ na-akwụsị n’ala $220 mgbe ọ nọbu n’elu $410, nke bụ ihe usoro ahụ na-eme.
Atụmatụ ahụ
Gbaa nzọ $10 na uhienzọUhieNzọ ego hara nhata na nọmba uhie 18. French: rouge.Gụọ ya niile →. Mgbe mfu gachara, mee ya okpukpu abụọ. Mgbe mmeri gachara, laghachi na $10. Oke tebụltebụlOke tebụlNzọ kacha nta na nke kachasị ukwuu a na-ekwe. Nke kachasị ukwuu bụ ihe na-akwụsị usoro mmụba nzọ okpukpu abụọ.Gụọ ya niile → $500, ya mere ego nzọ bụ 10, 20, 40, 80, 160, 320 na mgbe ahụ nzọ $640 nke tebụl ga-ajụ. Mfu isii n’usoro na-emebi usoro ahụ; mgbalị ọ bụla nwere (19/37)⁶ ≈ 1.8% nke ime nke ahụ, oge egwuregwu nke ntụgharị 100 nwekwara ihe dị ka mgbalị 50. A tụrụ anya: ihe dị ka ohere 60% nke imebi n’ime ntụgharị 100, na mfu $630 mgbe ọ mere.
Ntụgharị 1–30
MartingaleatụmatụMartingaleUsoro mmụba nzọ na-eme nzọ okpukpu abụọ mgbe mfu ọ bụla gasịrị. Lee ngalaba Atụmatụ maka ihe ọ na-eme na ihe ọ naghị eme.Gụọ ya niile → nkịtị: usoro mfu otu ruo atọ, nke ọ bụla mmeri na-akwụsị ya nke na-ewete +$10. Ka ọ na-erule ntụgharị 30 anyị enwetala mmeri 17, nke ọ bụla na-emechi cycle, anyị nọkwa n’elu $170. Ego nzọ kachasị ukwuu ruo ugbu a bụ $80 mgbe mfu atọ gachara. Ọ dị ka igwe na-ebipụta akwụkwọ ego $10.
Ntụgharị 31–60
Otu ihe ahụ ọzọ, na otu cycle nwere mfu anọ (ego nzọ ruo $160, mgbe ahụ mmeri) nke tinyere $310 na tebụl nwa oge ma dị ka obi ike. Mgbe ntụgharị 60 gachara: cycle 41 zuru ezu, n’elu $410, ebe kachasị ala nke ego egwuregwuegoEgo egwuregwuNgụkọta ego e debere maka igwu egwu. Njikwa ego egwuregwu bụ ikpebi ole n’ime ya a ga-etinye n’ihe egwu kwa nzọ na kwa oge egwuregwu.Gụọ ya niile → bụkwa $1,040. Histogram nke oge egwuregwu Martingale ọ bụla na-adị otú a n’ọtụtụ ogologo ya.
Ntụgharị 61–66
F F F F F F. Ego nzọ 10, 20, 40, 80, 160, 320: e tufuru $630. Nzọ na-esote ga-abụ $640; oke ahụ bụ $500. Usoro ahụ emebiela. Anyị nwere ike ịgba nzọ $500 (ọ bụrụkwa na o meriri, anyị ka ga-anọ n’ala $130 na cycle ahụ) ma ọ bụ laghachi na $10 ma nabata mfu ahụ. OjinzọOjiNzọ ego hara nhata na nọmba oji 18. French: noir.Gụọ ya niile → ma ọ bụ efuwiilEfuOtu oghere akwụkwọ ndụ nke nzọ ego hara nhata, dozen ma ọ bụ column ọ bụla na-ekpuchighị; isi mmalite uru ụlọ. A na-akpọkwa ya: single zero, 0.Gụọ ya niile → isii n’usoro nwere oheremgbakọOhereOhere nke otu nsonaazụ, site na 0 ruo 1 ma ọ bụ 0% ruo 100%. Otu nọmba: 1/37 = 2.70%.Gụọ ya niile → 1.8% kwa cycle. Anyị agbaala ihe dị ka cycle 45. Ohere iru ebe a n’ebe ụfọdụ n’ime cycle 45 bụ ihe dị ka 55%. Ọ bụghị ọdachi; ọ bụ etiti.
- p10 −$1,000
- p25 −$1,000
- median −$1,000
- p75 +$790
- p90 +$1,690
Akaụntụ
N’elu $410 mgbe ntụgharị 60 gachara, n’ala $220 mgbe 66 gachara. Ngụkọta nzọ: ihe dị ka $2,100 n’ime ntụgharị 66, megide $660 maka onye na-agba nzọ otu ọnụ $10. Mfu a tụrụ anyamgbakọMfu a tụrụ anyaUru a tụrụ anya mụbara na ngụkọta ego e tinyere na nzọ; nkezi ego a na-atụfu n’otu oge egwuregwu ma ọ bụ n’otu oge.Gụọ ya niile → na $2,100 nke ngụkọta nzọegoNgụkọta nzọNgụkọta ego e tinyere na nzọ n’otu oge egwuregwu ma ọ bụ otu oge, gụnyere mmeri a gbara nzọ ọzọ. A na-akpọkwa ya: handle, action.Gụọ ya niile → bụ $57; −$220 anyị nwetara n’ezie dị ihe dị ka otu ụzọ n’ụzọ atọ nke standard deviationmgbakọStandard deviationMgbọrọgwụ square nke mgbasa; anya nkịtị dị n’etiti otu nsonaazụ na uru a tụrụ anya.Gụọ ya niile → n’okpuru ya, nke abụghị ihe ijuanya maka usoro nke nkesa ya nwere ọdụ aka ekpe dị ogologo. Ọ bụrụ na anyị kwụsịrị na ntụgharị 60 na stop-winatụmatụStop-winEbumnuche uru a kara aka tupu oge eruo, nke ị ga-akwụsị oge egwuregwu ma i rute ya.Gụọ ya niile → nke $400, anyị gaara apụ n’elu $410, oge egwuregwu na-esote gaara ebukwa otu 1.8% ahụ kwa cycle.
Ihe oge egwuregwu a na-egosi
Martingale na-agbanwe nzọ 48.65% ka ọ bụrụ usoro na-emeri 98% nke cycle ya ma tufuo unitegoUnitEgo nzọ ntọala nke otu usoro ma ọ bụ onye egwuregwu na-eji arụ ọrụ. A na-akọwa usoro mmụba nzọ na unit ka ha metụta tebụl ọ bụla.Gụọ ya niile → 63 na 2% nke ọzọ. Ọ naghị agbanwe mfu a tụrụ anya kwa dollar; ọ na-amụba dollar ndị ahụ. Onye na-agba nzọ otu ọnụ nọ n’akụkụ anyị gbara otu ụzọ n’ụzọ atọ nke ego ahụ ma tufuo, na nkezi, otu ụzọ n’ụzọ atọ. Onye egwuregwu na-agba usoro a otu afọ ga-emeri ọtụtụ mgbede ma tufuo afọ ahụ.
Ugboro ole usoro mfu na-abịa
Nzọ ego hara nhata na wiil otu efu na-atụfu ntụgharị 19 n’ime 37. Ahịrị ọ bụla bụ ohere na otu usoro ntụgharị niile ga-atụfu, na ihe onye na-egwu Martingale, onye na-eme ka nzọ okpukpu abụọ mgbe mfu ọ bụla gasịrị, tufuola ruo mgbe ahụ.
| mfu n’usoro | ohere | ihe dị ka 1 n’ime | e tufuola ruo ugbu a | nzọ na-esote |
|---|---|---|---|---|
| 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 |
Ohere ahụ bụ 19/37 a mụbara n’onwe ya otu ugboro kwa mfu, a gụrụ site n’otu ntụgharị e nyere. Oge egwuregwu dị ogologo nwere ọtụtụ ntụgharị ebe usoro dị otú ahụ nwere ike ịmalite, ya mere n’otu mgbede ọ ka nwere ike ime karịa ka otu ahịrị na-egosi.
Ajụjụ
Mfu itoolu na-emebi ya kama isii: 0.25% kwa cycle, na $5,110 a na-atụfu mgbe ọ mere. Ndagwurugwu na-adịkarịghị, ndagwurugwu dị elu karịa, otu −2.70%.
Ọ gaara emeri 48.65% nke oge ma hapụ cycle ahụ na −$130 n’agbanyeghị. Ọ dịghị ezigbo mmegharị mgbe Martingale mebiri; ọ bụ naanị ego nzọ ị họọrọ na-esote.
Ee, maka oge egwuregwu ahụ. Ọ bụghị maka nkezi n’oge egwuregwu niile.
Egwuregwu Mgbakọ
Buru ụzọ nwaa ha n’onwe gị. A pịachiri azịza ọ bụla; meghee ya mgbe ị dị njikere.
Na tebụl $1 ruo $500, onye egwuregwu MartingaleatụmatụMartingaleUsoro mmụba nzọ na-eme nzọ okpukpu abụọ mgbe mfu ọ bụla gasịrị. Lee ngalaba Atụmatụ maka ihe ọ na-eme na ihe ọ naghị eme.Gụọ ya niile → na-amalite na $1 na uhienzọUhieNzọ ego hara nhata na nọmba uhie 18. French: rouge.Gụọ ya niile → na wiil otu efuwiilEfuOtu oghere akwụkwọ ndụ nke nzọ ego hara nhata, dozen ma ọ bụ column ọ bụla na-ekpuchighị; isi mmalite uru ụlọ. A na-akpọkwa ya: single zero, 0.Gụọ ya niile →. Mfu ole n’usoro na-akwụsị ime okpukpu abụọ ahụ, ego ole ka a tụfuru ka ọ na-erule mgbe ahụ, ugboro ole ka ọ na-emekwa?
Gosi azịza ya
Azịza Mfu itoolu: $511 a tụfuru, nzọ na-esote ga-abụkwa $512. Ọ na-eme otu ugboro n’ime ihe dị ka usoro 403.
Ego nzọ ndị ahụ bụ 1, 2, 4, 8, 16, 32, 64, 128 na 256: ọnụ $511. Nke iri ga-abụ $512, karịrị oke ahụ. Nzọ $500 meriri ka na-ahapụ onye egwuregwu ahụ $11 n’ala; nke tufuru na-ahapụ ya $1,011 n’ala.
Uhie na-atụfu na ohere 19/37, ya mere mfu itoolu n’usoro nwere ohere (19/37)⁹ ≈ 0.25%, otu ugboro n’ime ihe dị ka usoro 403. Usoro ọ bụla zuru ezu na-emeri $1, ya mere onye egwuregwu ahụ na-atụ anya ihe dị ka $402 nke obere mmeri tupu otu mfu $511 ahụ, a ka na-atụfukwa 2.70% nke ihe niile a gbara na nzọ na nkezi.
Na wiil efu abụọ, ohere ahụ bụ (20/38)⁹, otu ugboro n’ime ihe dị ka 323. Bollman (2021) bipụtara “ihe dị ka 1 n’ime 833”, nke bụ (18/38)⁹, ohere nke mmeri itoolu n’usoro.
Ihe ọchị
Obere mmeri iri anọ na otu na otu mfu buru ibu. Nke ahụ bụ usoro ahụ niile.
Isi Mmalite
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”