Nkyerɛkyerɛmu: Martingale agorɔ bere
Dɔla du wɔ kɔkɔɔ so, a wobɔ ho mmienu ahwereɛ biara akyi, wɔ $500 ɛpono so. Kyinhyia biara so, a kyinhyia a ɛde ba awieeɛ no ka ho.
Martingale agorɔ bere a ɛyɛ sɔhwɛ firi agorɔ dwetire $1,000 mu. Nkonim nketewa aduanan baako, afei ahwereɛ nsia a ɛtoatoa so ne bɛt a ɛtɔ so nson a ɛpono no amma kwan. Agorɔ bere no ba awieeɛ a ɛkɔ fam $220, na kane no na ɛkɔɔ soro $410; ɛno ne deɛ nhyehyɛe no yɛ.
Nhyehyɛe no
To $10 bɛt wɔ kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → so. Sɛ wohwere a, bɔ ho mmienu. Sɛ wodi nkonim a, san kɔ $10 so. Ɛpono ahyeɛɛponoƐpono ahyeɛBɛt sika ase koraa ne soro koraa a wɔma kwan. Ahyeɛ soro no na ɛsiw mmɔho mmienu bɛt nsakraeɛ ntoatoasoɔ.Kenkan ne nyinaa → yɛ $500, enti bɛt sika no yɛ 10, 20, 40, 80, 160, 320 na afei $640 bɛt a ɛpono no remma kwan. Ahwereɛ nsia a ɛtoatoa so bu nhyehyɛe no; mmɔden biara wɔ (19/37)⁶ ≈ 1.8% sɛ ɛbɛyɛ saa, na agorɔ bere a ɛwɔ kyinhyia 100 mu bɛyɛ mmɔden 50. Deɛ wɔhwɛ kwan: bɛyɛ 60% hokwan sɛ ɛbɛbu wɔ kyinhyia 100 mu, ne ahwereɛ $630 sɛ ɛba saa a.
Kyinhyia 1–30
MartingaleɔkwanMartingaleBɛt nsakraeɛ ntoatoasoɔ a ɛbɔ bɛt no mmɔho mmienu ahwereɛ biara akyi. Hwɛ Akwan ɔfa no na hunu deɛ ɛyɛ ne deɛ ɛnyɛ.Kenkan ne nyinaa → a ɛyɛ daa: ahwereɛ baako kɔsi mmiɛnsa ntoatoasoɔ, na biara wie wɔ nkonim a ɛde +$10 ba. Kyinhyia 30 so no, yɛadi nkonim 17, a biara wie ɔkwan no kyinhyia mua, na yɛkɔ soro $170. Bɛt sika a ɛkɔɔ soro sen biara kɔsii saa bere no yɛ $80 wɔ ahwereɛ mmiɛnsa akyi. Ɛyɛ sɛ afidie a ɛtintim $10 krataa sika.
Kyinhyia 31–60
Saa ara bio, ne kyinhyia mua baako a ahwereɛ ɛnan wom (bɛt sika kɔɔ $160, na afei nkonim), a ɛde $310 too ɛpono no so bere tiaa bi na ɛyɛɛ sɛ akokoduru. Kyinhyia 60 akyi: kyinhyia mua 41 awie, yɛkɔ soro $410, na agorɔ dwetiresikaAgorɔ dwetireSika a woayi asie nyinaa ama agorɔ. Agorɔ dwetire so hwɛ ne sɛ wobɛsi gyinaeɛ wɔ dodoɔ a wode bɛto asiane mu wɔ bɛt biara ne agorɔ bere biara mu.Kenkan ne nyinaa → no baabi a ɛbaa fam sen biara yɛ $1,040. Martingale agorɔ bere biara ho mfonin te saa wɔ ne tenten no dodoɔ no ara mu.
Kyinhyia 61–66
H H H H H H. Bɛt sika 10, 20, 40, 80, 160, 320: $630 ahwere. Bɛt a ɛdi so no bɛyɛ $640; ahyeɛ no yɛ $500. Nhyehyɛe no abu. Yɛbɛtumi de $500 ato bɛt (na sɛ ɛdi nkonim mpo a, yɛda so kɔ fam $130 wɔ kyinhyia mua no mu) anaa yɛsan kɔ $10 so na yɛgye ahwereɛ no tom. TuntumbɛtTuntumSika pɛ bɛt wɔ nɔma tuntum 18 no so. Franse kasa mu: noir.Kenkan ne nyinaa → anaa hweentwahonanHweeTokuru ahabammono baako a sika pɛ bɛt, dumienu kuo bɛt anaa santen tee bɛt biara nkata so; kasino mfasoɔ fibea. Wɔfrɛ no nso hwee baako, 0.Kenkan ne nyinaa → nsia a ɛtoatoa so hokwanakontaabuHokwanHokwan a biribi bɛba, firi 0 kɔsi 1 anaa 0% kɔsi 100%. Nɔma baako: 1/37 = 2.70%.Kenkan ne nyinaa → yɛ 1.8% kyinhyia mua biara so. Na yɛadi bɛyɛ kyinhyia mua 45. Hokwan a yɛbɛduru ha baabi wɔ kyinhyia mua 45 mu no yɛ bɛyɛ 55%. Ɛnyɛ nkrabea bɔne; ɛyɛ deɛ ɛtaa ba mfinimfini mu.
- p10 −$1,000
- p25 −$1,000
- mfinimfini nɔma −$1,000
- p75 +$790
- p90 +$1,690
Akontaa no
Yɛkɔɔ soro $410 kyinhyia 60 akyi, na yɛkɔɔ fam $220 kyinhyia 66 akyi. Bɛt sika nyinaa: bɛyɛ $2,100 wɔ kyinhyia 66 mu, na agorɔfoɔ a ɔto $10 pɛ daa deɛ yɛ $660. Ahwereɛ a wɔhwɛ kwanakontaabuAhwereɛ a wɔhwɛ kwanBoɔ a wɔhwɛ kwan bɔ bɛt sika nyinaa ho; ahwereɛ mfinimfini boɔ wɔ agorɔ bere anaa bere bi mu.Kenkan ne nyinaa → wɔ bɛt sika nyinaasikaBɛt sika nyinaaSika nyinaa a wɔde to bɛt wɔ agorɔ bere anaa bere bi mu, a nkonim sika a wɔsan de to ka ho. Wɔfrɛ no nso handle, action.Kenkan ne nyinaa → $2,100 so yɛ $57; yɛn deɛ ɛbaa ankasa −$220 no bɛyɛ gyinapɛn nsakraeɛakontaabuGyinapɛn nsakraeɛNsakraeɛ ntini; ntam kwan a ɛtaa da deɛ ɛfiri mu ba ne boɔ a wɔhwɛ kwan ntam.Kenkan ne nyinaa → mmiɛnsa mu baako wɔ ɛno ase, na ɛno nnyɛ nwanwa ma nhyehyɛe a ne nkyekyɛmu wɔ dua tenten wɔ benkum so. Sɛ yɛgyaee wɔ kyinhyia 60 so a mfasoɔ ahyeɛɔkwanMfasoɔ ahyeɛMfasoɔ botaeɛ a wode asi hɔ dada a sɛ woduru ho a, wode agorɔ bere no ba awieeɛ.Kenkan ne nyinaa → yɛ $400 a, anka yɛakɔ a yɛkɔ soro $410, na agorɔ bere a ɛdi so no nso anka ɛkura 1.8% koro no ara kyinhyia mua biara so.
Deɛ agorɔ bere no kyerɛ
Martingale dane bɛt 48.65% ma ɛyɛ ntoatoasoɔ a ɛdi nkonim wɔ ne kyinhyia mua 98% mu na ɛhwere kyɛfasikaKyɛfaBɛt sika a ɛwɔ ase a nhyehyɛe anaa agorɔfoɔ de yɛ adwuma. Wɔka bɛt nsakraeɛ ntoatoasoɔ ho asɛm wɔ kyɛfa mu sɛdeɛ ɛbɛyɛ a ɛbɛfata ɛpono biara.Kenkan ne nyinaa → 63 wɔ 2% a aka no mu. Ɛnsesa ahwereɛ a wɔhwɛ kwan wɔ dɔla biara so; ɛbɔ dɔla no ho. Agorɔfoɔ a ɔto sika pɛ daa wɔ yɛn nkyɛn no de mmiɛnsa mu baako too bɛt na ɔhweree, wɔ mfinimfini mu, mmiɛnsa mu baako. Agorɔfoɔ a ɔde saa nhyehyɛe yi di agorɔ afe mua no bɛdi nkonim anwummerɛ dodoɔ no ara na wahwere afe no.
Mprɛ dodoɔ a ahwereɛ ntoatoasoɔ ba
Sika pɛ bɛt wɔ hwee baako ntwahonan so hwere kyinhyia 19 wɔ 37 mu. Santen biara kyerɛ hokwan a ɛbɛma kyinhyia ntoatoasoɔ bi nyinaa ahwere, ne sika a Martingale agorɔfoɔ, a ɔbɔ bɛt no mmɔho mmienu ahwereɛ biara akyi, ahwere kɔsi saa bere no.
| ahwereɛ a ɛtoa so | hokwan | bɛyɛ 1 wɔ mu | ahwereɛ kɔsi seesei | bɛt a ɛdi so |
|---|---|---|---|---|
| 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 |
Hokwan no yɛ 19/37 a wɔde bɔ ne ho mmɔho mprɛ baako ahwereɛ biara mu, a wɔfiri kyinhyia baako bi so kan. Agorɔ bere tenten wɔ kyinhyia pii a ntoatoasoɔ a ɛte saa betumi afi ase, enti anwummerɛ mu no, ɛbɛtumi aba sene sɛdeɛ santen baako kyerɛ.
Nsɛmmisa
Ahwereɛ nkron na ɛbu no mmom sen nsia: 0.25% kyinhyia mua biara so, na sɛ ɛba a, wohwere $5,110. Ɔbota a ɛnntaa mma, ɔbota a ɛkorɔn, −2.70% koro no ara.
Anka ɛbɛdi nkonim 48.65% wɔ mprɛ no mu na ama kyinhyia mua no ada so ayɛ −$130. Ɔkwan pa biara nni hɔ Martingale a abu akyi; bɛt sika a wobɛpaw no akyiri nko ara na ɛwɔ hɔ.
Aane, ma saa agorɔ bere no. Ɛnyɛ ma agorɔ bere nyinaa mfinimfini boɔ.
Akontaabu ho anigyeɛ
Di kan yɛ eyinom ara wo ho. Wɔakata mmuaeɛ biara so; sɛ woasiesie wo ho a, bue no.
Wɔ ɛpono a ɛyɛ $1 kosi $500 so no, MartingaleɔkwanMartingaleBɛt nsakraeɛ ntoatoasoɔ a ɛbɔ bɛt no mmɔho mmienu ahwereɛ biara akyi. Hwɛ Akwan ɔfa no na hunu deɛ ɛyɛ ne deɛ ɛnyɛ.Kenkan ne nyinaa → agorɔfoɔ bi fi aseɛ wɔ $1 wɔ kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → so wɔ hweentwahonanHweeTokuru ahabammono baako a sika pɛ bɛt, dumienu kuo bɛt anaa santen tee bɛt biara nkata so; kasino mfasoɔ fibea. Wɔfrɛ no nso hwee baako, 0.Kenkan ne nyinaa → baako ntwahonan so. Ahwereɛ ahe a ɛtoatoa so na ɛgyina mmɔho mmienu no, wahwere ahe saa bere no, na mpɛn ahe na ɛsi?
Kyerɛ mmuaeɛ no
Mmuaeɛ Ahwereɛ nkron: wahwere $511, na bɛt a ɛdi so no bɛyɛ $512. Ɛsi prɛko wɔ ntoatoasoɔ bɛyɛ 403 mu.
Bɛt sika no yɛ 1, 2, 4, 8, 16, 32, 64, 128 ne 256: ne nyinaa $511. Ɛtɔ so du no bɛyɛ $512, aboro ahyeɛ no so. $500 bɛt a edi nkonim mpo gyaw agorɔfoɔ no wɔ $11 ahwereɛ mu; deɛ ɛhwere no gyaw no wɔ $1,011 ahwereɛ mu.
Kɔkɔɔ hwere wɔ hokwan 19/37, enti ahwereɛ nkron a ɛtoatoa so hokwan yɛ (19/37)⁹ ≈ 0.25%, prɛko wɔ ntoatoasoɔ bɛyɛ 403 mu. Ntoatoasoɔ biara a awie nya $1, enti agorɔfoɔ no hwɛ kwan sɛ ɔbɛnya bɛyɛ $402 nkonim nketewa ansa na $511 ahwereɛ baako no aba, na wɔ mfinimfini mu ɔda so hwere biribiara a wɔde ato bɛt mu no mu 2.70%.
Wɔ hwee mmienu ntwahonan so no, hokwan no yɛ (20/38)⁹, prɛko wɔ bɛyɛ 323 mu. Bollman (2021) tintim “bɛyɛ 833 mu 1”, a ɛyɛ (18/38)⁹, nkonim nkron a ɛtoatoa so hokwan.
Serew kakra
Nkonim nketewa aduanan baako ne ahwereɛ kɛseɛ baako. Ɛno ne nhyehyɛe no nyinaa.
Nsɛm fibea
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”