Gyidie hunu: roulette ɔkwan a ɛdi nkonim daa
“Mewɔ nhyehyɛe bi a ɛdi nkonim bere no mu 80%.” Ebia wowɔ. Nanso ɛda so hwere sika.
Nhyehyɛe tumi ma agorɔ bere a wodi nkonim yɛ adeɛ a ɛtaa ba. Ɛntumi mma boɔ a wɔhwɛ kwan no nyɛ mfasoɔ, ɛfiri sɛ bɛt biara a ɛto no yɛ ne bɛt sika no −1/37 na boɔ a wɔhwɛ kwan ka bom. Nhyehyɛe a ɛtaa di nkonim sene biara no na ɛhwere bebree sene biara bere a ɛhwere.
Asɛm a wɔka
Gyidie no: baabi bi wɔ hɔ a roulette ɔkwan a ɛdi nkonim daa wɔ, bɛt sika nsakraeɛ nhyehyɛe a egyina nea efi mu baa a atwam so a ɛdane roulette ma ɛyɛ agorɔ a wodi so nkonim. Adanseɛ a wɔde ma: agorɔ bere a wɔdii nkonim a ɛtoatoa so, video a ɛkyerɛ sɛdeɛ wobɛdi nkonim wɔ roulette mu bere biara, obi adanseɛ, nsɛm pon a ɛkyerɛ nnawɔtwe a akwantuo pa baeɛ. Mpɛn pii no asɛm no mu wɔ nokorɛ; onipa no gye di ɛfiri sɛ na ɛreyɛ adwuma.
Deɛ enti a ɛnteɛ, wɔ santen baako mu
Boɔ a wɔhwɛ kwanakontaabuBoɔ a wɔhwɛ kwanNsunsuansoɔ mfinimfini boɔ wɔ bɛt biara so wɔ bere tenten mu. Bɛt sika no −1/37 wɔ Yuropu bɛt biara a ɛyɛ daa deɛ so.Kenkan ne nyinaa → ka bom. Sɛ bɛt biara EV = ne bɛt sika no −1/37 a, bɛt ntoatoasoɔ biara EV = bɛt sika nyinaa −1/37, mmara biara a ɛyii bɛt sika no mfa ho. Nhyehyɛe yɛ mmara a wɔde yi bɛt sika. Enti nhyehyɛe biara EV = 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 → −1/37. Eyi yɛ akontaabu nokorɛ (Doob ne Halmos kyerɛɛ ho adanseɛ wɔ 1930 mfeɛ no mu; Thorp 1969 ka nhyehyɛe a ɛhia ho asɛm), na ɛnni nea ɛmfa ho ma mmara a nyansa wom. Nhyehyɛe baako a ɛsɛ sɛ wohunu ne bɛt ahyeɛ ase: Thorp nhwɛsoɔ no to $1,000 wɔ kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → so, afei sɛnt 90, afei sɛnt 9 ne nea ɛkeka ho, a ɛkɔ so tew so daa. Wɔ hokwan 18/37 no, bɛt a edi kan no di nkonim na agorɔfoɔ no tena mfasoɔ mu daa, ɛwom sɛ nea wɔhwɛ kwan sɛ ɛbɛfi mu aba no da so yɛ biribiara a wɔde ato bɛt mu no −1/37 de. Ɛpono ankasa ahyeɛ ase si ɛno kwan, na ɛne no nyinaa, anidasoɔ biara sɛ wobɛtena mfasoɔ mu bere tenten mu.
Deɛ enti a ɛte sɛ nea ɛyɛ adwuma
Bɛt nsakraeɛ ntoatoasoɔɔkwanBɛt nsakraeɛ ntoatoasoɔMmara biara a ɛsesa bɛt sika no gyina deɛ atwam so. Ntoatoasoɔ a ɛkɔ soro ahwereɛ akyi ma no kɔ soro ahwereɛ akyi, na deɛ ɛkɔ soro nkonim akyi ma no kɔ soro nkonim akyi.Kenkan ne nyinaa → a ɛkɔ soro wɔ ahwereɛ akyi ma agorɔ bere a wodi nkonim yɛ adeɛ a ɛtaa ba. 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 efi $10 wɔ ahyeɛ $500 so wie kyinhyia 100 agorɔ bere no mu bɛyɛ 80% wɔ mfasoɔ 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 → kakraa bi mu. Agorɔfoɔ a ɔde yɛ adwuma agorɔ bere aduonu no di wɔn mu dunsia nkonim na ɔkae ɛno. Agorɔ bere ɛnan a ɔhweree no mu biara hwere sene nea agorɔ bere du a odii nkonim nya, na akontaabu a ɛwɔ agorɔ bere aduonu no so no yɛ ahwereɛ. Nhyehyɛe no nsesaa mfinimfini no; ɛde ahwereɛ no akɔ agorɔ bere kakraa bi a ɛyɛ akɛseɛ mu, faako a ɛyɛ mmerɛ sɛ wɔbɛfrɛ no musuo.
Sɔhwɛ a obiara bɛtumi ayɛ
Bɛt ɔkwan sɔhwɛ agorɔ a ɛwɔ wɛbsaet yi so no di nhyehyɛe biara, anaa wo ankasa code, agorɔ bere 10,000 wɔ anibuo baako mu. Hyehyɛ no ma nhyehyɛe a wogye di no na kenkan mfinimfini no. Sɛ anka mfinimfini no yɛ mfasoɔ wɔ nhyehyɛe biara so a, anka krataafa yi bɛka. Nhyehyɛe biara, ɔkwan biara, 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 → biara ma mfinimfini a ɛyɛ bɛt sika nyinaa mu −2.70% ne basabasa kakra. Adanseɛ yɛ nhwɛsoɔ baako; sɔhwɛ agorɔ no yɛ nhwɛsoɔ mpem du.
Nhyehyɛe a ɛrentumi nhwere
Wɔ 1997 mu no, poker kyerɛwfoɔ Mike Caro de roulette nhyehyɛe bi too intanɛt so sɛ serewa, na Gambling Times san tintim wɔ 2001 mu. Ɛyɛ bɛt a ɛsɛ sɛ wokwati ho nsensaneɛ: kɔkɔɔ anaa tuntumbɛtTuntumSika pɛ bɛt wɔ nɔma tuntum 18 no so. Franse kasa mu: noir.Kenkan ne nyinaa →, ɛnkyɛ pɛ anaa ɛkyɛ pɛ, 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 → no da; nɔma kɔkɔɔ a ɛnkyɛ pɛ ne nɔma tuntum a ɛkyɛ pɛ biara; na biribiara nni 30 so, anaa ntokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → ntoatoasoɔ tenten a efi 11 fa dɔnhwerew kwan so twa kosi 14 wɔ Amerika ntwahonan so no so. Ka mmara no bom na nɔma biara renka. Ntokuru a ɛwɔ saa ntoatoasoɔ no akyi nko ara ne 0, 28, 9, 26, 30 ne 2; wɔde din bra 30, na nkaeɛ no yɛ hwee, ɛkyɛ pɛ na ɛyɛ tuntum, anaa ɛnkyɛ pɛ na ɛyɛ kɔkɔɔ. Agorɔfoɔ a ɔdi nhyehyɛe no so nto bɛt da na ɔnhwere da. Ne kasino mfasoɔ yɛ hwee, na ɛno nko ara ne roulette nhyehyɛe a ɛka nokorɛ fa sɛdeɛ ɛduru hɔ ho.
Nhyehyɛe a wɔato din, santen baako biara
Nhyehyɛe a wɔtɔn wɔ din bi ase, anaa sɛ roulette nkonimdie akwan, nyɛ soronko. Biara yɛ bɛt bi, na bɛt biara tua ntwahonan no ne 2.70%. Bollman (2024) hwɛ ebi mu ma Amerika ntwahonan, faako a biara boɔ yɛ 5.26%; ha deɛ yɛde wɔn ato Yuropu deɛ so.
Nokorɛ deɛ no
Nhyehyɛe sesa agorɔ bere nsɛsoɔ: mpɛn dodoɔ a wodi nkonim, nkonim no kɛseɛ, sɛdeɛ deɛ ɛyɛ bɔne sene biara te. Eyinom yɛ nneɛma ankasa a wobɛtumi ayi, na agorɔfoɔ bɛtumi apɛ nsɛsoɔ baako asene ɔfoforɔ. Deɛ nhyehyɛe nsesa ne boɔ no, a ɛyɛ biribiara a wɔde to bɛt mu no mu 2.70%, na esiane sɛ bɛt nsakraeɛ ntoatoasoɔ de sika pii to bɛt mu sene sika pɛ a wɔto daaɔkwanSika pɛ a wɔto daaSika dodoɔ koro no ara a wode to bɛt kyinhyia biara. Ɛno ne gyinapɛn a wɔde bɛt nsakraeɛ ntoatoasoɔ biara toto ho.Kenkan ne nyinaa → nti, wɔtua ne mu pii.
Nsɛmmisa
Abosome nsia a wodi agorɔ nnawɔtwe biara yɛ bɛyɛ agorɔ bere 25. Martingale di wɔn mu 80% nkonim. Agorɔ bere a wobɛhwere no reba, na ɛyɛ akɛseɛ.
Gyae mmara no tew bɛt sika nyinaa so, enti ɛtew 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 → so. Ɛmma ɛnyɛ mfasoɔ.
Ɛnyɛ wɔ ntwahonan a ɛyɛ pɛ so. Wɔ ntwahonan a ɛyɛ animhwɛnhwehwɛmu danNtwahonan a ɛyɛ animhwɛNtwahonan a ne honam so mfomsoɔ ma ntokuru bi hokwan boro 1/37. Ɛnnsɛ ho pii, na wobɛtumi ahunu no ɛnkyɛ sɛ wode kyinhyia mpempem a woakyerɛw ahwɛ.Kenkan ne nyinaa → so, a ɛyɛ abɔdeɛ mmara asɛm, ɛnyɛ nhyehyɛe.
Akontaabu ho anigyeɛ
Di kan yɛ eyinom ara wo ho. Wɔakata mmuaeɛ biara so; sɛ woasiesie wo ho a, bue no.
Mike Caro serewa nhyehyɛe a ɔyɛɛ wɔ 1997 mu maa Amerika ntwahonan no bra kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → ne tuntumbɛtTuntumSika pɛ bɛt wɔ nɔma tuntum 18 no so. Franse kasa mu: noir.Kenkan ne nyinaa →, ɛnkyɛ pɛ ne ɛkyɛ pɛ, ne 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 → no; nɔma kɔkɔɔ a ɛnkyɛ pɛ ne nɔma tuntum a ɛkyɛ pɛ; nɔma 30; ne tokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → biara a ɛwɔ ntoatoasoɔ a efi 11 fa dɔnhwerew kwan so twa kosi 14 no mu. Fa mmara no di dwuma baako baako. Nɔma bɛn na aka a wobɛto bɛt wɔ so?
Kyerɛ mmuaeɛ no
Mmuaeɛ Hwee. Nhyehyɛe no nto bɛt da, enti ne kasino mfasoɔ yɛ hwee pɛpɛɛpɛ.
Sɛ wobra kɔkɔɔ, tuntum, ɛnkyɛ pɛ, ɛkyɛ pɛ ne hwee a, ɛgyaw nɔma baako baako ne kuo nketewa wɔ 1 kosi 36 mu.
Sɛ kɔkɔɔ a ɛnkyɛ pɛ ne tuntum a ɛkyɛ pɛ nni hɔ a, ɛgyaw kɔkɔɔ a ɛkyɛ pɛ (12, 14, 16, 18, 30, 32, 34, 36) ne tuntum a ɛnkyɛ pɛ (11, 13, 15, 17, 29, 31, 33, 35): nɔma dunsia. Sɛ wobra 30 a, ɛgyaw dunum.
Wɔ Amerika ntwahonan so no, ntoatoasoɔ a efi 11 fa dɔnhwerew kwan so kosi 14 no kata ntokuru 38 no mu 32 so. Nsia a ɛwɔ akyi no yɛ 0, 28, 9, 26, 30 ne 2. Dunum a aka no nyinaa wɔ ntoatoasoɔ no mu, enti mmara a etwa to no yi wɔn nso. Nhyehyɛe a ɛnto bɛt da no nko ara na ɛnhwere da, na ɛno ne asɛm a Caro pɛ sɛ ɔka.
Kryptos di 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 → mmiɛnsa prɛko, baako wɔ sika pɛ bɛtbɛtSika pɛ bɛtKɔkɔɔ/tuntum, ɛnkyɛ pɛ/ɛkyɛ pɛ, soro/fam. Nɔma 18, akatua 1:1.Kenkan ne nyinaa → mmienu biara so (soro anaa fam, ɛnkyɛ pɛ anaa ɛkyɛ pɛ, kɔkɔɔ anaa tuntum), a bɛt sika yɛ 1, 2, 4, 8, 16, 32 na ɛgyina ahwereɛ nsia akyi. Fa mmiɛnsa no mu baako wɔ Yuropu ntwahonan so. Mpɛn ahe na ɛhwere bɛt nsia no nyinaa, ɔkwan no kyinhyia mua baako nya ahe wɔ mfinimfini mu, na ɛno yɛ sika a wɔde to bɛt mu no kyɛfa bɛn?
Kyerɛ mmuaeɛ no
Mmuaeɛ Ɛhwere nsia no nyinaa bɛyɛ prɛko wɔ kyinhyia mua 55 mu, bere no mu 1.83%, na ɛno gye 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 mfinimfini mu no, kyinhyia mua hwere bɛyɛ kyɛfa 0.17 wɔ kyɛfa 6.42 a wɔde to bɛt mu: 2.70%, bɛt biara boɔ wɔ ntwahonan no so.
Bɛt hwere wɔ hokwan 19/37, a hwee ka ho. Nsia a ɛtoatoa so: (19/37)⁶ = 0.0183, bɛyɛ 55 mu 1, na afei bɛt sika 1 + 2 + 4 + 8 + 16 + 32 = 63 kɔ. Sɛ ɛnte saa a, kyinhyia mua no wie wɔ nkonim ne kyɛfa +1 mu.
Mfinimfini: 1 × (1 − 0.0183) − 63 × 0.0183 = 1 − 64 × 0.0183 = kyɛfa −0.17.
Sika a wɔde to bɛt mu: wɔto bɛt a edi kan daa, ɛtɔ so mmienu no ahwereɛ akyi nko ara, na ɛkɔ so saa: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = kyɛfa 6.42. Na −0.17/6.42 = −2.70%.
Kyinhyia nsia a wɔakyerɛw no kyerɛ afa a bɛt biara wɔ nko ara, na ntwahonan no ntumi nhu wɔn. Sɛ wodi mmiɛnsa no nyinaa a, ɛma sika a wɔde to bɛt mu ne ahwereɛ a ɛwɔ mfinimfini no nyinaa yɛ mmɔho mmiɛnsa. Bollman (2024) de nhyehyɛe no yɛ adwuma wɔ Amerika ntwahonan so, faako a wɔn mu biara hwere nsia a ɛtoatoa so wɔ bere no mu 2.1%.
Serew kakra
Nkonim a ɛtaa ba ne sika a wonya yɛ nɔma ahodoɔ.
Nsɛm fibea
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.