Ahyiaeɛ wɔ bere tenten mu: dodoɔ kɛseɛ mmara wɔ roulette mu
Sɛdeɛ mfinimfini no tena ase kɔ −2.70% so, ne deɛ enti a ɛgye bere tenten sen sɛdeɛ adwene ka.
Ahwereɛ mfinimfini wɔ kyinhyia biara mu kɔ −1/37 so bere a kyinhyia dodoɔ kɔ soro, na ne trɛtrɛ tew te sɛ 1/√N. Kyinhyia 1,000 wɔ kɔkɔɔ so akyi no, mfinimfini no taa wɔ ±3% mu fa deɛ wɔhwɛ kwan no ho.
Dodoɔ kɛseɛ mmara
Bɛt a ɛmfa ho mfinimfini a ɛkɔ so no kɔ 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 → no so. Sika pɛ kyinhyia N wɔ 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 → baako so akyi no, mfinimfini deɛ ɛfiri mu ba wɔ kyinhyia biara mu no deɛ wɔhwɛ kwan yɛ −1/37 na ne gyinapɛn nsakraeɛakontaabuGyinapɛn nsakraeɛNsakraeɛ ntini; ntam kwan a ɛtaa da deɛ ɛfiri mu ba ne boɔ a wɔhwɛ kwan ntam.Kenkan ne nyinaa → yɛ 1/√N. Wɔ N = 100 so no, trɛtrɛ no yɛ 10% wɔ bɛt sika no so, bɛyɛ mmɔho ɛnan wɔ nsɛnkyerɛnne 2.7% no so. Wɔ N = 1,000 so no, ɛyɛ 3.2%, bɛyɛ sɛ nsɛnkyerɛnne no ara. Wɔ N = 10,000 so no, ɛyɛ 1%, na kasino mfasoɔ no da adi pefee. Kasino mfasoɔ no nna adi wɔ agorɔ bere baako mu, na wɔ afe baako mu deɛ, ɛda adi a wontumi mmu w'ani ngu so.
Deɛ ɛkɔ baabi koro ne deɛ ɛnkɔ
Mfinimfini wɔ kyinhyia biara mu kɔ baabi koro. Ne nyinaa deɛ, ɛnkɔ: ɛtwe kɔ akyiri firi hwee ho bere a N kɔ soro, bɛyɛ 2.7% wɔ N so wɔ deɛ wɔhwɛ kwan mu, a ne trɛtrɛ yɛ √N wɔ ho. Agorɔfoɔ a wadi kyinhyia 10,000 wɔ $10 so no, wɔhwɛ kwan sɛ wahwere $2,700, ebia nkyɛn $1,000. KɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → nkyɛmu a ɛkɔ so no atena ase bɛn 48.65% bere tenten ni; nanso sika a aka a ɛkɔ so no ntenaa baabiara.
- p10 −$440
- p25 −$280
- mfinimfini nɔma −$140
- p75 +$0
- p90 +$140
Adɛn nti na adwene ka mfomsoɔ
Nnipa hwɛ kwan sɛ kasino mfasoɔ no bɛda adi ntɛm ɛfiri sɛ 2.70% te sɛ deɛ ɛdɔɔso, na wɔhwɛ kwan sɛ ntoatoasoɔ tenten bɛ“yɛ pɛ” ɛfiri sɛ dodoɔ kɛseɛ mmaraakontaabuDodoɔ kɛseɛ mmaraNsɛm a ɛmfa ho mfinimfini boɔ kɔ hyia boɔ a wɔhwɛ kwan bere a sɔhwɛ dodoɔ renyini.Kenkan ne nyinaa → no ka sɛ mfinimfini kɔ baabi koro. Saa adwene mmienu no nyinaa nhu kɛseɛ no yie: kasino mfasoɔ no sua sɛ wode toto kyinhyia baako nsakraeɛakontaabuNsakraeɛNsusuiɛ a ɛkyerɛ sɛdeɛ nsɛm a ɛfiri mu ba no trɛ wɔ boɔ a wɔhwɛ kwan ho. Ɛso ma nɔma baako bɛt, ɛsua ma sika pɛ bɛt.Kenkan ne nyinaa → ho a (σ = kyɛfa 1 tia EV = 0.027), ɛno nti ɛgye (1/0.027)² ≈ kyinhyia 1,400 ansa na ada adi wɔ sigma baako mu. Na mfinimfini no a ɛkɔ baabi koro no ntwe ne nyinaa nsan mma; ɛma nsakraeɛ a atwam no yɛ ketewa wɔ dodoɔ kɛseɛ mu kɛkɛ.
Sɛdeɛ bɛt afoforɔ kɔ baabi koro
Wɔ nɔma baako bɛtbɛtNɔma baako bɛtNɔma baako pɛ, ɛtua 35:1.Kenkan ne nyinaa → so no, σ = 5.84, ɛno nti akontaabu koro no ara ma (5.84/0.027)² ≈ kyinhyia 47,000 ansa na kasino mfasoɔ no aduru sigma baako. Agorɔfoɔ a ɔto nɔma baako bɛt betumi adi agorɔ mfeɛ pii a ɔrentumi nhu kasino mfasoɔ no nsonsonoeɛ ne akyiresɛm wɔ n'ankasa ne nkrataa mu, nanso ɔtua 2.70% koro no ara sɛ agorɔfoɔ a ɔto kɔkɔɔ so a ɔhu no wɔ nnawɔtwe kakraa bi mu no.
Deɛ ɛkyerɛ ma nhyehyɛe sɔhwɛ
Obiara a ɔka sɛ nhyehyɛe bi yɛ adwuma no, ɛsɛ sɛ ɔtumi kyerɛ wɔ kyinhyia 10,000 anaa deɛ ɛboro saa mu a mfinimfini papa a wɔakyerɛw wom. Wɔ kyinhyia 1,000 so no, mfinimfini papa wɔ sika pɛ so yɛ asɛm a ɛba enum mu baako bere a kasino mfasoɔ no nsesa; wɔ kyinhyia 100 so no, ɛkame ayɛ sika kɔɔbere a wɔto. Sɔhwɛ agorɔ a ɛwɔ site yi so no di agorɔ bere 2,000 a ne tenten yɛ deɛ wopaw wɔ sima baako mu, na ɛno yɛ adanseɛ a ɛdɔɔso sen adanseɛ biara a obi di.
Akontaabu kwan
Nsɛmmisa
HokwanakontaabuHokwanHokwan a biribi bɛba, firi 0 kɔsi 1 anaa 0% kɔsi 100%. Nɔma baako: 1/37 = 2.70%.Kenkan ne nyinaa → a wobɛsan anya mfasoɔ da no tew kɔ hwee so bere a wokɔ so di agorɔ no. Ne nyinaa siane a ano nni hɔ.
Dabi. Ɛkyerɛ sɛ nsakraeɛ a atwam no bɛyɛ ketewa wɔ nhwɛsoɔ a ɛyɛ kɛseɛ mu.
Ma sika pɛ, bɛyɛ 10,000 ansa na kasino mfasoɔ no ada adi pefee. Ma nɔma baako bɛt, bɛyɛ 50,000.
Akontaabu ho anigyeɛ
Di kan yɛ eyinom ara wo ho. Wɔakata mmuaeɛ biara so; sɛ woasiesie wo ho a, bue no.
Nnamfo mmienu di agorɔ a ɛyɛ pɛakontaabuAgorɔ a ɛyɛ pɛAgorɔ a afa biara nni mfasoɔ: bɛt biara boɔ a wɔhwɛ kwan yɛ hwee.Kenkan ne nyinaa → agorɔ mprɛ 20, sika ti ne akyi anaa kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → tia tuntumbɛtTuntumSika pɛ bɛt wɔ nɔma tuntum 18 no so. Franse kasa mu: noir.Kenkan ne nyinaa → a wɔsan de 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 sika ma, na wɔkɔ so kan akontaa no. Kan agorɔ mprɛ a obiara di kan (sɛ wɔyɛ pɛ a, ɛkɔ obi a na odi kan ansa no so). Ɛhe na ebetumi aba sen: sɛ wɔbɛkyɛ dikan no agorɔ mprɛ 10 tia 10, anaa sɛ nnamfo no mu baako bɛdi kan 20 no nyinaa?
Kyerɛ mmuaeɛ no
Mmuaeɛ Nnamfo no mu baako a ɔbɛdi kan agorɔ mprɛ 20 no nyinaa na ebetumi aba kɛseɛ: 35.2%, sɛ wokan nnamfo no mu biara a, sɛ wode toto 6.1% a ɛyɛ 10 tia 10 pɛ ho a.
Hokwan a akontaa a ɛyɛ pɛ bɛyɛ pɛ agorɔ mprɛ 2k akyi yɛ u = C(2k, k)/2²ᵏ: 0.246 agorɔ mprɛ 10 akyi ne 0.176 agorɔ mprɛ 20 akyi. Tete nsunsuansoɔ bi, arc-sine mmara no, ka sɛ hokwan a nnamfo baako a wɔabɔ ne din bɛdi kan agorɔ mprɛ 2k pɛpɛɛpɛ wɔ 2n mu yɛ u(2k) × u(2n − 2k).
Sɛ obi di kan 20 no nyinaa a: u(20) × u(0) = 0.176 ma nnamfo biara, 35.2% ma emu biara. Nkyekyɛmu pɛ: u(10) × u(10) = 0.246² = 6.1%, nkyekyɛmu a ebetumi aba sua sen biara.
Enti wɔ agorɔ a ɛyɛ pɛ mu no, dikan no nnsakra nsa mpɛn pii. Agorɔfoɔ a odii kan anadwo no nyinaa, anaa ɔtenaa akyi anadwo no nyinaa, nhunuu biribi soronko, na ɛnkyerɛ hwee wɔ ntwahonan no anaa nimdeɛ ho. Epstein (2013) de mmara korɔ no ara ma agorɔ tenten: bere no fa mu no, ɔfa a ne ti ye no di kan boro agorɔ no mu 85%.
Serew kakra
Mfinimfini no kɔ baabi koro. Ne nyinaa deɛ, ɛkɔ kɛkɛ.
Nsɛm fibea
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.