Roulette gyinapɛn nsakraeɛ
Roulette gyinapɛn nsakraeɛ, 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 → no square root, ne kwan tenten a ɛtaa da nsunsuansoɔ bi ne deɛ wɔhwɛ kwan no ntam.
Wɔ $1 biara a wode to bɛt mu so, σ yɛ 5.84 ma nɔma baako bɛt na 1.00 ma kɔkɔɔ. Fa bɛt sika no ne kyinhyia dodoɔ no square root bɔ ho na woanya agorɔ bere baako deɛ.
Mmara a ɛnyɛ den
Agorɔ bere bɛyɛ nkyɛmu mmiɛnsa mu mmienu ba σ baako mu wɔ deɛ wɔhwɛ kwan no ho, na 95% ba mmienu mu. Kyinhyia 100 wɔ kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → so wɔ $10 (deɛ wɔhwɛ kwan −$27, σ = $100) mu no, agorɔ bere dodoɔ no ara ba −$127 ne +$73 ntam, na ɛkame ayɛ ne nyinaa ba −$227 ne +$173 ntam. Nsunsuansoɔ a ɛwɔ saa ntam no akyi nkyerɛ hwee, gye sɛ agorɔ bere baako wɔ aduonu mu yɛ saa.
Adɛn nti na ɛyɛ √N
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 → kɔ soro sɛdeɛ N kɔ soro no ara; ntrɛmu no kɔ soro sɛdeɛ √N kɔ soro. Sɛ N sua a, ntrɛmu no na ɛdi so na agorɔ bere biara te sɛ sika a wotow hwɛ ti anaa akyi a ɛbɔ ne mu kakra. Sɛ N yɛ kɛseɛ a, ahwereɛ no di ntrɛmu no anim. Baabi a ɛsesa, baabi a ahwereɛ a wɔhwɛ kwan no ne gyinapɛn nsakraeɛakontaabuGyinapɛn nsakraeɛNsakraeɛ ntini; ntam kwan a ɛtaa da deɛ ɛfiri mu ba ne boɔ a wɔhwɛ kwan ntam.Kenkan ne nyinaa → baako yɛ pɛ no, ne N = (σ/kasino mfasoɔ)² = (1/0.027)² ≈ kyinhyia 1,370 ma sika pɛ ne (5.84/0.027)² ≈ 46,800 ma nɔma baako bɛtbɛtNɔma baako bɛtNɔma baako pɛ, ɛtua 35:1.Kenkan ne nyinaa →. Sɛ ɛwɔ saa nɔma no ase a, akwadwerɛ na ɛsi gyinaeɛ; sɛ ɛboro so a, kasino mfasoɔ na ɛsi.
Sɛdeɛ wode di dwuma
Sɛ wopɛ sɛ wohunu sɛ agorɔ bere bi yɛ soronko anaa a, bu (nsunsuansoɔ − EV)/σ. Kɔkɔɔ bɛtfoɔ a ɔde $10 wie kyinhyia 100 wɔ +$150 no wɔ (150 + 27)/100 = 1.77σ, nsunsuansoɔ a ɛba prɛko wɔ 25 mu: akwadwerɛ, ɛnyɛ nwonwa. Nɔma baako bɛtfoɔ a ɔwɔ +$150 korɔ no ara no wɔ 0.3σ: anadwo a ɛyɛ daa deɛ. Dɔla nsunsuansoɔ korɔ no ara kyerɛ nneɛma ahodoɔ wɔ bɛt ahodoɔ so.
Kyɛfa bi standard error
Akontaabu korɔ no ara kyerɛ wo kyinhyia dodoɔ a ɛhia na woahunu kasino mfasoɔ no wɔ nsɛm no mu. Nkonim kyɛfa a wohunuiɛ standard error yɛ √(p(1 − p)/N). Kɔkɔɔ a N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Nsonsonoeɛ a ɛda sika a wotow a ɛyɛ pɛ ne kɔkɔɔ ntam yɛ 1.35%, enti kyinhyia 1,000 akyi mpo worentumi mfa ahotosoɔ nhunu wɔn ntam nsonsonoeɛ. Kyinhyia 10,000 akyi no, standard error no yɛ 0.5% na wobɛtumi. Ɛno nso nti na ntwahonan animhwɛ a wɔhwehwɛ no hia kyinhyia pii saa.
Kɔkɔbɔ a ɛfa ɛkyea ho
Nɔma baako bɛt nsunsuansoɔ wɔ agorɔ bere tiawa mu nni normal distribution koraa: agorɔ bere dodoɔ no ara yɛ −$10 daa kyinhyia biara mu a ɛtɔ da a +$350 huri ba. ±1σ mmara no kyerɛkyerɛ ntrɛmu no mu yie nanso ne nsɛsoɔ deɛ ɛnyɛ yie kɔsi sɛ N bɛduru ɔhaha pii. Sika pɛ bɛtbɛtSika pɛ bɛtKɔkɔɔ/tuntum, ɛnkyɛ pɛ/ɛkyɛ pɛ, soro/fam. Nɔma 18, akatua 1:1.Kenkan ne nyinaa → deɛ, normal distribution bɛyɛ no yɛ papa fi bɛyɛ kyinhyia 30.
Akontaabu kwan
Nsɛmmisa
Ɛyɛ adansedie sɛ wodii agorɔ bere bɛyɛ 40, anaa na wowɔ baako a akwadwerɛ wom wɔ aduanan mu no mu. San yɛ bio.
Ɛsesa kakra kakra: mfinimfini boɔ standard error yɛ σ/√N. Sɛ N = 10,000 a, ɛyɛ 1% wɔ bɛt sika mu.
Akontaabu ho anigyeɛ
Di kan yɛ eyinom ara wo ho. Wɔakata mmuaeɛ biara so; sɛ woasiesie wo ho a, bue no.
Wɔ Yuropu ntwahonan kyinhyia 100 mu no, 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 wɔ kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → so di kan sɛ onya nkonim 51 dodoɔ yi a, na kyɛfa baako wɔ nɔma baako bɛtbɛtNɔma baako bɛtNɔma baako pɛ, ɛtua 35:1.Kenkan ne nyinaa → so di kan sɛ ne nɔma ba mprɛ 3 dodoɔ yi a. Fa dɔn nhwɛsoɔ (bell curve) no susu hokwan mmienu no, na afei fa toto mmuaeɛ pɛpɛɛpɛ no ho.
Kyerɛ mmuaeɛ no
Mmuaeɛ Kɔkɔɔ: dɔn nhwɛsoɔ no ma 35.6% na mmuaeɛ pɛpɛɛpɛ no yɛ 35.5%. Nɔma baako bɛt: dɔn nhwɛsoɔ no ma 55.0% na mmuaeɛ pɛpɛɛpɛ no yɛ 50.9%. Ɔkwan tiawa no yɛ adwuma ma kɔkɔɔ na ɛnyɛ adwuma ma nɔma baako no.
Kɔkɔɔ: nkonim mfinimfini boɔ yɛ 100 × 18/37 = 48.6, a ne trɛ yɛ √(100 × 18/37 × 19/37) = 5.0. Dikan kyerɛ 51 anaa nea ɛboro saa; mfinimfini agyiraeɛ, 50.5, wɔ trɛ 0.37 wɔ mfinimfini boɔ no so, na dɔn nhwɛsoɔ no de 35.6% si saa so. Sɛ wode nkonim 51, 52 … 100 hokwan pɛpɛɛpɛ bom a, ɛma 35.5%.
Nɔma baako bɛt: ne ba mfinimfini boɔ yɛ 100/37 = 2.70, a ne trɛ yɛ √(100 × 1/37 × 36/37) = 1.62. Ba mprɛ mmiɛnsa anaa nea ɛboro saa kyerɛ sɛ ɛboro 2.5, trɛ 0.12 wɔ mfinimfini boɔ no ase: 55.0% wɔ dɔn nhwɛsoɔ no so. Pɛpɛɛpɛ no, ɛyɛ 1 tew hokwan a ɛbɛba mprɛ 0, 1 ne 2, 6.5% + 17.9% + 24.7%, na ɛgya 50.9%.
Dɔn nhwɛsoɔ no hia nsunsuansoɔ pii wɔ mfinimfini boɔ no afa mmienu no nyinaa so. Kɔkɔɔ wɔ bi kyinhyia 100 akyi; nɔma a ɛba mprɛ a ɛnnuru mmiɛnsa wɔ mfinimfini mu no nni bi. Dɔn nhwɛsoɔ no mpo de 8.7% ma “ɛmma koraa”, baabi a hokwan ankasa yɛ 6.5%. Taylor (2021) de binomial ne dɔn nhwɛsoɔ no si nkyɛn wɔ ɔkwan korɔ no ara so.
Serew kakra
Agorɔ bere baako wɔ aduonu mu wɔ sigma mmienu akyi. Obi wɔ awieeɛ hɔ daa.
Nsɛm fibea
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.