Sika agorɔfoɔ adwene mfomsoɔ
Gyidie a ɛka sɛ nsunsuansoɔ bi “ne bere aso” ɛfiri sɛ ɛmmaa bere bi.
Kɔkɔɔ du akyi no, tuntum hokwan da so yɛ 18/37. Ntwahonan no nkyerɛw biribiara nto hɔ na ɛnni obiara ka.
Adwene mfomsoɔ no
Sɛ kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → aba mpɛn du a, agorɔfoɔ pii te nka sɛ tuntumbɛtTuntumSika pɛ bɛt wɔ nɔma tuntum 18 no so. Franse kasa mu: noir.Kenkan ne nyinaa → “ne bere aso” na wɔto bɛt sɛdeɛ ɛte. Afoforɔ te nka sɛ kɔkɔɔ “ahye” na wɔto bɛt wɔ ɛno so. Wɔn mmienu nyinaa fi ntoatoasoɔ a atwam dedaw so dwene kɔ kyinhyia a ɛnsiiɛ so. Bɔɔlnneɛma a wɔde diBɔɔlBɔɔl ketewa a wɔto no ma ɛtu mmirika wɔ ne kwan mu tia rotor no. Ɛnnɛ bɔɔl yɛ ivorine anaa Teflon, 18–21 mm.Kenkan ne nyinaa → no nnim deɛ kyinhyia du a atwam no yɛeɛ; ntokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → no kɛseɛ yɛ pɛ sɛdeɛ na ɛte dɔnhwerew baako a atwam no; tuntum hokwanakontaabuHokwanHokwan a biribi bɛba, firi 0 kɔsi 1 anaa 0% kɔsi 100%. Nɔma baako: 1/37 = 2.70%.Kenkan ne nyinaa → yɛ 18/37 sɛdeɛ na ɛte daa no.
Deɛ enti a ɛte sɛ nokorɛ
Wɔ bere tenten mu no, kɔkɔɔ ne tuntum kyɛfa ankasa kɔ 18/37 biara so. 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 hyɛ ho bɔ. Nanso ahyiaeɛ no ba denam nneɛma foforɔ a ɛfra mu so, ɛnyɛ nteɛsoɔ so: kyinhyia 1,000 foforɔ akyi no, kɔkɔɔ du a ɛboro so no yɛ nkontaabu mu ketewa bi wɔ kyɛfa no mu, ɛnyɛ sɛ tuntum atoa so na mmom ɛfiri sɛ nhwɛsoɔ dodoɔ no ayɛ kɛseɛ. Ɔkwan biara nni hɔ a ɛma tuntum hokwan kɔ soro, na dodoɔ kɛseɛ mmara no nhia bi.
Monte Carlo, 18 Ɔsanaa 1913
Tuntum baa mpɛn 26 a ɛtoatoa so wɔ ɛpono bi so wɔ Casino de Monte-Carlo. Efi bɛyɛ tuntum a ɛtɔ so dunum so no, agorɔfoɔ kɔboaboaa wɔn ho ano wɔ kɔkɔɔ so, bɔɔ wɔn bɛt mmɔho ne mmɔho bio, kyinhyia biara “yɛ nokorɛ” sene deɛ ɛdi kan no. Kasino no nyaa franc ɔpepem pii. Ntoatoasoɔ no hokwan yɛ ɔpepem 137 mu 1 fi tuntum a edi kan no so, na hokwan a awieeɛ no ɛbɛsi baabi bi wɔ wiase kasino ahodoɔ mu no deɛ, ɛkame ayɛ baako. Ɛno nti na wɔsan frɛ sika agorɔfoɔ adwene mfomsoɔ no Monte Carlo adwene mfomsoɔ.
Ɛnyɛ nwonwa. Ɛsi prɛko wɔ 44 mu.
Agorɔfoɔ fi aseɛ hunu. Kɔkɔɔ “ne bere aso”.
Nnipa ayɛ ɛpono no ma. Wɔbɔ bɛt sika a ɛwɔ kɔkɔɔ so mmɔho wɔ ahwereɛ biara akyi.
Wɔhwere ahonyadeɛ. Tuntum foforɔ biara ma kɔkɔɔ te sɛ nokorɛ kɛseɛ.
Ntoatoasoɔ no ba awieeɛ. Kasino no anya franc ɔpepem pii afiri nnipa a wɔtoo bɛt tiaa ntoatoasoɔ a na entumi “nhunu” sɛ ɛyɛ ntoatoasoɔ no hɔ.
Nsa a ɛhye
Bɛt a wode to kɔla bi so ɛfiri sɛ ɛwɔ ntoatoasoɔ mu no yɛ mfomsoɔ korɔ no ara a wɔadane: wɔhwɛ kwan sɛ ntoatoasoɔ no bɛkɔ so mmom sene sɛ ɛbɛba awieeɛ. Adwene ho nhwehwɛmufoɔ frɛ no nsa a ɛhyegyidie hunuNsa a ɛhyeGyidie a ɛka sɛ nkonim ntoatoasoɔ, anaa deɛ ɛfiri mu ba baako ntoatoasoɔ, ma ebi foforɔ ba ntɛm. Wɔ ntwahonan no ho no, ɛyɛ sika agorɔfoɔ adwene mfomsoɔ a wɔadane no.Kenkan ne nyinaa →, fi nhwehwɛmu bi a ɛfiri 1985 a Gilovich, Vallone ne Tversky yɛeɛ a wɔhwehwɛɛ ntoatoasoɔ wɔ basketball bɔɔl tow mu na wɔanhunu bi a ɛboro akwadwerɛ so. Wɔ 2018 mu, Miller ne Sanjurjo kyerɛɛ sɛ sɔhwɛ no ankasa akyea: wɔ nkrataa tiawa mu no, kyɛfa a ɛkɔ mu wɔ deɛ ɛkɔ mu akyi pɛɛ no ba fam sene deɛ ɔtowfoɔ no taa nya wɔ mfinimfini mu, enti agorɔfoɔ a ɔnni nsa a ɛhye koraa mpo te sɛ deɛ ne nsa ayɛ nwini kakra. Sɛ wɔsiesie a, nsɛm korɔ no ara kyerɛ nsa a ɛhye ketewa bi. Onipa betumi ahye; ntwahonan deɛ, ɛnni tebea biara a ɛbɛtena mu. Agorɔfoɔ bi kura gyidie mmienu no nyinaa bere korɔ mu, sɛ ntoatoasoɔ bɛkɔ so kɔsi sɛ ɛbɛyɛ “tenten dodo” na afei ɛbɛba awieeɛ. Wɔ ntwahonan a ɛyɛ pɛ so no, emu biara 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 → yɛ pɛ sɛ deɛ wode sika a wotow bɛpaw kɔla: −2.70% wɔ bɛt sika mu.
Wɔ ɛpono ankasa ho
Croson ne Sundali (2005) hwɛɛ ahobammɔ video dɔnhwerew 18 a ɛfiri 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 → mmienu ɛpono baako so wɔ kasino kɛseɛ bi mu wɔ Reno: agorɔfoɔ 139 a wɔtoo bɛt 24,131. Wɔ sika pɛ bɛtbɛtSika pɛ bɛtKɔkɔɔ/tuntum, ɛnkyɛ pɛ/ɛkyɛ pɛ, soro/fam. Nɔma 18, akatua 1:1.Kenkan ne nyinaa → so no, agorɔfoɔ no kyɛ mu bɛyɛ pɛ wɔ wɔn a wɔdi ntoatoasoɔ tiawa akyi ne wɔn a wɔtia no ntam. Bere a adeɛ korɔ aba mpɛn enum a ɛtoatoa so akyi no, wɔtwe kɔɔ ntoatoasoɔ no atiafoɔ so, na nsia anaa nea ɛboro saa akyi no, wɔn bɛt mu 85% kɔɔ ɔfa foforɔ no so. Agorɔfoɔ korɔ no ara kyerɛɛ nsa a ɛhye wɔ wɔn ankasa ho: nkonim wɔ nɔma so akyi no, wɔkataa nɔma 13.6 so wɔ kyinhyia a ɛdi so no mu wɔ mfinimfini mu, a ɛtia 9.2 wɔ ahwereɛ akyi. Wɔn ntwahonan no ankyerɛ animhwɛ biara, enti eyinom mu biara ansesa deɛ wɔn mu biara betumi ahwɛ kwan.
Kasino no akyi
Saa twe korɔ no ara da adi wɔ baabi a wɔsi gyinaeɛ ankasa. Clotfelter ne Cook (1993) dii Maryland nɔma agorɔ a wɔdi da biara no akyi: sika a wɔde to nɔma bi so no tew so ntɛm ara bere a wɔayi no na ɛgyee abosome pii ansa na ɛsan kɔɔ soro, ɛwom sɛ nɔma yie no nkae biribiara deɛ. Chen, Moskowitz ne Shue (2016) hunuu no wɔ nnipa a wɔnim adwuma no mu. Amerika asɛnnifoɔ a wɔhwɛ wɔn a wɔhwehwɛ guankɔbea nsɛm so no hokwan a wɔbɛpo asɛm bi kɔɔ soro kɔsi percentage points 3.3 sɛ wɔmaa deɛ ɛdii kan no kwan a. Baseball atemmufoɔ hokwan a wɔbɛka strike tew so points 1.5 wɔ deɛ wɔkaa bi akyi, na ɛboro saa mmɔho mmienu wɔ bɔɔl a ɛyɛ den sɛ wobɛhunu so. Wɔ sɔhwɛ bi a wɔyɛɛ wɔ bosea adwumayɛfoɔ a wɔtua wɔn ka korɔ mu no, gyinaeɛ a ɛkɔ soro kɔsi 9% sesaa saa kwan yi so. Nsɛm no baa wɔ nhyehyɛe a ɛba kwa mu, enti gyinaeɛ a etwa toɔ no ankyerɛ hwee wɔ deɛ ɛdi so no ho, sɛdeɛ kyinhyia a etwa toɔ nkyerɛ hwee wɔ deɛ ɛdi so no ho no ara.
Sika agorɔfoɔ adwene mfomsoɔ a ɛdane
Nyansapɛfoɔ Ian Hacking (1987) de din too deɛ ɛtɔ so mmiɛnsa so. Obi kɔ dan bi mu, ɔhunu sɛ dice mmienu tɔ nsia mmienu na ɔka sɛ ɛsɛ sɛ na wɔatow wɔn mpɛn pii dedaw. Towee biara hokwan a ɛbɛyɛ nsia mmienu yɛ pɛ, sɛ ɛyɛ anwummerɛ no deɛ a edi kan anaa deɛ ɛtɔ so apem, enti deɛ ɔhunuiɛ no nkyerɛ hwee wɔ bere tenten a agorɔ no akɔ so ho. Wɔ roulette mu no, ɛyɛ agorɔfoɔ a ɔduru pon bi a ɛkyerɛ kɔkɔɔ nwɔtwe na ɔsi gyinaeɛ sɛ ɛsɛ sɛ ɛpono no akyini nnɔnhwerew pii ansa na ayɛ saa. Adwene mfomsoɔ a ɛtaa ba no kenkan deɛ atwam no de kɔ kyinhyia a ɛdi so no so; yei deɛ ɛkenkan adeɛ a ɛnnu saa a wohunuiɛ de kɔ deɛ atwam a obiara anhunu so.
Adwene ho nhwehwɛmufoɔ bi a ɔgye dii
Adwene mfomsoɔ no anya nhomanimfoɔ a wɔbɔ ho ban. Germany adwene ho nhwehwɛmufoɔ Karl Marbe hwehwɛɛ awoɔ nkrataa nwoma ɛnan a emu biara wɔ awoɔ 49,152 mu, ɔhunuu sɛ mmabarima anaa mmabaa ntoatoasoɔ a ɛware sene biara yɛ 17, na ɔkaa sɛ ntoatoasoɔ tenten nnu saa sene sɛdeɛ akwadwerɛ ma kwan, enti ntoatoasoɔ ma nsunsuansoɔ foforɔ no hokwan kɔ soro. Akwadwerɛ nko ara ka asɛm foforɔ: wɔ awoɔ 196,608 mu no, ntoatoasoɔ 17 anaa nea ɛboro saa ba bɛyɛ mpɛn ɛnan wɔ enum mu. Deɛ Marbe hunuiɛ no ne sɛdeɛ nneɛma a ɛba kwa ntoatoasoɔ te pɛpɛɛpɛ. Epstein (2013) san ka asɛm no; “Ntoatoasoɔ hokwan wɔ roulette mu” de roulette deɛ no ma.
Baabi a adwene mfomsoɔ no mfa ho
Sɛ ntwahonan no yɛ animhwɛ wɔ ne nipadua mu a, anka kyinhyia a atwam no bɛkyerɛ biribi, ɛfiri sɛ anka ɛyɛ adansedie a ɛfa ntokuru no ho mmom sene akwadwerɛ. Ɛno ne nhwehwɛmu dan no asɛm, na ɛhia kyinhyia mpempem fi ntwahonan baako a wonim so ansa na ɛbɛka biribi. Kɔkɔɔ ntoatoasoɔ du wɔ ntwahonan a wonnim so deɛ, animhwɛ nkyerɛkyerɛmu no hokwan sua koraa sene akwadwerɛ deɛ no.
Nsɛmmisa
Dabi. Ɛfa adeɛ biara a ɛmfa ho a ɛsan si ho: dice, sika a wotow, lɔtri nɔma.
Kyɛfa no bɛbɛn wɔn ho. Wo nsunsuansoɔ deɛ, ɛda so bɛyɛ bɛyɛ −2.70% wɔ deɛ wode too bɛt mu no mu.
Mfinimfini mmara biara nni hɔ. Dodoɔ kɛseɛ mmara na ɛwɔ hɔ, na ɛyɛ adwuma denam nneɛma foforɔ a ɛfra mu so.
Akontaabu ho anigyeɛ
Di kan yɛ eyinom ara wo ho. Wɔakata mmuaeɛ biara so; sɛ woasiesie wo ho a, bue no.
Sɛ wotow sika kɛtɛ mprɛ 10 a, ɛkyerɛ ti 7 ne akyi 3. Sɛ wotow no mprɛ 1,000 a, ɛkyerɛ ti 517 ne akyi 483. Akyi no tiw ti no tooe?
Kyerɛ mmuaeɛ no
Mmuaeɛ Daabi. Nsonsonoeɛ no nyinii fi 4 kɔɔ 34. Nkyɛmu no nko ara na ɛbɛn pɛ.
Ti ne akyi nkyɛmu no tew so fi 7/3, bɛyɛ 2.33, kɔɔ 517/483, bɛyɛ 1.07. Ɛno ne dodoɔ kɛseɛ mmaraakontaabuDodoɔ kɛseɛ mmaraNsɛm a ɛmfa ho mfinimfini boɔ kɔ hyia boɔ a wɔhwɛ kwan bere a sɔhwɛ dodoɔ renyini.Kenkan ne nyinaa → a ɛreyɛ adwuma.
Nsonsonoeɛ a ɛda wɔn ntam no nyinii, fi 4 kɔɔ 34. Sika kɛtɛ a ɛyɛ pɛ deɛ, nsonsonoeɛ bɛyɛ 30 wɔ ntow 1,000 akyi yɛ adeɛ a ɛtaa ba: nsonsonoeɛ a ɛtaa ba no nyini bɛyɛ sɛdeɛ ntow dodoɔ no square root teɛ, bere a nkyɛmu no rekɔ 1 so.
Biribiara antwe akyi no ansan amma. Ti a ɛboroo so mfiaseɛ no, ntow 990 a ɛdii so no frafraa mu, na ɛnyɛ sɛ wɔsiesiee no.
Tow sika kɛtɛ mprɛ ɛnan na hwɛ ntow a ɛba ti akyi pɛɛ no nko ara. Wɔn mu kyɛfa bɛn na ɛyɛ ti? Bu no ma ntoatoasoɔ 16 a ebetumi aba no mu biara na fa kyɛfa no mfinimfini. Ɛyɛ 50%?
Kyerɛ mmuaeɛ no
Mmuaeɛ Daabi. Ɛyɛ 17/42, bɛyɛ 40.5%. Sɛ wohwɛ no saa ɔkwan yi so a, ɛte sɛ nea sika kɛtɛ a ɛyɛ pɛ dwo wɔ ti akyi.
Kyerɛw ntoatoasoɔ 16 no. Wɔn mu mmienu, TTTT ne TTTH, nni ti wɔ ntow mmiɛnsa a edi kan no mu, enti biribiara nni ti akyi; ɛgyaw 14.
Wɔn mu biara mu no, fa ntow a ɛdi ti akyi na hwehwɛ kyɛfa a ɛyɛ ti. HHHH ma 3 wɔ 3 mu. HHHT ma 2 wɔ 3 mu. HTHT ma 0 wɔ 2 mu. Sɛ wofa 14 no nyinaa mu a: ntoatoasoɔ nsia ma 0, ɛnan ma 1/2, baako ma 2/3 na mmiɛnsa ma 1 (HHHH, THHH ne TTHH).
Ka kyɛfa no bom: 4 × 1/2 + 2/3 + 3 = 17/3. Fa 14 kyɛ mu: 17/42 ≈ 40.5%.
Ntow biara mmoa akyi; biara yɛ 50–50. Nkyea no fi mfinimfini a wobu wɔ ntoatoasoɔ biara so: ntoatoasoɔ a ti ahyɛ no ma no wɔ ntow pii a wobɛhwɛ nanso wɔkan no prɛko, sɛ ntoatoasoɔ a baako pɛ wom pɛ. Miller ne Sanjurjo (2018) kyerɛe sɛ nsa a ɛhye nhwehwɛmu a ɛwɔ 1985 mu no susuu ne basketball agorɔfoɔ saa ɔkwan yi so, enti agorɔfoɔ a ɛte sɛ nea wɔn ntoatoasoɔ mmoro deɛ ɛba kwa no, nokwasɛm mu na wɔboro so kakra.
Serew kakra
Ɛfra mu, ɛnsiesie. Ntwahonan no nni obiara ka.
Nsɛm fibea
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Croson, R. & Sundali, J. “The gambler’s fallacy and the hot hand: empirical data from casinos.”
- Chen, D. L., Moskowitz, T. J. & Shue, K. “Decision making under the gambler’s fallacy: evidence from asylum judges, loan officers, and baseball umpires.”
- Clotfelter, C. T. & Cook, P. J. “The ‘gambler’s fallacy’ in lottery play.”
- Gilovich, T., Vallone, R. & Tversky, A. “The hot hand in basketball: on the misperception of random sequences.”
- Miller, J. B. & Sanjurjo, A. “Surprised by the hot hand fallacy? A truth in the law of small numbers.”
- Hacking, I. “The inverse gambler’s fallacy: the argument from design. The anthropic principle applied to Wheeler universes.”