Te Pōhēhē a te Kaipetipeti
Te whakapono kua “tae te wā” o tētahi hua nā te mea kua roa kāore i puta.
I muri i ngā whero tekau, ko te tūponotanga o te pango he 18/37 tonu. Kāore te wīra e pupuri rekoata, kāore hoki he nama ki a ia.
Te pōhēhē
Mēnā kua tekau ngā putanga o te wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia →, ka whakaaro te maha o ngā kaitākaro kua “tae te wā” o te pangopetiPangoHe peti utu ōrite ki ngā tau pango e 18. Wīwī: noir.Pānuitia katoatia →, ā, ka peti pērā. Ka whakaaro ētahi atu he “wera” te whero, ā, ka peti ki tērā. Kei te whakaaro rāua tahi mai i tētahi raupapa kua mutu kē ki tētahi hurihanga kāore anō kia puta. Kāore te pōrotaputapuPōroTe pōro iti ka panga ki te ara, ki te ahunga kōaro ki te rōta. Ko ngā pōro o nāianei he ivorine, he Teflon rānei, 18–21 mm.Pānuitia katoatia → e mōhio he aha ngā hurihanga tekau whakamutunga; he ōrite te rahi o ngā kōhaotaputapuKōhaoTētahi o ngā wehenga e 37 kua tauia i te rōta. Arā anō: slot, cup.Pānuitia katoatia → ki tō rātou rahi i te hāora kua pahure; ko te tūponotangapāngarauTūponotangaTe tūpono o tētahi putanga, mai i te 0 ki te 1, mai i te 0% ki te 100% rānei. Tau kotahi: 1/37 = 2.70%.Pānuitia katoatia → o te pango he 18/37, pērā i ngā wā katoa.
He aha i rite ai ki te pono
I te wā roa ka tata tonu ngā ōwehenga o te whero me te pango ki te 18/37 ia. Mā te ture o ngā tau nuipāngarauTure o ngā tau nuiKa tata atu te toharite o ngā hua motuhake ki te uara tūmanako i te tipu o te maha o ngā whakamātautau.Pānuitia katoatia → tērā e whakapūmau. Engari ka puta te tatanga mā te whakawaimeha, kaua mā te whakatika: i muri i ētahi atu hurihanga 1,000, ko ngā whero tāpiri tekau he hapa porotaka noa i te ōwehenga, ehara nā te mea i hopu te pango, engari nā te mea i tupu te tauira. Kāore he tikanga e whakanui ake ai i te tūpono o te pango, ā, kāore te ture o ngā tau nui e hiahia ana ki tētahi.
Monte Carlo, 18 Ākuhata 1913
E 26 ngā wā i puta ai te pango i muri tonu i a rātou i tētahi tēpu i te Casino de Monte-Carlo. Mai i te pango tekau mā rima pea, ka popoki ngā kaitākaro ki te whero, ka whakaruarua, ka whakaruarua anō, ko ia hurihanga “ka tino pono ake” i tērā o mua. He miriona wārangi i toa ai te whare petipeti. Ko te tūponotanga o taua raupapa he 1 i roto i te 137 miriona mai i te pango tuatahi, ā, ko te tūponotanga ka puta ā tōna wā ki tētahi wāhi o ngā whare petipeti o te ao tata tonu ki te kotahi. Koinā te take e kīia ai te pōhēhē a te kaipetipeti ko te pōhēhē o Monte Carlo hoki.
He mea noa. Ka puta kotahi i roto i ngā wā 44.
Ka tīmata ngā kaitākaro ki te kite. Kua “tae te wā” o te whero.
Kua kī te tēpu. Ka whakaruaruatia ngā moni peti ki te whero i muri i ia hinga.
Kua ngaro ngā rawa nui. Ko ia pango hou ka rite ake te whero ki te mea tino pono.
Ka mutu te raupapa. He miriona wārangi kua toa te whare petipeti i ngā tāngata e peti ana ki te raupapa kāore i taea te “mōhio” he raupapa ia.
Te ringa wera
Ko te peti ki tētahi tae nā te mea kei te raupapa ia, ko taua hapa anō kua hurihia: ka tūmanakohia ka haere tonu te raupapa, kaua ka mutu. Ka kīia e ngā kaimātai hinengaro ko te ringa werapakiwaitaraRinga weraTe whakapono mā te raupapa toa, raupapa hua kotahi rānei, ka nui ake te tūpono o tētahi atu. I te wīra, ko te pōhēhē a te kaipetipeti kua hurihia kōarotia.Pānuitia katoatia →, i muri i tētahi rangahau o 1985 nā Gilovich, Vallone me Tversky i rapu i ngā raupapa i te panga pōro i te poitūkohu, ā, kāore i kitea he aha i tua atu i te tūpono. I te tau 2018 i whakaatu a Miller rāua ko Sanjurjo he tītaha te whakamātautau tonu: i tētahi rekoata poto, ko te ōwehenga o ngā tukinga i muri tonu i tētahi tukinga ka iti iho i te toharite i te reiti katoa o te kaipanga, nō reira ko te kaitākaro kāore rawa he ringa wera ka paku makariri te āhua. Ina whakatikaina, ka whakaatu aua raraunga anō i tētahi ringa wera iti. Ka taea e te tangata te whakamahana; kāore he āhua o te wīra hei noho ai. Ka mau ētahi kaitākaro ki ngā whakapono e rua i te wā kotahi, ka haere tonu te raupapa kia “roa rawa”, kātahi ka mutu. I tētahi wīra tōkeke, he ōrite te uara tūmanakopāngarauUara tūmanakoTe hua toharite mō ia peti i te wā roa. −1/37 o te moni peti mō ia peti Ūropi paerewa.Pānuitia katoatia → o ia momo ki te kōwhiri i tētahi tae mā te maka moni: −2.70% o te moni peti.
I tētahi tēpu tūturu
I mātakitaki a Croson rāua ko Sundali (2005) i ngā hāora 18 o te ataata haumarutanga mai i tētahi tēpu korewīraKoreTe kōhao kākāriki kotahi kāore e kapia e tētahi peti utu ōrite, tatini, tīwae rānei; te pūtake o te painga o te whare. Arā anō: kore kotahi, 0.Pānuitia katoatia →-rua i tētahi whare petipeti nui i Reno: 139 ngā kaitākaro e tuku ana i ngā peti 24,131. I ngā peti utu ōritepetiPeti utu ōriteWhero/pango, kehe/taurite, teitei/hakahaka. 18 ngā tau, ko te utunga 1:1.Pānuitia katoatia →, tata ōrite te wehenga o ngā kaitākaro i waenga i te whai i ngā raupapa poto me te whakahē. I muri i ngā mea ōrite e rima i muri tonu i a rātou ka tītaha rātou ki te whakahē i te raupapa, ā, i muri i te ono, nui ake rānei, ko te 85% o ā rātou peti i tērā taha. I whakaatu aua kaitākaro anō i te ringa wera mō rātou anō: i muri i te toa i ngā tau ka kapi rātou i ngā tau 13.6 i te hurihanga e whai ake ana i te toharite, ki te 9.2 i muri i te hinga. Kāore he tohu tītaha i tō rātou wīra, nō reira kāore tētahi o ēnei i whakarerekē i tā tētahi o rātou e tūmanako ai.
I waho o te whare petipeti
Ka puta taua kukume anō ki ngā wāhi e whakatauria ai ngā whakataunga tūturu. I whai a Clotfelter rāua ko Cook (1993) i te kēmu tau o ia rā o Maryland: ka heke kaha te moni ka petihia ki tētahi tau i te wā tonu i tōna tōnga, ā, he marama te roa e ora anō ai, ahakoa kāore he maharatanga o te tō. I kitea e Chen, Moskowitz rāua ko Shue (2016) i waenga i ngā ngaio. Ko ngā kaiwhakawā whakaruruhau o Amerika ka tae ki te 3.3 ōrau pāpātanga te nui ake o te tūpono ka whakakāhore i tētahi kēhi mēnā i whakaaetia e rātou te mea o mua. Ko ngā kaiwawao poipātū he 1.5 pāpātanga te iti iho o te tūpono ka karanga strike i muri i te karanga i tētahi, ā, neke atu i te rua whakarea o tērā i ngā panga tata. I tētahi whakamātautau ā-mara me ngā āpiha taurewa e utua ana ki te utu pūmau, ka tae ki te 9% o ngā whakataunga i hurihia pēnei. I tae mai ngā kēhi i te raupapa matapōkere, nō reira kāore te whakataunga whakamutunga i kī mai he aha mō te mea e whai ake ana, pērā i te hurihanga whakamutunga kāore e kī mai he aha mō te mea e whai ake ana.
Te pōhēhē kōaro a te kaipetipeti
I whakaingoatia e te tohunga whakaaro a Ian Hacking (1987) tētahi momo tuatoru. Ka hīkoi tētahi ki roto i tētahi rūma, ka kite i ngā mataono e rua ka taka hei ono-rua, ā, ka whakatau kua maha kē ngā wā i makaia ai. He ōrite te tūpono o ia maka kia ono-rua, ko te tuatahi o te ahiahi, ko te tuamano rānei, nō reira kāore te kitenga e kī mai he aha mō te roa o te kēmu. I te rūreti ko te kaitākaro ka tae ki tētahi papa e whakaatu ana i ngā whero e waru, ā, ka whakatau kua huri te tēpu mō ngā hāora hei whakaputa i ērā. Ko te pōhēhē noa ka pānui i ngā mea o mua ki te hurihanga e whai ake ana; ko tēnei ka pānui i tētahi kitenga onge ki tētahi wā o mua kāore tētahi i kite.
He kaimātai hinengaro i whakapono
He kaitaunaki mātauranga ō te pōhēhē. I tirotiro te kaimātai hinengaro Tiamana a Karl Marbe i ngā rēhita e whā o ngā whānautanga 49,152 ia, ka kitea ko te raupapa roa rawa o ngā tama, o ngā kōtiro rānei i muri tonu i a rātou he 17, ā, ka whakatau he onge ake ngā raupapa roa i tā te tūpono e whakaae ai, nō reira ka whakanui ake te raupapa i te tūpono o tērā atu putanga. He rerekē tā te tūpono anake e kī ana: i ngā whānautanga 196,608 ka puta te raupapa 17, nui ake rānei, tata ki te whā wā i roto i te rima. I kitea e Marbe te āhua tonu o tētahi raupapa matapōkere. Ka kōrero anō a Epstein (2013) i te kēhi; kei te whārangi Tūponotanga o ngā Raupapa te momo rūreti.
Ngā wāhi kāore e pā te pōhēhē
Mēnā he tītaha ā-tinana te wīra, ka whai mōhiohio ngā hurihanga o mua, nā te mea he taunakitanga ērā mō ngā kōhao, kaua mō te waimarie. Koinā te kaupapa o te Taiwhanga, ā, me mano ngā hurihanga mai i tētahi wīra kotahi kua tautohua kia kī ai i tētahi mea. Mō te raupapa whero tekau i tētahi wīra kāore e mōhiotia ana, he iti iho rawa te tūpono o te whakamārama tītaha i te whakamārama tūpono.
Ngā pātai
Kāo. Ka pā ki ia takahanga motuhake auau: ngā mataono, ngā moni maka, ngā tau rotarota.
Ka tata ngā ōwehenga. Ko tō hua ka tata tonu ki te −2.70% o te moni i petihia e koe.
Kāore he ture o ngā toharite. He ture o ngā tau nui, ā, ka mahi mā te whakawaimeha.
He Pārekareka te Pāngarau
Me whakamātau koe i ēnei i te tuatahi. Kua kōpakina ia otinga; whakatuwherahia ina rite koe.
I muri i ngā makanga 10, ka whakaatu tētahi moni i ngā upoko 7 me ngā hiku 3. I muri i ngā makanga 1,000, ka whakaatu i ngā upoko 517 me ngā hiku 483. I mau rānei ngā hiku i ngā upoko?
Whakaaturia te otinga
Whakautu Kāo. I tupu te āputa mai i te 4 ki te 34. Ko te ōwehenga anake i tata atu ki te ōrite.
I heke te ōwehenga o ngā upoko ki ngā hiku mai i te 7/3, tata ki te 2.33, ki te 517/483, tata ki te 1.07. Ko te ture o ngā tau nuipāngarauTure o ngā tau nuiKa tata atu te toharite o ngā hua motuhake ki te uara tūmanako i te tipu o te maha o ngā whakamātautau.Pānuitia katoatia → tērā e mahi ana.
I tupu te āputa i waenga i a rāua, mai i te 4 ki te 34. Mēnā he moni tōkeke, he noa te āputa tata ki te 30 i muri i ngā makanga 1,000: ka tupu te āputa noa, tata atu, i te taha o te pūtake rua o te maha o ngā makanga, ā, ka tau haere te ōwehenga ki te 1.
Kāore he mea i tō whakamuri i ngā hiku. Ko te nui o ngā upoko i te tīmatanga, i waimehatia e ngā makanga 990 i muri mai, kāore i whakatikaina.
Makahia tētahi moni kia whā ngā wā, ā, tirohia anake ngā makanga e whai tonu ana i te upoko. He aha te wāhanga o ērā he upoko? Tātaihia mō ia raupapa o ngā raupapa 16 ka taea, ā, tangohia te toharite o ngā wāhanga. He 50% rānei?
Whakaaturia te otinga
Whakautu Kāo. He 17/42, tata ki te 40.5%. Ki te tirohia pēnei, he āhua makariri haere te moni tōkeke i muri i te upoko.
Whakarārangitia ngā raupapa 16 (U = upoko, H = hiku). E rua o rātou, ko HHHH me HHHU, kāore he upoko i ngā makanga tuatahi e toru, nā reira kāore he mea e whai ana i te upoko; ka toe ko ngā 14.
I ia mea, tangohia ngā makanga e whai ana i te upoko, ā, kimihia te wāhanga he upoko. Ka hoatu e UUUU te 3 i ngā 3. Ka hoatu e UUUH te 2 i ngā 3. Ka hoatu e UHUH te 0 i ngā 2. Ki te haerea ngā 14 katoa: e ono ngā raupapa ka hoatu i te 0, e whā ka hoatu i te 1/2, kotahi ka hoatu i te 2/3, ā, e toru ka hoatu i te 1 (UUUU, HUUU me HHUU).
Tāpirihia ngā wāhanga: 4 × 1/2 + 2/3 + 3 = 17/3. Wehea ki te 14: 17/42 ≈ 40.5%.
Kāore tētahi makanga e manako ana ki ngā hiku; he 50–50 ia mea. Ka ahu mai te tītaha i te tango toharite i tēnā raupapa, i tēnā raupapa: ko te raupapa kī tonu i te upoko, he maha ōna makanga hei tirotiro, engari kotahi noa tōna tatauranga, ōrite ki te raupapa kotahi noa te upoko. I whakaatu a Miller rāua ko Sanjurjo (2018) i ine te rangahau ringa wera o te tau 1985 i ōna kaitākaro poitūkohu pēnei, nā reira ko ngā kaitākaro i āhua kore raupapa ake i te tūpono noa, he raupapa ake kē rātou, paku nei.
He katakata iti
He whakawaimeha, ehara i te whakatika. Kāore he nama a te wīra.
Ngā Puna
- 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.”