Te Tūponotanga o ngā Raupapa i te Rūreti
He mea noa ngā raupapa roa o te tae kotahi. He horihori noa hoki mō te hurihanga e whai ake nei.
E rima ngā whero i muri tonu i a rātou: 2.7%. Tekau: 0.074%. I tētahi wā tākaro o ngā hurihanga 200, ko te raupapa e ono o te tae kotahi ka puta i te nuinga o ngā wā.
Kia hia te auau o te raupapa hinga
Ka hinga te peti utu ōrite i te wīra kore kotahi i ngā hurihanga 19 o ia 37. Ko ia rārangi te tūpono ka hinga katoa tētahi raupapa hurihanga, me te nui kua ngaro i taua wā i te kaitākaro Martingale, e whakarua ana i muri i ia hinga.
| ngā hinga raupapa | tūpono | tata ki te 1 i ia | kua ngaro tae noa ki nāianei | peti e whai ake ana |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Ko te tūpono, ko te 19/37 kua whakareatia ki a ia anō kotahi te wā mō ia hinga, ka tatauria mai i tētahi hurihanga kua tohua. He maha ngā hurihanga i te wā tākaro roa e tīmata ai pea taua raupapa, nō reira i te pō katoa he nui ake rawa tōna tūpono i tā te rārangi kotahi e whakaatu ana.
Te raupapa kotahi
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 → kia wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia → katoa ngā hurihanga k e whai ake nei he (18/37)ᵏ. E rua: 23.7%. E rima: 2.7%. Tekau: 0.074%, tata ki te 1 i roto i te 1,350. Rua tekau: 1 i roto i te 1.8 miriona. Rua tekau mā ono, te rekoata o Monte Carlo: 1 i roto i te 137 miriona. Ko ēnei ngā tūponotanga o tētahi raupapa motuhake ka tīmata i tētahi hurihanga motuhake, ā, tata kāore tētahi e tino pātai ana i taua pātai.
I tētahi wā tākaro
Ko te pātai e kōrerotia ana e te tangata ko “ka puta tētahi raupapa k ki tētahi wāhi o taku wā tākaro?”, ā, he nui ake rawa te whakautu i te (18/37)ᵏ, nā te mea ko te wā tākaro o ngā hurihanga 200 tata ki te 200 ngā wāhi e tīmata ai tētahi raupapa. Ko te raupapa e ono, nui ake rānei, o te tae kotahi, he whero, he pangopetiPangoHe peti utu ōrite ki ngā tau pango e 18. Wīwī: noir.Pānuitia katoatia → rānei, ka puta i tētahi wā tākaro o ngā hurihanga 200 tata ki te 94% o ngā wā; e waru, nui ake rānei, tata ki te 47%; tekau, nui ake rānei, tata ki te 14%. Ki te whakaingoatia te tae i mua, ka heke ngā tūpono, tata ki te 75%, te 27% me te 7%. Ko te kaitākaro ka noho mō te ahiahi katoa ka kite i ngā raupapa roa i ia ahiahi.
He aha i whai take ai ki te Martingale
Ko ia kaunekerautakiKaunekeIa ture e huri ana i te moni peti i runga i ngā hua o mua. Ka whakapiki ngā kauneke whakarunga i te hinga i muri i ngā hinga, ko ngā kauneke whakarunga i te toa i muri i ngā toa.Pānuitia katoatia → whakarunga i te hinga he roa raupapa e pakaru ai: e ono ngā hinga mai i te tūāpapa $10 i te tepe $500, tekau mō te FibonaccirautakiFibonacciHe kauneke e whai ana i te raupapa 1, 1, 2, 3, 5, 8, 13…: kotahi te hīkoi whakamua i muri i te hinga, e rua ngā hīkoi whakamuri i muri i te toa.Pānuitia katoatia →, e rima mō te whakatoru i ngā tatinipetiTatini1–12, 13–24, 25–36 rānei, ko te utunga 2:1.Pānuitia katoatia →. Ko te tūponotanga o te raupapa hinga e ono i te utu ōrite he (19/37)⁶ ≈ 1.8% i ia ngana, ā, tērā pea 100 ngā ngana i tētahi wā tākaro o ngā hurihanga 200, nō reira ka tae mai te pakaru tata ki ngā wā tākaro e whā i roto i te rima o taua roa. Ko te tūponotanga o ngā raupapa i te rūreti te take ehara te pari i te mea onge.
Ngā tau wera me ngā tau makariri
Ka pā taua tātai anō ki ngā tau kotahipetiTau kotahiHe tau kotahi, ko te utunga 35:1.Pānuitia katoatia →. I ngā hurihanga 300 ko te tatau tūmanako mō ia tau he 8.1; ko te hipanga paerewapāngarauHipanga paerewaTe pūtake rua o te tītaringa; te tawhiti noa o te hua i te uara tūmanako.Pānuitia katoatia → tata ki te 2.8. Ka 15 ngā putanga o tētahi tau, ka 2 o tētahi atu, nā te tūpono anake, i ia wā. Ko te papa hua e whakanui ana i ngā tau “wera” e whakanui ana i te tihi o tētahi tohatoha noa. Ka whakamārama te Taiwhanga e hia ngā hurihanga i mua i te whai tikanga o tētahi tau werapakiwaitaraTau weraHe tau kua nui ake te puta i tērā i tūmanakohia i nā tata nei. I te wīra tōkeke, kāore he matapae.Pānuitia katoatia → (he mano, i tētahi wīra kotahi kua tautohua).
Ko te motuhaketanga te take katoa
Ko te raupapa whero tekau kāore e whakanui ake i te tūpono o te pango, kāore hoki e whakanui ake i te tūpono o te whero. He 18/37 rāua tahi. He āhuatanga ngā raupapa o ngā raupapa matapōkere, ā, ka whakapae mēnā kāore i puta: ko te raupapa o ngā hurihanga 200 kāore he raupapa e roa ake ana i te whā, he taunakitanga kaha ake rawa o te raweke i tētahi he raupapa tekau mā rua tōna.
Tātai
Ngā pātai
Ko ngā pango 26 i Monte Carlo i te 18 o Ākuhata 1913 te mea rongonui. E 32 ngā whero i muri tonu i a rātou i pūrongotia i tētahi whare petipeti i Amerika i te tau 1943. E hāngai ana rāua tahi ki te tūpono, i te maha o ngā hurihanga e whakahaerehia ana e ngā whare petipeti.
He 18/37 ahakoa te aha. Petihia tā tō mahere e kī ana, kaua rānei e peti.
Kāo. Ka kitea te tītaha ina auau ake te puta o ētahi kōhaotaputapuKōhaoTētahi o ngā wehenga e 37 kua tauia i te rōta. Arā anō: slot, cup.Pānuitia katoatia → i ngā mano hurihanga, kaua i ngā raupapa o tētahi tae.
He Pārekareka te Pāngarau
Me whakamātau koe i ēnei i te tuatahi. Kua kōpakina ia otinga; whakatuwherahia ina rite koe.
E hia ngā hurihanga o te wīra Ūropi, i te toharite, kia puta ia tau o ngā tau 37 kia kotahi te wā, nui ake rānei?
Whakaaturia te otinga
Whakautu Tata ki ngā hurihanga 155 i te toharite; ko te tau waenga ko te 147.
Tatauria te tatari, kotahi te tau hou i te wā kotahi. Ka puta i te hurihanga tuatahi he tau hou i ngā wā katoa. Ina kitea e koe te 1 tau, e 36 o ngā kōhaotaputapuKōhaoTētahi o ngā wehenga e 37 kua tauia i te rōta. Arā anō: slot, cup.Pānuitia katoatia → 37 he hou, nō reira ka 37/36 ngā hurihanga i te toharite mō te tau hou e whai ake ana. Ina kitea e koe ngā tau k, ka 37/(37 − k).
Tāpirihia ngā tatari: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = 155.5 hurihanga.
Ko te nuinga o tēnā kei te mutunga. Ko te tau whakamutunga anake e 37 ngā hurihanga i te toharite, ā, ko ngā tau whakamutunga e rima tata ki te 85. I te wīra Amerika ka tata ki te 161 taua tapeke anō. Ko te rapanga a te kaikohi kūpona tēnei; ka puta taua toharite anō i te tātaitanga paerewa.
I ngā hurihanga 37 o te wīra Ūropi, kotahi te hurihanga mō ia kōhao, e hia ngā tau rerekē ka tūmanakohia e koe kia kitea?
Whakaaturia te otinga
Whakautu Tata ki te 23.6. Tata ki te hautoru o ngā tau, tata ki te 13, kāore e puta rawa.
Tīpakohia tētahi tau, hei tauira te 17. I ia hurihanga ka kore e puta ko te tūpono 36/37, nō reira ka hapa i ngā hurihanga katoa e 37 ko te tūpono (36/37)³⁷ ≈ 0.363.
He ōrite te tūpono o ia tau, nō reira i te toharite e 37 × 0.363 ≈ 13.4 ngā tau ka ngaro, ā, e 37 − 13.4 ≈ 23.6 ka puta, he maha o ēnei e rua ngā wā, nui ake rānei.
Ka kīia tēnei e ngā kaitākaro rūreti ko te ture o ngā hautoru. Ehara i te ture, he tātai anake o ngā tukurua: i tētahi raupapa e rite ana te roa ki te wīra, tata ki te hautoru o ngā tau ka noho wahangū, i runga i te wīra tōkeke pērā i ētahi atu. I ngā kōhao 38 ko te wāhanga ko (37/38)³⁸ ≈ 0.363 anō; mō te wīra nui ka tata ki te 1/e ≈ 0.368.
Ka whakaatu tētahi hoa ki a koe i ngā rārangi e rua o ngā tae 50, he wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia →, he pangopetiPangoHe peti utu ōrite ki ngā tau pango e 18. Wīwī: noir.Pānuitia katoatia → rānei, ā, e ai ki te kōrero i ahu mai ia rārangi i tētahi wīra kua whakarērea ngā 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 →. E 25 ngā whakawhitinga tae o tētahi, ā, ko tōna raupapa roa rawa e ono. E 35 ngā whakawhitinga o tērā atu, ā, kāore rawa tōna raupapa e roa ake i te toru. Ko tēhea i hangaia noatia?
Whakaaturia te otinga
Whakautu Ko te tuarua. Tata ki te 24, ki te 25 rānei ngā whakawhitinga o te rārangi tūturu. Ko te rārangi he 35 ōna whakawhitinga ka puta tata ki te kotahi i ngā rārangi 500, ā, ko te rārangi kāore he raupapa roa ake i te toru tata ki te rua i ngā 100.
Ka tukurua, ka whakawhiti rānei ia tae hou i te tae o mua, haurua, haurua, nō reira ka puta i ngā tūpono whakawhiti 49 ngā whakawhitinga 24.5 i te toharite, tāpiri, tango rānei tata ki te 3.5. Ko te toru tekau mā rima e toru o aua hīkoi ki runga ake i te toharite; ka puta i te wīra tōkeke taua maha o ngā whakawhitinga tata ki te kotahi i ngā rārangi 500.
Ka pērā anō te kōrero a ngā raupapa. He raupapa o te whā, nui ake rānei, kei te rārangi tūturu o te 50 tata ki te 98% o te wā, ā, ko tōna raupapa roa rawa he rima, he ono rānei te nuinga o te wā.
Ka nui rawa ngā whakawhitinga a te tangata ina tonoa kia hanga noa i tētahi rārangi matapōkere, nā te mea ki a rātou he tauira te āhua o te raupapa o te whā, o te rima rānei. Ka whakaatu a Taylor (2021) i taua tohu anō i ngā rārangi whiunga moni i hangaia noatia e ngā ākonga: he nui ake ngā raupapa o te matapōkere tūturu i tā te tangata e whakaaro ai.
Ka kōrero tētahi pukapuka o ngā kōrero whare petipeti mō tētahi kaitākaro i puta tōna tau e rima ngā wā karapīpiti, ā, ka kīia he rekoata. He pēhea te onge o tēnā i te wīra Ūropi? Ā, kia hia te auau o tōna putanga i tētahi wāhi o te whare petipeti kotahi he 20 ōna tēpu, ka hurihia ia tēpu kia 40 ngā wā i te hāora, i te ao, i te pō?
Whakaaturia te otinga
Whakautu He tau kua whakaingoatia e rima ngā wā karapīpiti: 1 i ngā 69 miriona. Ko tētahi tau ka puta anō e whā ngā wā i muri i tōna putanga tuatahi: 1 i ngā 1.87 miriona. Tata ki te 7 miriona ngā hurihanga o taua whare petipeti i te tau, nō reira me kite ia i te raupapa o te rima e toru, e whā rānei ngā wā i te tau.
Ka puta te tau kua whakaingoatia ko te tūpono 1/37 i ia hurihanga, nō reira ko te tūpono o te rima karapīpiti ko (1/37)⁵ = 1 i ngā 69,343,957. Engari kāore tētahi e whakaingoa i te tau i mua. Ahakoa he aha te tau ka puta tuatahi, me tukurua e ngā hurihanga e whā e whai ake ana: (1/37)⁴ = 1 i ngā 1,874,161.
20 tēpu × 40 hurihanga × 24 hāora × 365 rā = 7,008,000 hurihanga i te tau. Ka taea e ia hurihanga te tīmata i tētahi raupapa, nō reira ka tūmanako te whare petipeti ki te 7,008,000/1,874,161 ≈ 3.7 raupapa o te rima i te tau.
Kāore he rekoata ōkawa pēnei, ā, kāore he take: ko te mea onge i te tēpu kotahi he mea noa puta noa i te whare petipeti, ā, ka kōrerotia ngā kōrero mō te tēpu i puta ai. Ko te kōrero, kei Goldman (2007), i runga i te wīra kore-rua, ā, ko ngā tatauranga ko te 1 i ngā 79 miriona me te 1 i ngā 2.09 miriona.
He katakata iti
Ko ngā raupapa roa te āhua o te matapōkere.
Ngā Puna
- 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.