Ntoatoasoɔ hokwan wɔ roulette mu

Akontaabu ho anigyeɛ

Di kan yɛ eyinom ara wo ho. Wɔakata mmuaeɛ biara so; sɛ woasiesie wo ho a, bue no.

1. Kyinhyia ahe na Yuropu ntwahonan hia, wɔ mfinimfini mu, ansa na nɔma 37 no mu biara aba mprɛ baako dodoɔ yi?

   Kyerɛ mmuaeɛ no

   Mmuaeɛ Bɛyɛ kyinhyia 155 wɔ mfinimfini mu; mfinimfini nɔma no yɛ 147.

   Kan twɛn no nɔma foforɔ baako baako. Kyinhyia a edi kan daa kyerɛ nɔma foforɔ. Sɛ woahu nɔma 1 a, ntokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → 36 wɔ 37 mu yɛ foforɔ, enti nɔma foforɔ a ɛdi so no gye kyinhyia 37/36 wɔ mfinimfini mu. Sɛ woahu nɔma k a, ɛgye 37/(37 − k).

   Ka twɛn no nyinaa bom: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = kyinhyia 155.5.

   Emu fa kɛseɛ no ara ne awieeɛ no. Nɔma a ɛtwa toɔ no nko ara gye kyinhyia 37 wɔ mfinimfini mu, na enum a ɛtwa toɔ no bɛyɛ 85. Wɔ Amerika ntwahonan so no, nkabom korɔ no ara ma bɛyɛ 161. Yei ne coupon collector asɛmmisa no; mfinimfini boɔ korɔ no ara firi nkontaabu a wɔtaa yɛ no mu ba.

2. Wɔ Yuropu ntwahonan kyinhyia 37 mu, kyinhyia baako ma tokuru biara, nɔma ahodoɔ ahe na ɛsɛ sɛ wohwɛ kwan sɛ wobɛhu?

   Kyerɛ mmuaeɛ no

   Mmuaeɛ Bɛyɛ 23.6. Nɔma no bɛyɛ nkyɛmu mmiɛnsa mu baako, bɛyɛ 13, mma koraa.

   Fa nɔma baako, te sɛ 17. Kyinhyia biara so no, ɛmma wɔ hokwan 36/37 mu, enti ɛtwa kyinhyia 37 no nyinaa ho wɔ hokwan (36/37)³⁷ ≈ 0.363 mu.

   Nɔma biara hokwan yɛ pɛ, enti wɔ mfinimfini mu nɔma 37 × 0.363 ≈ 13.4 yera na 37 − 13.4 ≈ 23.6 ba, na emu pii ba mprɛ mmienu anaa nea ɛboro saa.

   Roulette agorɔfoɔ frɛ yei nkyɛmu mmiɛnsa mmara. Ɛnyɛ mmara, ɛyɛ nsan-ba nkontaabu nko ara: wɔ ntoatoasoɔ a ne tenten te sɛ ntwahonan no mu no, nɔma no bɛyɛ nkyɛmu mmiɛnsa mu baako tena ase, wɔ ntwahonan a ɛyɛ pɛ so sɛdeɛ ɛte wɔ foforɔ biara so. Wɔ ntokuru 38 so no kyɛfa no nso yɛ (37/38)³⁸ ≈ 0.363; wɔ ntwahonan kɛseɛ so no ɛtena 1/e ≈ 0.368 nkyɛn.

3. Wo nnamfo bi kyerɛ wo kɔla 50 nsɛm nkyerɛwee mmienu, kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → anaa tuntumbɛtTuntumSika pɛ bɛt wɔ nɔma tuntum 18 no so. Franse kasa mu: noir.Kenkan ne nyinaa →, a wɔka sɛ biara firi ntwahonan bi a wɔayi 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 → afiri so. Baako sesa kɔla mprɛ 25 na ne ntoatoasoɔ a ɛware sen biara yɛ nsia. Ɔfoforɔ no sesa mprɛ 35 na ne ntoatoasoɔ mmoro mmiɛnsa da. Ɛhe na wɔbɔɔ no adwene mu?

   Kyerɛ mmuaeɛ no

   Mmuaeɛ Ɛto so mmienu no. Nkyerɛwee ankasa sesa bɛyɛ mprɛ 24 anaa 25. Deɛ ɛsesa mprɛ 35 ba bɛyɛ mprɛ baako wɔ nkyerɛwee 500 mu, na deɛ ne ntoatoasoɔ mmoro mmiɛnsa da no ba bɛyɛ mprɛ mmienu wɔ 100 mu.

   Kɔla foforɔ biara san yɛ deɛ atwam no anaa ɛsesa, fa ne fa, enti hokwan 49 a wɔde bɛsesa ma nsakraeɛ 24.5 wɔ mfinimfini mu, ɛkɔ soro anaa fam bɛyɛ 3.5. Aduasa enum yɛ saa anammɔn no mu mmiɛnsa wɔ mfinimfini boɔ no so; ntwahonan a ɛyɛ pɛ ma nsakraeɛ dodoɔ saa bɛyɛ mprɛ baako wɔ nkyerɛwee 500 mu.

   Ntoatoasoɔ no ka asɛm korɔ no ara. Nkyerɛwee ankasa a ne dodoɔ yɛ 50 wɔ ntoatoasoɔ ɛnan anaa nea ɛboro saa bɛyɛ 98% wɔ bere no mu, na ne ntoatoasoɔ a ɛware sen biara taa yɛ enum anaa nsia.

   Nnipa a wɔka kyerɛ wɔn sɛ wɔmmɔ nkyerɛwee a ɛba kwa adwene mu sesa mpɛn pii dodo, ɛfiri sɛ ntoatoasoɔ ɛnan anaa enum te sɛ nhyehyɛe wɔ wɔn ani so. Taylor (2021) kyerɛ agyiraeɛ korɔ no ara wɔ sika ti ne akyi ntoɔ nkyerɛwee a asuafoɔ bɔɔ no adwene mu no mu: deɛ ɛba kwa ankasa wɔ ntoatoasoɔ pii sen sɛdeɛ nnipa hwɛ kwan.

4. Kasino nsɛm nwoma bi ka agorɔfoɔ bi a ne nɔma baa mprɛ enum toatoa so ho asɛm na ɛfrɛ no record. Ɛno nnyɛ mpɛn pii dodoɔ sɛn wɔ Yuropu ntwahonan so? Na ɛsɛ sɛ ɛba mpɛn ahe wɔ baabi wɔ kasino baako a ɛpono 20 wom, a biara kyini mprɛ 40 dɔnhwerew biara, awia ne anadwo?

   Kyerɛ mmuaeɛ no

   Mmuaeɛ Nɔma a wɔabɔ ne din mprɛ enum toatoa so: 1 wɔ ɔpepepem 69 mu. Nɔma biara a ɛsan ba mprɛ ɛnan foforɔ wɔ bere a edi kan ba akyi: 1 wɔ ɔpepem 1.87 mu. Saa kasino no kyini bɛyɛ mprɛ ɔpepem 7 afe biara, enti ɛsɛ sɛ ɛhu ntoatoasoɔ enum mprɛ mmiɛnsa anaa ɛnan afe biara.

   Nɔma a wɔabɔ ne din ba wɔ hokwan 1/37 mu kyinhyia biara, enti enum a ɛtoatoa so hokwan yɛ (1/37)⁵ = 1 wɔ 69,343,957 mu. Nanso obiara mmɔ nɔma no din ansa. Biribiara a edi kan ba no, ɛsɛ sɛ kyinhyia ɛnan a ɛdi so no san ba: (1/37)⁴ = 1 wɔ 1,874,161 mu.

   Ɛpono 20 × kyinhyia 40 × dɔnhwerew 24 × nna 365 = kyinhyia 7,008,000 afe biara. Kyinhyia biara tumi hyɛ ntoatoasoɔ ase, enti kasino no hwɛ kwan sɛ ɛbɛhu 7,008,000/1,874,161 ≈ ntoatoasoɔ enum 3.7 afe biara.

   Record ankasa biara a ɛte saa nni hɔ, na ɛnhia: adeɛ a ɛnnyɛ mpɛn pii wɔ ɛpono baako so yɛ adeɛ a ɛtaa ba wɔ kasino mu nyinaa, na wɔka nsɛm no fa ɛpono a ɛbaa so ho. Asɛm no, wɔ Goldman (2007) mu no, si hwee mmienu ntwahonan so, baabi a nɔma no yɛ 1 wɔ ɔpepem 79 mu ne 1 wɔ ɔpepem 2.09 mu.