Roulette akontaabu · Akontaabu asɛmmisa · simma 7

Asɛmmisa: ɛbɛkyɛ ahe ansa na hwee aba

Hwee ba kyinhyia baako wɔ 37 mu wɔ mfinimfini mu. Bere tenten bɛn na wotwɛn ampa, na ɛdeɛn na ɛno yɛ obi a ɔto sika pɛ bɛt?

Mmuaeɛ tiawa

Twɛn a wotwɛn hwee no yɛ geometric: mfinimfini kyinhyia 37, mfinimfini nɔma 25, na twɛn baako wɔ aduonu mu sen kyinhyia 110. Wɔ agorɔ bere a kyinhyia 200 wom mu no, obi a ɔto sika pɛ bɛt hwɛ kwan sɛ hwee bɛba mpɛn 5.4 na ɔbɛhu baabi firi 1 kɔsi 10.

mfinimfini twɛn
kyinhyia 37
mfinimfini nɔma twɛn
kyinhyia 25
p(hwee biara mma wɔ kyinhyia 100 mu)
6.5%
hwee dodoɔ wɔ kyinhyia 200 mu
5.4 ± 2.3

Asɛmmisa no

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 → hokwanakontaabuHokwanHokwan a biribi bɛba, firi 0 kɔsi 1 anaa 0% kɔsi 100%. Nɔma baako: 1/37 = 2.70%.Kenkan ne nyinaa → yɛ 1/37 wɔ kyinhyia biara mu. (a) Hokwan bɛn na ɛwɔ hɔ sɛ hwee biara remma wɔ kyinhyia 37 a ɛdi hɔ mu? (b) Mfinimfini nɔma twɛn yɛ ahe? (c) Wɔ sika pɛ agorɔ bere a kyinhyia 200 wom mu no, mpɛn ahe na ɛsɛ sɛ agorɔfoɔ hwɛ kwan sɛ hwee bɛba, na ne ntam yɛ ahe?

Mmuaeɛ

(a) (36/37)³⁷ = 36.3%. Ɛboro nkyɛmu mmiɛnsa mu baako wɔ bere no mu no, kyinhyia 37 twam a hwee biara mma koraa, a ɛne akontaabu a ɛma “ɛba mpɛn baako anaa deɛ ɛboro saa wɔ nɔma baako bɛtbɛtNɔma baako bɛtNɔma baako pɛ, ɛtua 35:1.Kenkan ne nyinaa → so wɔ kyinhyia 37 mu” yɛ 63.7% pɛ no yɛ pɛ. (b) Twɛn W no yɛ geometric; p(W > k) = (36/37)ᵏ; mfinimfini nɔma no ne k a ɛha na eyi twam 0.5, a ɛyɛ k ≈ 25. Twɛn no fa yɛ kyinhyia 25 anaa deɛ ɛsua saa na fa nso ware sen saa; mfinimfini 37 no, dua tenten no twe kɔ soro. (c) Hwee dodoɔ wɔ kyinhyia 200 mu yɛ binomial a ne mfinimfini yɛ 200/37 = 5.4 na ne gyinapɛn nsakraeɛakontaabuGyinapɛn nsakraeɛNsakraeɛ ntini; ntam kwan a ɛtaa da deɛ ɛfiri mu ba ne boɔ a wɔhwɛ kwan ntam.Kenkan ne nyinaa → yɛ √(200 × (1/37) × (36/37)) ≈ 2.3. Ntam a ɛyɛ 95% yɛ bɛyɛ 1 kɔsi 10.

twɛn a wotwɛn hweehokwan
wɔ kyinhyia 10 mu24.0%
wɔ kyinhyia 25 mu49.6%
wɔ kyinhyia 37 mu63.7%
wɔ kyinhyia 50 mu74.6%
wɔ kyinhyia 100 mu93.5%
ɛboro kyinhyia 110≈ 5%
ɛboro kyinhyia 2000.4%
p(W ≤ k) = 1 − (36/37)ᵏ. Mfinimfini 37, mfinimfini nɔma 25.

Deɛ hwee bɔ ka ma obi a ɔto sika pɛ bɛt

Hwee biara bɔ bɛt sika baako ka, na hwee ne kasino mfasoɔ no nyinaa wɔ kɔkɔɔbɛtKɔkɔɔSika pɛ bɛt wɔ nɔma kɔkɔɔ 18 no so. Franse kasa mu: rouge.Kenkan ne nyinaa → so: wɔ kyinhyia 37 a ɛyɛ mfinimfini mu no, nkonim 18 ne ahwereɛ 18 pepa wɔn ho wɔn ho, na hwee baako no ne −1/37 no. Wɔ agorɔ bere a kyinhyia 200 wom wɔ $10 so no, hwee 5.4 a wɔhwɛ kwan no bɔ $54 ka, a ɛyɛ 200 × $10 / 37 pɛpɛɛpɛ. Agorɔ bere a hwee 2 baa mu no anya akyiresɛm pa $34; agorɔ bere a hwee 9 baa mu no anya akyiresɛm bɔne $36, na ɛbɛyɛ te sɛ deɛ wɔadaadaa. Wɔ la partagemmaraLa partageFranse mmara: sɛ hwee ba a, wɔsan de sika pɛ bɛt sika no fa ma. Ɛtew kasino mfasoɔ a ɛwɔ saa bɛt no so mu fa kɔ 1.35%.Kenkan ne nyinaa → ɛpono so no, hwee biara bɔ bɛt sika fa ka na nɔma no tew yɛ fa.

Hwee dodoɔ wɔ agorɔ bere a kyinhyia 200 wom mu% wɔ agorɔ bere so
0–1
2.5%
2–3
18%
4–5
34%
6–7
28%
8–9
13%
10 anaa deɛ ɛboro saa
4.5%
% wɔ agorɔ bere so
01734%
Binomial(200, 1/37). Obi a ɔde $10 to kɔkɔɔ so tua $10 wɔ hwee biara so; hwee dodoɔ trɛtrɛ ne anadwo no boɔ trɛtrɛ.

La Partage mmara wɔ roulette muWɔasisi roulette a ɛwɔ intanɛt so anaa? Gyidie hunu no

Deɛ ɛdi so

Hokwan bɛn na ɛwɔ hɔ sɛ hwee mmienu bɛdi so? (1/37)² = 1/1,369. Wɔ kasino a ɛpono 20 wom a ɛkyini mpɛn 50 dɔnhwere biara mu no, ɛyɛ bɛyɛ hwee mmienu a ɛdi so baako baabi dɔnhwere 1.4 biara. Agorɔfoɔ a wɔhu no si gyinaeɛ sɛ ntwahonan no asɛe; akontaabu no ka sɛ ɛyɛ da biara da.

Sɔ hwɛ

Session Simulator no kan hwee dodoɔ wɔ agorɔ bere biara mu. Di kyinhyia 100 mpɛn ɔhaha kakraa bi na kyerɛw dodoɔ no wɔ mfonini so: histogram a ɛwɔ soro no bɛda adi, a ne nifa dua tenten wɔ hɔ. Dua no ne baabi a anansesɛm no firi.

Akontaabu kwan

p(W > k) = (36/37)ᵏ
E[W] = 37 · mfinimfini nɔma ≈ 25
hwee dodoɔ wɔ kyinhyia N mu ~ Binomial(N, 1/37)

Nsɛmmisa

Hwee hokwan kɔ soro wɔ ntwahonan binom so?

Ɛnyɛ wɔ deɛ ɛyɛ pɛ so. Wɔ ntwahonan a ɛyɛ animhwɛnhwehwɛmu danNtwahonan a ɛyɛ animhwɛNtwahonan a ne honam so mfomsoɔ ma ntokuru bi hokwan boro 1/37. Ɛnnsɛ ho pii, na wobɛtumi ahunu no ɛnkyɛ sɛ wode kyinhyia mpempem a woakyerɛw ahwɛ.Kenkan ne nyinaa → so no, tokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → biara betumi ayɛ saa, na ɛbɛgye kyinhyia mpempem ansa na woahu.

Ɛsɛ sɛ mede agorɔ sika to hwee so daa sɛ ahobanbɔ?

Ɛyɛ 2.70% bɛt te sɛ afoforɔ nyinaa. Ɛsesa agorɔ bere no nsɛsoɔ (hwee bɛyɛ nkonim) na ɛnsesa ka no.

Adɛn nti na mfinimfini nɔma no sua sen mfinimfini no?

Ɛfiri sɛ twɛn nkyekyɛmu no nkɔ pɛ: twɛn tiatia pii, ne kakraa bi a ɛware koraa.

Serew kakra

Mfinimfini 37, mfinimfini nɔma 25, ne dua tenten a anansesɛm te mu.

Mfinimfini 37, mfinimfini nɔma 25, ne dua tenten a anansesɛm te mu.

Nsɛm fibea

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gambler’s ruin, ti XIV.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Ti 13, roulette.
wɔsan hwɛɛ mu 2026-09-28nhwɛsoɔ: Yuropu, hwee baakoakontaabu ɔkwan ↗nsɛm fibea ↗