Afidie a wɔde hyɛ roulette nkɔm
Sɛdeɛ kɔmputa susu bɔɔl no berɛ, wɔn a wɔyɛɛ deɛ edi kan, ne sɛdeɛ ɛsɛ sɛ ɛyɛ pɛpɛɛpɛ.
Roulette kɔmputa susu bɔɔl ne rotor berɛ wɔ kyinhyia bi sikani kakra a edi kan mu, na ɛbɔ ntwahonan no ɔfa a ɛsɛ sɛ bɔɔl no tɔ mu din. Edward Thorp ne Claude Shannon yɛɛ deɛ edi kan wɔ 1961, na Eudaemons kuo no yɛɛ digital deɛ firi 1976. Ɔkwan no hia sɛ wɔgye bɛt wɔ bɔɔl no to akyi: ɛnnɛ live studio ahodoɔ to bɛt mu berɛ a wɔto bɔɔl no, na Nevada abara saa afidie yi firi 1985.
Sɛdeɛ wɔyɛɛ roulette kɔmputa nhyehyɛe a edi kan
Adwene no baa Edward Thorp tirim wɔ 1955 asusowbere mu, berɛ a na ɔyɛ nyansahu suani a ɔresua nwoma kɛseɛ wɔ UCLA: ntwahonan a wɔayɛ no yie araa sɛ ɛnyɛ animhwɛ no, ɛsɛ sɛ ɛma 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 twa ho hyia wɔ ɔkwan a wobɛtumi ahyɛ ho nkɔm sɛ okyinnsoromma bi. Ɔfaa ntwahonan bi a ne boɔ nyɛ den na ne kɛseɛ yɛ fa no video a berɛ susu afidie wɔ mfonini no mu, na ɔhunuu sɛ ne kyini nhyehyɛe ntumi nyɛ adwuma ma nkɔmhyɛ, na akwantuo a ɔkɔɔ Nevada wɔ December 1958 kyerɛɛ no sɛ kasino ntwahonan kyini yie. Afei blackjack faa n’adwene. Wɔ November 1960, wɔ MIT, ɔka kyerɛɛ Claude Shannon sɛ ɔmfa ne krataa a ɛfa nkrataa kan ho nkɔma National Academy of Sciences; nhyiamu no awieeɛ no, Shannon bisaa no sɛ ɛdeɛn bio na ɔreyɛ ho adwuma, na roulette adwuma no tu kɔɔ Shannon ofie ase dan mu. Wɔtɔɔ ntwahonan a ɛfata mmara firi Reno $1,500, de too tete billiard ɛpono bi a wɔde ɔboɔ ayɛ so, na wɔde hann a ɛbɔ ne ho ne berɛ susu afidie a ɛkenkan kɔsi sikani ɔha mu baako susuu bɔɔl no berɛ. Sɛ wɔsua ho kɔɔ so a, wɔn berɛ susu mfomsoɔ so tew firi bɛyɛ 0.03 kɔɔ 0.01 sikani. Ɛduruu June 1961 no, na kɔmputa no wɔ transistor dumienu na ne kɛseɛ te sɛ sigaret adaka: switch bi a ɛwɔ mpaboa mu, a wɔde nan kokuromoti kɛseɛ pia, susuu rotornneɛma a wɔde diRotorNtwahonan no fa a ɛkyini a ntokuru no wɔ so.Kenkan ne nyinaa → ne bɔɔl no berɛ, na nnyegyeɛ bi wɔ aso baako mu bɔɔ ntwahonan no afantwahonanƆfaNtokuru a ɛtoa so wɔ ntwahonan no so, a ɛnyɛ kuo a ɛwɔ bɛt nhyehyɛe no so.Kenkan ne nyinaa → nwɔtwe no mu baako din. Saa asusowbere no mu wɔ Las Vegas no, Shannon susuu berɛ wɔ ntwahonan no ho na ɔkyerɛw nɔma sɛ nhyehyɛe agorɔfoɔ biara, berɛ a Thorp to sika nketewa bɛt wɔ ɛpono no ano baabi a ɛwɔ akyiri. Nkɔmhyɛ no yɛɛ adwuma, nanso ahoɔden ahama a ɛyɛ teateaa sɛ tirinwi a ɛkɔ aso mu afidie no mu no kɔɔ so bubuu, na berɛ bi ɔbaa bi a ɔte Thorp nkyɛn de ehu hwɛɛ afidie a ɛreyi nne a na ɛrepue afiri n’aso mu no. Wɔanto bɛt kɛseɛ biara da. Thorp bɔɔ roulette kɔmputa nhyehyɛe no ho dawuro wɔ 1966 na ɔtintim ho nsɛm wɔ 1979 ne 1984.
Digital kɔmputa a edi kan
Thorp ne Shannon afidie no yɛ analog: ne ahoɔden kwan no ne ne nhyehyɛe, na sɛ wopɛ sɛ wosesa ɔkwan no a, ɛsɛ sɛ wosan hyehyɛ ahama no. Microprocessor yii saa ahyeɛ no firii hɔ. Alan Lewis, suani bi wɔ Caltech, de digital kɔmputa a ɔno ara yɛeɛ wɔ kamera adaka mu kɔɔ Circus Circus wɔ Las Vegas wɔ 1972, susuu ntwahonan berɛ firi abansoro bi a ɛwɔ ɛpono no atifi, na ɔde radio kyerɛɛ ne yɔnko a ɔwɔ aseɛ no nkɔmhyɛ no. Ɛyɛɛ adwuma, nanso wannya sika biara; akyiri yi ɔhunuu sɛ wanfa ntwahonan no ntwea ho nsɛm anka ho. Firi 1976 no, nyansahu asuafoɔ kuo bi wɔ Santa Cruz, Eudaemons kuo no, yɛɛ adwuma no yie. Wɔtɔɔ kasino ntwahonan bi, susuu bɔɔl no, rotor no, ntwea no ne huruhuruw no, na wɔkyerɛw akontaabu nhyehyɛe a nsakraeɛ enum wom a agorɔfoɔ no siesie ma ntwahonan biara denam nan kokuromoti switch a ɔpia bɛyɛ simma aduonu ansa na ɔto bɛt so. Wɔn kɔmputa no bɔɔ afa nwɔtwe no mu baako din sikani kakra wɔ kyinhyia no mfitiaseɛ akyi. Wɔ ɛpono ankasa ho wɔ January 1978 no, ɛmaa wɔn mfasoɔ a wɔbuu no 25%; afidie no, a wɔde kyekyeree nipadua ho na akyiri yi wɔde hyɛɛ mpaboa mu, sɛeɛ mpɛn pii kɛse sene nyansahu no (hwɛ Eudaemons kuo no).
Adɛn nti na bɛt akyiri ho hiaeɛ
Kasino betumi asiw nkɔmhyɛ kwan koraa sɛ ɛmpene bɛt biara so wɔ bɔɔl no to akyi. Thorp hunuu sɛ ɛkame ayɛ sɛ biara nyɛɛ saa: wɔ Reno, Las Vegas, London, Monte Carlo, Nice, Venice ne Puerto Rico no, na amammerɛ ne sɛ wɔka “Mma bɛt foforɔ bioadwumayɛ kwanMma bɛt foforɔ bioDila no frɛ (anaa nsɛm a ɛba screen so) a ɛto bɛt bere mu. Wontumi mfa agorɔ sika nsi hɔ, nsesa ne baabi, anaa nyi bio.Kenkan ne nyinaa →” ntwahonan kyinhyia mua baako anaa mmienu ansa na bɔɔl no atɔ. Saa bɛt bere no na nkɔmhyɛ nhyehyɛe biara a ɛbaa akyiri yi ahia, firi Eudaemons kuo no so kɔsi Ritz kuo no bɛt a wɔkaa no akyiri wɔ racetrackɛponoRacetrackRacetrack (ntwahonan nhyehyɛe kwan) yɛ ɔfa a ɛyɛ kurukuruwa tenten wɔ live ne afidie bɛt nhyehyɛe so a ɛkyerɛ nɔma no wɔ ntwahonan so nhyehyɛe mu, a wɔde to fipam nɔma bɛt ne ɔfa bɛt prɛko pɛ.Kenkan ne nyinaa → (ntwahonan nhyehyɛe kwan) so. Nevada bubuu nkɔmhyɛ afidie mmara wɔ May 1985, na ɛnnɛ live studio ahodoɔ to bɛt mu berɛ a wɔto bɔɔl no.
Sɛdeɛ kasino ahodoɔ ko tiaa
Wɔ mfeɛ a na wɔda so gye bɛt wɔ bɔɔl no to akyi no, kasino ahodoɔ denam dila no so ko tiaa agorɔfoɔ a wɔsusu wɔn ho. Nsɛm a ɛfa Norman Leigh nhyehyɛe agorɔfoɔ ho wɔ Nice wɔ 1966 ne nkɔmhyɛ akuo a wɔbaa akyiri yi ho ka croupiernnipaCroupierDila a ɔwɔ roulette ɛpono ho.Kenkan ne nyinaa → foforɔ wɔ kyinhyia biara mu, bɔɔl a wɔsesaa, kyinhyia a wɔma ɛyɛɛ tiawa anaa ntɛm, ɛpono a kasino no ankasa nnipa ahyɛ so ma, na awieeɛ no ɛpono a wɔato mu. Saa nsɛm yi firi agorɔfoɔ no nkyɛn, na ɛyɛ den sɛ wobɛhwɛ mu (Goldman, 2007). Nanso akwan no wɔ ntease: kyinhyia a ɛyɛ tiawa anaa ntɛm ntumi mfa bɔɔl no nkɔ tokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → pɔtee bi mu, nanso ɛsɛe berɛ a nkɔmhyɛfoɔ susu no.
Roulette dilafoɔ betumi abɔ nɔma bi so pɛpɛɛpɛ anaa? Gyidie hunu no
Sɛdeɛ ɛsɛ sɛ nkɔmhyɛ no yɛ papa
Thorp (1984) buu deɛ nkɔmhyɛ bi som ho akontaa berɛ a ne mfomsoɔ di dɔn nhyehyɛe (bell curve) akyi: wɔ kyinhyia a ɛyɛ daa deɛ mu no, tokuru a wɔahyɛ ho nkɔm no fom ntokuru σ kɔ ɔfa baako anaa foforɔ so. To bɛt wɔ nɔma a wɔahyɛ ho nkɔm no nko ara so, anaa ɛno ne ne fipam nɔmabɛtFipam nɔmaNɔma bi ne ntokuru mmienu a ɛwɔ ne nkyɛn biara wɔ ntwahonan no so, nɔma baako bɛt agorɔ sika enum.Kenkan ne nyinaa → mmienu wɔ ɔfa biara so, na mfasoɔ no gyina σ nko ara so. Nkɔmhyɛ a ɛyɛ pɛpɛɛpɛ bɛdi nɔma baako bɛtbɛtNɔma baako bɛtNɔma baako pɛ, ɛtua 35:1.Kenkan ne nyinaa → biara so nkonim. Wɔ σ = ntokuru 10 so, pɛpɛɛpɛyɛ a Thorp ne Shannon duruu so, nɔma baako bɛt de bɛyɛ +44% ba, nɔma a Thorp de ma wɔn afidie; ne kyerɛwtohɔ a ɛfiri 1998 no de si ntwahonan no nkyɛmu nwɔtwe mu baako a ɛboa sene biara no so. Mfasoɔ no so tew ntɛm sɛ mfomsoɔ no kɔ soro a, na ɛyera bɛyɛ ntokuru 17 so wɔ Yuropu ntwahonan so ne 16 wɔ Amerika deɛ so, berɛ a nkɔmhyɛ no fom bɛyɛ ntwahonan no fa. Thorp ankasa mfomsoɔ akontaa kyerɛ deɛ enti a saa ahyeɛ no bɛn: mfomsoɔ a ɛtetew mu a ɛyɛ ntokuru 1.4 ne 5.5 a ɛfiri rotor ne bɔɔl berɛ susu mu, 7 a ɛfiri bɔɔl no a ɛtɔ fa akwansideɛnneɛma a wɔde diAkwansideɛDadeɛ akwansideɛ a ɛwɔ ɔfa a ɛsian no so no mu baako a ɛbɔ bɔɔl a ɛretɔ no ma ɛhwete. Wɔfrɛ no nso canoe, diamond, pin.Kenkan ne nyinaa → no so, ne 6 a ɛfiri huruhuruw wɔ ntokuru no mu ka bom yɛ bɛyɛ 10.8.
Nsɛmmisa
Daabi. Bɔɔl biara nni hɔ. Software no twe nɔma no ansa na mfonini a ɛkeka ho no afiri aseɛ.
Berɛ susu bɛtumi adi wɔn so, na ɛno nti na wɔnyɛ emu biara saa.
Akontaabu ho anigyeɛ
Di kan yɛ eyinom ara wo ho. Wɔakata mmuaeɛ biara so; sɛ woasiesie wo ho a, bue no.
Fipam nɔmabɛtFipam nɔmaNɔma bi ne ntokuru mmienu a ɛwɔ ne nkyɛn biara wɔ ntwahonan no so, nɔma baako bɛt agorɔ sika enum.Kenkan ne nyinaa → bɛt a wɔka de agorɔ sikasikaAgorɔ sikaAdeɛ a ɛgyina hɔ ma sika dodoɔ bi a ɛnsesa, a wode to bɛt nhyehyɛe no so de to bɛt. Wɔfrɛ no nso check.Kenkan ne nyinaa → baako to nɔma bi so ne ntokurunneɛma a wɔde diTokuruRotor no so tokuru 37 a nɔma wom no mu baako. Wɔfrɛ no nso slot, cup.Kenkan ne nyinaa → mmienu a ɛwɔ ne nkyɛn biara wɔ ntwahonan no so: agorɔ sika enum. Mpɛn ahe na ɛsɛ sɛ nkɔmhyɛ kɔtɔ saa ntokuru enum no mu na woaduru baabi a wonnya na wonhwere, na ɛnya ahe sɛ ɛyɛ nokware mprɛ baako wɔ enum mu a?
Kyerɛ mmuaeɛ no
Mmuaeɛ Ɛduru baabi a wonnya na wonhwere wɔ 5 wɔ 36 mu, 13.9%, sɛ wode toto 13.5% a ɛfiri hokwan nko ara ho a. Sɛ ɛyɛ nokware mprɛ baako wɔ enum mu a, ɛsan de 44% ba boro deɛ ɛto so.
Sɛ bɛt no ba a, agorɔ sika baako di nkonim 35 tia 1 na ɛsan ba ne ne nkonim sika, agorɔ sika 36, na ɛnan a aka no hwere. Enti sɛ ɛba a, ɛsan de 36 ba wɔ 5 a wɔto so, na bɛt no duru baabi a wonnya na wonhwere sɛ ɛba mprɛ 5 wɔ 36 mu a, 13.9%. Wɔ hokwan nko ara mu no, ɛba mprɛ 5 wɔ 37 mu, 13.5%. Saa nsonsonoeɛ ketewa no, a ɛnnuru ɔha mu ɔfa fa mpo no, ne baabi a 2.70% no nyinaa firi.
Wɔ baako wɔ enum mu so no, 0.2 × 36 = agorɔ sika 7.2 san ba wɔ 5 biara a wɔto so, +44%. Wɔ baako wɔ ɛnan mu so no, +80%.
Ɛno nti na nokwaredi mu nkɔsoɔ ketewa som bo kɛseɛ saa, na ɛno nti na kasino ahodoɔ to bɛt a wɔkaɛponoBɛt a wɔkaBɛt a wɔka kyerɛ dila no mmom sene sɛ wode wo nsa bɛto so, a ɛtaa yɛ ntwahonan ɔfa bɛt te sɛ voisins anaa tiers. Wɔfrɛ no nso “bɛt a wɔbɔ ho dawuro”.Kenkan ne nyinaa → mu ntɛm wɔ bɛt sika kɛseɛ so: saa nsonsonoeɛ ketewa no ne kasino no mfasoɔ nyinaa. Wɔka sɛ Ritz agorɔfoɔ a wɔwɔ 2004 mu no too bɛt saa.
Thorp kyerɛw mfomsoɔ ɛnan a ɛmfa ho wɔ ne nkɔmhyɛ mu, wɔ ntokuru mu: 1.4 firi rotornneɛma a wɔde diRotorNtwahonan no fa a ɛkyini a ntokuru no wɔ so.Kenkan ne nyinaa → no bere susu mu, 5.5 firi 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 bere susu mu, 7 firi bɔɔl no hwe a ɛtwa akwansideɛnneɛma a wɔde diAkwansideɛDadeɛ akwansideɛ a ɛwɔ ɔfa a ɛsian no so no mu baako a ɛbɔ bɔɔl a ɛretɔ no ma ɛhwete. Wɔfrɛ no nso canoe, diamond, pin.Kenkan ne nyinaa → no mu ne 6 firi ne huruw wɔ ntokuru no mu. Ne nyinaa kɛseɛ yɛ sɛn, na bere susu mfomsoɔ mmienu no de dodoɔ sɛn ka ho?
Kyerɛ mmuaeɛ no
Mmuaeɛ Bɛyɛ ntokuru 10.8 nyinaa. Sɛ bere susu mfomsoɔ no nni hɔ a, anka ɛbɛyɛ 9.2, enti bere susu mmienu no de 1.6 pɛ ka ho.
Mfomsoɔ a ɛmfa ho nka bom tee; wɔn ahinanan na ɛka bom. Ne nyinaa kɛseɛ a ɛtaa ba ne ahinanan no nkabom ntini: 1.4² + 5.5² + 7² + 6² = 1.96 + 30.25 + 49 + 36 = 117.2, na √117.2 ≈ 10.8.
Sɛ bere susu mfomsoɔ mmienu no nni hɔ a: √(49 + 36) = √85 ≈ 9.2.
Ntokuru 10.8 nyinaa wɔ ntokuru 17 ahyeɛ a ɛwɔ pon a ɛwɔ krataafa yi so no mu na ɛsom bɛyɛ +34% wɔ nɔma baako so. Adesua a Thorp nyaeɛ: sɛ bɔɔl no hwe a ɛtwa akwansideɛ no mu yɛ mfomsoɔ kɛseɛ sen biara a, bere susu a ɛyɛ papa ntɔ hwee kɛseɛ.
Serew kakra
Nyansahu no yɛ adwuma. Bɛt bere no too mu.
Nsɛm fibea
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”
- Bass, T. A. The Eudaemonic Pie.
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Goldman, N. Great Gambling Scams.
- Nevada Revised Statutes, chapter 465.