Ngaahi Meʻa Kehe · Lisi tohi ke lau · miniti ʻe 8

Ngaahi Tohi ki he Lulēti: Ko ha Lisi ke Lau

Ko e ngaahi tohi mo e ngaahi pepa ki he lulēti ʻoku makatuʻunga ai ʻa e uepisaiti ni, ʻe uofulu mā ua, mei ha tohi ʻo e 1657 ki he ʻamanekina ki ha tohi ako ʻo e 2025, mo ha sētesi ʻe taha ki he ʻuhinga ʻoku mahuʻinga ai ʻa e taki taha.

Tali nounou

Ko e matematika (Huygens, Bernoulli, Halmos, Feller, Thorp, Epstein, Ethier, mo e ngaahi tohi ako foʻou ʻa Bollman, Taylor mo Hunacek), ko e hisitōlia (Lablée, Barnhart, Schwartz, Kavanagh, Marcus, Goldman), ko e fisiki (Bass, Small & Tse) pea mo e tohi talanoa pē ʻe taha ʻoku lelei ange ʻi he kotoa (Dostoevsky). Ko e meʻa kotoa pē ʻi he uepisaiti ni ʻoku makatuʻunga ʻi he fata tohi ko ʻeni.

motuʻa taha
Huygens, 1657
foʻou taha
Hunacek, 2025
tohi lelei taha ʻe taha
Ethier, 2010
tohi talanoa lelei taha
The Gambler, 1866

Matematika

ngāuetaʻuko e hā ke lau ai
Huygens, De Ratiociniis in Ludo Aleae1657ko e ʻuluaki fakamatala kuo paaki ki he ʻamanekina; ko e tupuʻanga ʻo e EV
Bernoulli, Ars Conjectandi1713ko e lao ʻo e ngaahi fika lalahi, ʻa ia ʻoku taʻemahinoʻi ʻe he ngaahi sisitemi
Halmos, “Invariants of certain stochastic transformations”1939ko e ʻuluaki fakamoʻoni fakalūkufua ʻoku ʻikai liliu ʻe ha sisitemi peti ʻa e ola ʻamanekina
Feller, An Introduction to Probability Theory, vol. 11968ʻosi ʻa e paʻanga ʻa e tokotaha peti, ngaahi ʻeveʻeva taʻefakataumuʻa, ngaahi hokohoko; ko e tohi tefito
Thorp, “Optimal gambling systems for favorable games”1969ʻi he taimi ʻe lava ai ke tokoni ha sisitemi peti (ʻi ha vaʻinga ʻoku lelei ki he tokotaha vaʻinga pē) mo e ngaahi tuʻunga ʻoku makatuʻunga ai ʻa e ola ʻoku ʻikai ha sisitemi
Thorp, The Mathematics of Gambling1984ko e komipiuta lulēti ʻo fakamatalaʻi ʻe hono tokotaha faʻu, mo e fika ʻo e lahi ke peti ʻaki ʻi ha tuʻunga lelei
Epstein, The Theory of Gambling and Statistical Logic2013 (paaki 2)ko e vaʻinga kasino kotoa pē kuo vakaiʻi; ko e lulēti ʻi hono tuʻunga
Ethier, The Doctrine of Chances2010ko e fakamatala fakamatematika kakato taha ki he lulēti kuo paaki
Bollman, Mathematics of the Big Four Casino Table Games2021ngaahi peti tafaʻaki, ngaahi veʻeteka kehe mo e lulēti kaati, ʻoku fika hono mahuʻinga taki taha, mo e ngaahi ngāue
Taylor, Games, Gambling, and Probability2021 (paaki 2)ngaahi hokohoko, peti Kelly mo e ʻosi ʻa e paʻanga ʻa e tokotaha peti, ʻo ngāueʻi ko ha kōsi
Bollman, Basic Gambling Mathematics2024 (paaki 2)ngaahi fakatau fakalahi mo e paʻanga fakafoki ʻa e kasino, mo e vave ʻo hono totongi ʻe ha papa ola ia ki he kasino
Hunacek, Quantitative Literacy Through Games and Gambling2025ko ha ʻuluaki kōsi faingofua; vakaiʻi ʻene pehē ʻoku tatau ʻa e mahuʻinga ʻamanekina ʻo e peti kotoa pē, ʻa ia ʻoku maumauʻi ʻe he peti fika ʻe nima

Hisitōlia

ngāuetaʻuko e hā ke lau ai
Lablée, La Roulette, ou le Jour1801ko e ʻuluaki fakamatala kakato ki he vaʻinga, ʻi ha tohi talanoa
Barnhart, Beating the Wheel1992ko e hisitōlia ʻo e vaʻinga ki he hehema: Jagger, ko e kau muʻa ʻi he kau Pelayo, ngaahi founga
Schwartz, Roll the Bones2006ko e hisitōlia fakalūkufua ʻo e vaʻinga paʻanga; ko e tuʻunga ʻo e lulēti ʻi ai
Kavanagh, Dice, Cards, Wheels2005anga fakafonu ʻo e vaʻinga paʻanga ʻi Falanisē; ko e Palais-Royal mo e ngaahi kolo vai mafana
Marcus, American Roulette2003ko e tuku peti hili ʻa e ola, ʻo fakamatalaʻi mei loto ʻe hono tokotaha fai ʻiloa taha
Goldman, Great Gambling Scams2007Leigh ʻi Nice, Marcus mo e Ritz ʻo toe talanoaʻi; ʻoku fakaoli, ka ʻoku hala ʻi ha ngaahi meʻa moʻoni ʻe niʻihi (vakai ki he Kākā ʻi he Lulēti)

Fisiki mo e vaʻinga kumi tuʻunga lelei

ngāuetaʻuko e hā ke lau ai
Bass, The Eudaemonic Pie1985ko e talanoa ʻo e komipiuta ʻi he sū; ko e tohi lelei taha ki he kakai lahi ki he fisiki ʻo e lulēti
Small & Tse, “Predicting the outcome of roulette”2012ko e fisiki ʻo e tala kikite, kuo fua; ko e hā ʻoku fiemaʻu ki ha tuʻunga lelei
Pearson, “On the criterion…”1900ko e sivi chi-square, ʻo fakahā ʻi he ngaahi vilo lulēti

Fisiki ʻo e Veʻeteka Lulēti

Ko e tohi talanoa

Dostoevsky, The Gambler (1866). Naʻe tohi ia ʻi he ʻaho ʻe 26 ke aʻu ki he ʻaho fakaʻosi ʻo ha aleapau mo ha tokotaha pulusi, ʻe ha faʻu tohi naʻe moʻua lahi koeʻuhi ko e lulēti; ko e fehalaaki ʻa e tokotaha peti, ko e sisitemi, ko e holi taʻemapuleʻi mo e kasino ʻi he kolo vai mafana mei loto. ʻOku nounou ange ia ʻi ha tohi lulēti pē ʻi ʻolunga pea moʻoni ange ʻi hono lahi taha.

Bad Homburg mo e Ngaahi Kasino ʻi he Ngaahi Kolo Vai MafanaRoulettenburg ʻa Dostoevsky

Ko e ngaahi tohi lulēti lelei taha ki he taumuʻa taki taha

Ki he fika, ko Ethier pea hoko ai ʻa Feller. Ki he ngaahi talanoa, ko Barnhart mo Bass. Ki he ʻuhinga ʻoku vaʻinga pē ai ʻa e kakai, ko Dostoevsky. Ki he fakamoʻoni ʻoku ne fakaʻosi ʻa e fakakikihi kotoa pē ki he sisitemi, ko Halmos, pea ki he ola tatau ʻi he lea faingofua, ko e tohi ʻa Thorp ʻo e 1984. Ki he ngaahi ngāue, ko Taylor pe Bollman. ʻOku lave ʻa e puha Ngaahi Maʻuʻanga ʻi he fakamatala taki taha ʻi he uepisaiti ni ki he fata tohi ko ʻeni.

Ngaahi fehuʻi

ʻOku ʻi ai ha ngaahi tohi lelei ki he founga lulēti?

ʻIkai ha taha ʻoku ne fakatau atu ha sisitemi. ʻOku ʻi he tohi ʻa Thorp ʻo e 1984 ha vahe nounou ki he ʻuhinga ʻoku tō ai kinautolu; ʻoku fakamatalaʻi ʻe Epstein mo Ethier ʻa e fōtunga ʻo e taki taha.

Ko fē te u lau ai ʻa Pearson pe Huygens?

ʻOku ʻosi ʻa e totonu faʻu ʻo e ongo tohi fakatouʻosi pea ʻoku ʻi he ʻinitaneti. ʻOku mafatukituki ʻa Pearson; ʻoku nounou ʻa Huygens pea ʻoku faingofua ke lau ʻi he liliu lea.

Meʻa fakaoli

Ko e meʻa kotoa pē ʻi he uepisaiti ni ko ha fakamatala siʻi ki he fata tohi ko ʻeni.

Ko e meʻa kotoa pē ʻi he uepisaiti ni ko ha fakamatala siʻi ki he fata tohi ko ʻeni.

Ngaahi Maʻuʻanga

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Vahe 13, lulēti.
  2. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, paaki 3, 1968. ʻOsi ʻa e paʻanga ʻa e tokotaha peti, vahe XIV.
  3. Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.” Duke Mathematical Journal 5(2), 1939.
  4. Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
  5. Thorp, E. O. The Mathematics of Gambling. Gambling Times / Lyle Stuart, 1984.
  6. Bass, T. A. The Eudaemonic Pie. Houghton Mifflin, 1985.
  7. Barnhart, R. T. Beating the Wheel. Lyle Stuart, 1992.
  8. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021. Vahe 2, lulēti.
  9. Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed. CRC Press, 2024.
  10. Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
  11. Hunacek, M. Quantitative Literacy Through Games and Gambling. Chapman & Hall/CRC, 2025.
  12. Marcus, R. American Roulette: How I Turned the Odds Upside Down. St. Martin’s Press, 2003.
  13. Goldman, N. Great Gambling Scams. John Blake, 2007.
Ko kimautoluNgaahi MaʻuʻangaHisitōlia mo e Anga FakafonuaLulēti ʻi he Ngaahi TohiHisitōlia mo e Anga FakafonuaHisitōlia ʻo e Ngaahi Sisitemi LulētiHisitōlia mo e Anga FakafonuaKo e Kau Eudaemons
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