Eso tale · Lisi ni ivola · 8 na miniti

Na ivola me baleta na roulette: E dua na lisi ni ivola me wiliki

Na ivola kei na pepa me baleta na roulette e tudei kina na mataveilawa oqo, e ruasagavulu ka rua, mai na dua na ivola ni 1657 me baleta na isau e namaki ki na dua na ivola ni vuli ni 2025, kei na dua na yatuvosa me baleta na bibi ni yadua.

Isau lekaleka

Na fika (Huygens, Bernoulli, Halmos, Feller, Thorp, Epstein, Ethier, kei na ivola ni vuli vou i Bollman, Taylor kei Hunacek), na itukutuku makawa (Lablée, Barnhart, Schwartz, Kavanagh, Marcus, Goldman), na fiziki (Bass, Small & Tse) kei na dua ga na italanoa e vinaka cake mai vei ira kece (Dostoevsky). Na ka kece ena mataveilawa oqo e tudei ena kabakaba ni ivola oqo.

makawa duadua
Huygens, 1657
vou duadua
Hunacek, 2025
ivola vinaka duadua
Ethier, 2010
italanoa vinaka duadua
The Gambler, 1866

Fika

ivolayabakina vuna me wiliki kina
Huygens, De Ratiociniis in Ludo Aleae1657na imatai ni ivakamacala tabaki me baleta na isau e namaki; na vu ni EV
Bernoulli, Ars Conjectandi1713na lawa ni naba levu, ka sega ni kila vinaka na ivakarau
Halmos, “Invariants of certain stochastic transformations”1939na imatai ni ivakadinadina raraba ni sega ni dua na ivakarau ni vakacalaka e veisautaka na kena macala e namaki
Feller, An Introduction to Probability Theory, vol. 11968yali taucoko ni dauvakacalaka, lakolako vakaveitalia, veitaravi; na ivola dau vakayagataki
Thorp, “Optimal gambling systems for favorable games”1969na gauna e rawa ni vukei kina na ivakarau ni vakacalaka (ena dua ga na qito e tubu kina na dauqito) kei na ituvaki e tu ena dakuna na kena macala ni sega ni dua na ivakarau
Thorp, The Mathematics of Gambling1984na kompiuta ni roulette e tukuna o koya a buli ia, kei na fika ni levu ni lavo me vakacalakataki ni tiko e dua na tubu
Epstein, The Theory of Gambling and Statistical Logic2013 (ivolatabaki 2)na qito kece ni kasino e vakadidiketaki; na roulette ena kena ituvaki
Ethier, The Doctrine of Chances2010na ivakamacala vakafika taucoko duadua ni roulette e tabaki
Bollman, Mathematics of the Big Four Casino Table Games2021vakacalaka e yasana, wiriwiri tani kei na roulette ni kadi, e wiliki yadua na kedra isau, kei na cakacaka
Taylor, Games, Gambling, and Probability2021 (ivolatabaki 2)veitaravi, vakacalaka Kelly kei na yali taucoko ni dauvakacalaka me vaka e dua na vuli
Bollman, Basic Gambling Mathematics2024 (ivolatabaki 2)na ivakatubu ni voli kei na lavo e vakasukai ni kasino, kei na totolo ni kena vakasukai vua na kasino na isau ni dua na papa ni kena macala
Hunacek, Quantitative Literacy Through Games and Gambling2025e dua na imatai ni vuli malumalumu; mo ni vakadikeva na kena tukuna ni vakacalaka kece e tautauvata na kena isau e namaki, ka sa voroka na vakacalaka lima na naba

Itukutuku makawa

ivolayabakina vuna me wiliki kina
Lablée, La Roulette, ou le Jour1801na imatai ni ivakamacala taucoko ni qito, ena dua na italanoa
Barnhart, Beating the Wheel1992na itukutuku makawa ni qito ena wiriwiri sega ni dodonu: Jagger, ko ira na liu i ira na Pelayo, na ivakarau
Schwartz, Roll the Bones2006na itukutuku makawa raraba ni vakacalaka; na itutu ni roulette kina
Kavanagh, Dice, Cards, Wheels2005na itovo ni vakacalaka e Varanise; na Palais-Royal kei na vanua ni sili
Marcus, American Roulette2003na past-posting (vakacalaka ni sa kilai na kena macala) e vakamacalataka mai loma o koya e kilai levu duadua ena kena cakava
Goldman, Great Gambling Scams2007Leigh e Nice, Marcus kei na Ritz e tukuni tale; e bula, ka cala ena so na ka dina (raica na Veivakaisini ena roulette)

Fiziki kei na qito ni tubu

ivolayabakina vuna me wiliki kina
Bass, The Eudaemonic Pie1985na italanoa ni kompiuta e loma ni ivava; na ivola rogo vinaka duadua me baleta na fiziki ni roulette
Small & Tse, “Predicting the outcome of roulette”2012na fiziki ni vakatusa, e fuaki; na ka e gadrevi me rawa kina e dua na tubu
Pearson, “On the criterion…”1900na vakatovotovo chi-square, e vakaraitaki ena wiri ni roulette

Na fiziki ni wiriwiri ni roulette

Na italanoa

Dostoevsky, The Gambler (1866). A volai ena 26 na siga me rawa kina na iyalayala ni gauna ena veidinadinati kei na dua na dauvolavola, mai vua e dua na dauvolai e dinau vakalevu ena roulette; na cala ni dauvakacalaka, na ivakarau, na gadreva kaukauwa kei na kasino ena vanua ni sili e vakaraitaki mai loma. E lekaleka cake mai na ivola kece ni roulette e cake ka dina cake mai na kena levu.

Bad Homburg kei na kasino ni koro ni wai katakataNa Roulettenburg i Dostoevsky

Na ivola vinaka duadua ni roulette me baleta na inaki yadua

Me baleta na fika, o Ethier ka qai o Feller. Me baleta na italanoa, o Barnhart kei Bass. Me baleta na vuna era qito tiko ga kina na tamata, o Dostoevsky. Me baleta na ivakadinadina e vakaotia na veileti kece me baleta na ivakarau, o Halmos, ka me baleta na kena macala vata ena vosa rawarawa, na ivola i Thorp ni 1984. Me baleta na cakacaka, o Taylor se o Bollman. Na iwase ni Vu ni itukutuku ena tabana yadua ena mataveilawa oqo e cavuta na ivola ena kabakaba oqo.

Taro

E tiko beka na ivola vinaka me baleta na ivakarau ni roulette?

E sega ni dua e volitaka e dua na ivakarau. Na ivola i Thorp ni 1984 e tiko kina e dua na wase lekaleka me baleta na vuna era druka kina; o Epstein kei Ethier era vakamacalataka na kena ituvaki yadua.

Au na wilika mai vei o Pearson se o Huygens?

E sa sega ni taqomaki vakalawa ruarua ka tu ena initaneti. E dredre na wiliki i Pearson; e lekaleka o Huygens ka rawarawa sara na kena wiliki ena kena vakadewataki.

Ivakamamarau

Na ka kece ena mataveilawa oqo e dua na ivakamacala lailai ni kabakaba ni ivola oqo.

Na ka kece ena mataveilawa oqo e dua na ivakamacala lailai ni kabakaba ni ivola oqo.

Vuna ni itukutuku

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Wase 13, roulette.
  2. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, ivolatabaki 3, 1968. Yali taucoko ni dauvakacalaka, wase 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. Wase 2, roulette.
  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.
Me baleti keimamiVuna ni itukutukuItukutuku makawa kei na itovoNa roulette ena ivola talanoaItukutuku makawa kei na itovoItukutuku makawa ni ivakarau ni rouletteItukutuku makawa kei na itovoNa Eudaemons
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