Timerniwin · Umuɣ n tɣuri · 8 tsd

Idlisen ɣef rulit: umuɣ n tɣuri

Idlisen d yimagraden ɣef rulit i ɣef yebna usmel-a, sin u ɛecrin deg-sen, seg tezrawt ɣef wazal yettwaṛǧan n 1657 ɣer udlis n uselmed n 2025, s tefyirt ɣef wayɣer yal yiwen yesɛa azal.

Tiririt tawezlant

Tusnakt (Huygens, Bernoulli, Halmos, Feller, Thorp, Epstein, Ethier, d yidlisen n uselmed imaynuten n Bollman, Taylor d Hunacek), amezruy (Lablée, Barnhart, Schwartz, Kavanagh, Marcus, Goldman), tafizikt (Bass, Small & Tse) d yiwen wungal i ten-yifen meṛṛa (Dostoevsky). Kullec deg usmel-a yebna ɣef tidikelt-a.

aqdim akk

Huygens, 1657

amaynut akk

Hunacek, 2025

adlis yifen akk

Ethier, 2010

ungal yifen akk

The Gambler, 1866

Tusnakt

amahilaseggasayɣer ara t-teɣrem

Huygens, De Ratiociniis in Ludo Aleae1657tazrawt tamezwarut yettwasiggzen ɣef wazal yettwaṛǧan; seg da i d-yekka EV

Bernoulli, Ars Conjectandi1713alugen n wuṭṭunen imeqqranen, i ur fhimen ara yinagrawen

Halmos, “Invariants of certain stochastic transformations”1939aseknu amatu amezwaru belli ulac anagraw n rrhun ara ibeddlen agmuḍ yettwaṛǧan

Feller, An Introduction to Probability Theory, vol. 11968aɣelluy n umqemmer, tikliwin s ugacur, izrar; d tiɣbula tagejdant

Thorp, “Optimal gambling systems for favorable games”1969melmi i zemren yinagrawen n rrhun ad ɛiwnen (deg wurar s lmaziyya i umurar kan) d tewtilin ɣef yebna ugmuḍ n « ulac anagraw »

Thorp, The Mathematics of Gambling1984aselkim n rulit s yimi n win t-id-yesnulfan, d leḥsab n wacḥal ara yerhen yiwen ma yesɛa lmaziyya

Epstein, The Theory of Gambling and Statistical Logic2013 (taẓrigt tis 2)yal urar n lkazinu yettwasleḍ; rulit gar-asen

Ethier, The Doctrine of Chances2010tazrawt tusnakt ummidet akk ɣef rulit i yettwasiggzen

Bollman, Mathematics of the Big Four Casino Table Games2021rrhun n tama, iḍebsiyen ur nettwassen ara d rulit s tkarḍiwin yettwaḥesben yiwen yiwen, s tiwuriwin

Taylor, Games, Gambling, and Probability2021 (taẓrigt tis 2)izrar, rrehn n Kelly d uɣelluy n umqemmer yettwaxedmen am uselmed

Bollman, Basic Gambling Mathematics2024 (taẓrigt tis 2)leɛruḍ d tuɣalin n lexsara n lkazinu, d s wacḥal n tazzla i d-tettawi tfelwit n yigmaḍ ssuma-s i lkazinu

Hunacek, Quantitative Literacy Through Games and Gambling2025aselmed amezwaru afessas; senqdet ayen i d-yenna belli yal rrehn yesɛa yiwen wazal yettwaṛǧan, ayen i yerreẓ rrehn ɣef semmus n wuṭṭunen

Amezruy

amahilaseggasayɣer ara t-teɣrem

Lablée, La Roulette, ou le Jour1801aglam ummid amezwaru n wurar, deg wungal

Barnhart, Beating the Wheel1992amezruy n wurar ɣef umyal: Jagger, wid i yezwaren Pelayo, tarrayin

Schwartz, Roll the Bones2006amezruy amatu n lqmer; amkan n rulit deg-s

Kavanagh, Dice, Cards, Wheels2005idles n lqmer deg Faransa; Palais-Royal d yimdinen n waman iḥman

Marcus, American Roulette2003asers n rrehn deffir ugmuḍ yettwaglem seg daxel s ufus n win yettwassnen akk deg-s

Goldman, Great Gambling Scams2007Leigh deg Nice, Marcus d Ritz ttwalsen-d; yedder, u yeɣleḍ deg kra n tɣawsiwin (walit Lɣecc deg rulit)

Tafizikt d wurar n lmaziyya

amahilaseggasayɣer ara t-teɣrem

Bass, The Eudaemonic Pie1985tamacahut n uselkim deg usebbaḍ; adlis aɣerfan yifen akk ɣef tfizikt n rulit

Small & Tse, “Predicting the outcome of roulette”2012tafizikt n tifin uqbel n ugmuḍ, s uktazal; ayen yesra yiwen akken ad yesɛu lmaziyya

Pearson, “On the criterion…”1900akayad χ² (chi-square), yettwasekned ɣef tuzzyiwin n rulit

Tafizikt n uḍebsi n rulit

Ungal

Dostoevsky, The Gambler (1866). Yettwaru deg 26 n wussan akken ad yeḍfer talast n wakud n lɛaqed d umaẓrag, s ufus n umaru yeɣreq deg yimrusen n rulit; tuccḍa n umqemmer, anagraw, aṭṭan d lkazinu n tmdint n waman iḥman seg daxel. D amecṭuḥ ugar n yal adlis n rulit i d-nebder d asawen, u yesɛa tidet ugar n tuget-nsen.

Bad Homburg d lkazinu n yimdinen n waman iḥman Roulettenburg n Dostoevsky

Idlisen n rulit yifen i yal iswi

I leḥsab, Ethier sakin Feller. I tmucuha, Barnhart d Bass. I wayɣer i turaren medden ɣas akken, Dostoevsky. I useknu i yesseḥbasen yal amennuɣ ɣef yinagrawen, Halmos, u i ugmuḍ-nni s wawalen fessusen, adlis n Thorp n 1984. I tiwuriwin, Taylor neɣ Bollman. Agalis « Iɣbula » deg yal amagrad n usmel-a yettebbi-d seg tidikelt-a.

Isteqsiyen

Llan yidlisen yelhan ɣef tstratijit n rulit?

Ulac yiwen seg wid yettzenzin anagraw. Adlis n Thorp n 1984 yesɛa ixef awezlan ɣef wayɣer i ttɣelliden; Epstein d Ethier glemen talɣa n yal yiwen.

Anida i zemreɣ ad ɣreɣ Pearson neɣ Huygens?

I sin ffɣen seg yizerfan n umaru u llan deg Internet. Pearson yewɛer; Huygens d awezlan u yettwaɣra s sshala deg tsuqilt, ayen ur nettwaṛǧa ara.

Taḍsa i usgunfu

Kullec deg usmel-a d tazmilt ddaw n usebter n tidikelt-a.

Iɣbula

Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Ixef 13, rulit.
Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, taẓrigt tis 3, 1968. Aɣelluy n umqemmer, ixef XIV.
Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.” Duke Mathematical Journal 5(2), 1939.
Thorp, E. O. “Optimal gambling systems for favorable games.” Review of the International Statistical Institute 37(3), 1969.
Thorp, E. O. The Mathematics of Gambling. Gambling Times / Lyle Stuart, 1984.
Bass, T. A. The Eudaemonic Pie. Houghton Mifflin, 1985.
Barnhart, R. T. Beating the Wheel. Lyle Stuart, 1992.
Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021. Ixef 2, rulit.
Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed. CRC Press, 2024.
Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
Hunacek, M. Quantitative Literacy Through Games and Gambling. Chapman & Hall/CRC, 2025.
Marcus, R. American Roulette: How I Turned the Odds Upside Down. St. Martin’s Press, 2003.
Goldman, N. Great Gambling Scams. John Blake, 2007.

yettwasenqed 2026-09-28tamudemt: tawrupit, yiwen yilemtarrayt ↗iɣbula ↗