Siplemanter · Ledikasion · 7 min

Roulet ek lansegnman matematik

Q: Eski li apropriye pou bann elev lekol?

Avek larzan zwe ek enn kad kler ki dir ki lavantaz kazino li-mem leson-la, boukou kourikoulom deza servi de ek lotri; roulet se enn version pli ris mem zafer-la.

Enn rou roulet fer probabilite fasil pou imazine. Get kouma servi li dan enn leson san ankouraz zwe larzan.

Repons kourt

Trant-set rezilta ki ena mem sans, peman fix, independans, enn lesperans negatif ki nou kone, ek enn long listwar dimounn ki pe tronpe. Roulet montre lesperans, varyansmatematikVaryansEnn mezir lor kouma bann rezilta dispers otour valer atandi. For pou pari lor enn sel nimero, ba pou pari peman egal.Lir tou →, lalwa gran nonbmatematikLalwa gran nonbMwayenn bann rezilta independan aprose valer atandi kan nonb lesey ogmante.Lir tou →, erer zwer, test lipotez ek problem aniverser pli bien ki enn pyes larzan ouswa bann de.

lespas rezilta

37, iniform

konsep ki kouver

≥ 8

zouti lor sa sit-la

gratis, dan navigater

leson zero

EV = −1/37, touzour

Kifer roulet

Enn pyes larzan ena de rezilta ek enn de ena sis; tou le de tro tipti pou montre problem aniversermatematikProblem aniverserKomie dimounn bizin ena avan ki de probableman partaz mem aniverser, ouswa komie tour avan ki enn nimero probableman repete. Lor enn rou 37 kaz, 8 tour ase pou ena plis ki enn sans lor de.Lir tou → ouswa enn test ki-kare (χ²)laboratwarTest ki-kare (χ²)Test statistik ki konpar nonb fwa ki sak kaz sorti avek n/37 ki ou atann. Servi pou zize si enn rou ena defo.Lir tou → avek enpe drama. Enn pake kart ena memwar. Roulet ena 37 rezilta ki ena mem sans, pemanlarzanPemanSeki enn pari gagnan rapporte, ekrir kouma “X kont 1” anplis miz ki retourne.Lir tou → fix ki fer lesperans enn kalkil enn lign, independans par konsepsion fizik, ek enn lavantaz ase tipti pou kasiet dan enn sesion ek ase gran pou domine enn lane. Li osi ena de syek erer dokimante pou diseke.

Enn pyes larzan, enn de ek bann kart les plas pou 37 rezilta roulet ki ena mem sans.

Test ki-kare

Enn sekans leson

lesonkonsepegzanp rouletzouti lor sa sit-la

1probabilite kouma kontep(pari) = n/37Kalkilater Kot

2lesperansEV = (n/37)(36/n − 1) − (37 − n)/37 = −1/37Konstrikter pari

3independans ek regleman miltiplikasion(18/37)² pou de rouzProbabilite bann seri

4konpleman ek “omwin enn fwa”1 − (36/37)³⁷ = 63.7%Probabilite dan roulet

5varyans ek ekar-tipσ = 5.84 (lor enn sel nimero) kont 1.00 (rouz), mem EVVaryans

6lalwa gran nonb (ek seki li pa dir)mwayenn konverze; total diverzeKonverzans lor enn long dire

7erer zwer26 nwar, 1913Erer zwer

8mars aleatwar ek ruinformil ruin zwerKalkilater risk ruin

9test lipotezki-kare lor 37 kazAnalizer defo rou

10problem aniverserenn nimero ki revini dan 8 tour, 56%Problem: rou aniverser

11similasion Monte Carlo10,000 sesion dan enn segonnSimilater stratezi

12kifer bann sistem ratelinearite lesperansEski ou kapav bat roulet

Ansegn san ansegn zwe larzan

Servi larzan zwe ek Zwe demonstrasion, kot pena vre miz. Koumans par valer atandimatematikValer atandiRezilta mwayen par pari lor enn long dire. −1/37 miz-la pou sak pari eropeen standar.Lir tou → ek retourn lor li touletan: sak egzersis fini avek “ek valer atandi se −1/37 miz-la”. Servi bann sistem kouma kontr-egzanp, pa kouma metod: egzersis-la se rod defo-la, ek similater-la fer defo-la vizib dan kek segonn. Mete listwar bann dimounn ki ti perdi. Leson-la se ki kalkil-la gagne, ek sa se lekontrer enn reklam.

Bann egzersis ki marse

Fer bann elev devine komie tour avan enn nimero revini, apre lans Zwe demonstrasion dis fwa (problem aniverser). Fer zot ekrir enn “sistem” dan editer stratezi ek lans 10,000 sesion (linearite lesperans). Fer zot kalkil probabilitematematikProbabiliteSans enn rezilta, depi 0 ziska 1 ouswa depi 0% ziska 100%. Enn nimero: 1/37 = 2.70%.Lir tou → seri 1913 la, ek apre probabilite ki enn seri koumsa arive kek parti dan sinkant an Monte Carlo (diferans ant enn evenman presi ek nenport ki evenman). Fer zot rod kazekipmanKazEnn bann 37 konpartiman avek nimero lor rotor. Osi: slot, cup.Lir tou → “ki ena defo” dan enn istorik tour enn rou zis, ek apre melanz bann done (konparezon miltip).

Ki vitman lintiision bann elev tronpe (devinet tipik enn klas kont laverite)

tour avan enn nimero revini: devinet ≈ 19, laverite 8

8 kont 19

p(≥1 fwa dan 37 tour): devinet 100%, laverite 63.7%

63.7% kont 100%

p(rouz apre 10 rouz): devinet “mwins”, laverite 48.65%

48.65%

sesion an profi, Martingale: devinet ≈ 95%, laverite ≈ 78%

78% kont 95%

rezilta mwayen, Martingale: devinet “pozitif”, laverite negatif

negatif

050100

Sak ekar se enn leson. Dernie-la se kour-la.

Lir istorik tour ki finn piblie Sinifikasion statistik

Kifer li res dan latet

Bann elev rapel 26 nwarpariNwarPari peman egal lor 18 nimero nwar. An franse: noir.Lir tou →, rou Jagger, ek moman kan similater-la ti montre zot sistem pe perdi. Probabilite abstre oubliye avan legzamen; enn rou, non. Lalimit etik kler: ansegn kalkil ki fer zwe-la enn move pari, avek zwe-la limem, ek bann elev ki zwe plitar pou omwin kone pri-la.

Zwer roulet ki popiler

Kestion

Eski li apropriye pou bann elev lekol?

Avek larzan zwe ek enn kad kler ki dir ki lavantaz kazinomatematikLavantaz kazinoPart sak miz ki kazino gard an mwayenn: 2.70% dan roulet eropeen.Lir tou → li-mem leson-la, boukou kourikoulom deza servi de ek lotri; roulet se enn version pli ris mem zafer-la.

Ki paz enn profeser bizin koumanse ar li?

Lavantaz kazino, apre Zwe demonstrasion, apre Similater stratezi.

Eski Zwe demonstrasion li sir pou enn lasal klas?

Pena vre larzan, pena kont ek pena lien ar bann loperater.

Enpe riye

Trant-set rezilta, enn lavantaz, de syek erer pou aprann ladan.

Sours

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3em edision, 1968. Ruin zwer, sapit XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Sapit 13, roulet.

verifie 2026-09-28model: eropeen, enn sel zerometodolozi ↗sours ↗