Ol Narapela Samting · Skul · 7 min

Rulet na Skul bilong Matematik

Wil bilong rulet i mekim i isi long piksaim sans. Hia yu lukim hau long yusim long wanpela skul, na i no kirapim ol sumatin long gembling.

Sotpela bekim

Tritisevenpela ansa i gat wankain sans, ol pe i no save senis, ol tanim i no hangamap long narapela, wanpela negativ EV yu save long en, na longpela stori bilong ol manmeri i ting rong long en. Rulet i soim ekspektet velyu, variansmatematikVariansMak bilong hamas ol resal i kalap nabaut long ekspektet velyu. I bikpela long bet long wanpela namba, i liklik long bet wan-long-wan.Ritim olgeta →, lo bilong planti nambamatematikLo bilong planti nambaAvarej bilong ol resal i no hangamap long narapela i kam klostu long ekspektet velyu taim namba bilong ol traim i go antap.Ritim olgeta →, giaman tingting bilong gembla, pasin bilong testim tingting na hevi bilong de yu kamap gutpela moa long ol koin o das.

olgeta ansa i ken kamap

37, wankain sans

ol tingting em i kavarim

≥ 8

ol tul long dispela sait

fri, long brausa

skul namba siro

EV = −1/37, oltaim

Bilong wanem rulet

Koin i gat tupela ansa na das i gat sikispela; tupela i liklik tumas long soim hevi bilong de yu kamapmatematikHevi bilong de yu kamapHamas manmeri i mas i stap paslain long tupela i gat wankain de bilong kamap, o hamas tanim paslain long wanpela namba i kamap gen. Long wil i gat 37 hul, 8 tanim i inap long givim sans i winim hap.Ritim olgeta → o chi-square teslaboratoriChi-square tesTes bilong statistik i skelim hamas taim bal i pundaun long olgeta hul wantaim n/37 yu ting bai kamap. Ol i yusim bilong save sapos wil i gat bias o nogat.Ritim olgeta → long pasin i kirapim tingting. Pek kas i save tingim ol kas i go pinis. Rulet i gat 37 ansa i gat wankain sans, ol pemaniPeMani bet i win i givim yu, ol i tok olsem “X long 1”, antap long mani bilong bet i kam bek.Ritim olgeta → i no save senis na i mekim ekspektet velyu i kamap wanpela lain matematik, ol tanim i no hangamap long narapela long pasin ol i wokim wil, na edj i liklik inap long hait long wanpela sesen na i bikpela inap long bosim wanpela yia. Em i gat tu tupela handet yia bilong ol giaman tingting ol i raitim, bilong yu skelim.

Koin, das na kas i givim ples long 37 ansa bilong rulet i gat wankain sans.

Chi-Square Tes

Lain bilong ol skul

skultingtingpiksa bilong rulettul long dispela sait

1sans olsem kaunimp(bet) = n/37Kalkuleta bilong Ods long Rulet

2ekspektet velyuEV = (n/37)(36/n − 1) − (37 − n)/37 = −1/37Wokim Bet

3tanim i no hangamap long narapela na lo bilong taimsim(18/37)² bilong tupela retSans bilong Ol Ran long Rulet

4narapela hap na “wanpela taim o moa”1 − (36/37)³⁷ = 63.7%Sans long Rulet

5varians na standet diviesenσ = 5.84 (bet long wanpela namba) na 1.00 (ret), wankain EVVarians

6lo bilong planti namba (na wanem em i no tok)avarej i kam klostu; olgeta wantaim i go longweI Kam Klostu long Longpela Taim

7giaman tingting bilong gembla26 blak, 1913Giaman Tingting bilong Gembla

8wokabaut rendom na lusim olgeta manifomula bilong gembla i lusim olgeta maniKalkuleta bilong Hevi long Lusim Olgeta Mani

9testim tingtingchi-square long 37 hulTul bilong Skelim Bias bilong Wil bilong Rulet

10hevi bilong de yu kamapnamba i kamap gen insait long 8 tanim, 56%Hevi: Wil bilong De Yu Kamap

11Monte Carlo simulesen10,000 sesen long wanpela sekonSimulata bilong Strateji long Rulet

12bilong wanem ol sistem i no wokol ekspektet velyu i bung stret wantaimYu Ken Winim Rulet?

Skulim matematik na i no skulim gembling

Yusim mani bilong pilai na Demo Game, i no gat bet tru long en. Stat long ekspektet velyumatematikEkspektet velyuAvarej resal long wanpela bet long longpela taim. −1/37 bilong mani bilong bet long olgeta bet olpasin bilong Yurop.Ritim olgeta → na kam bek long en oltaim: olgeta wok i pinis long “na ekspektet velyu em −1/37 bilong mani bilong bet”. Yusim ol sistem olsem piksa i soim rong, i no olsem pasin bilong win: wok em long painim rong, na simulata i soim rong long sampela sekon. Putim tu stori bilong ol manmeri i bin lus. Skul i tok olsem matematik i save win, na em i narapela kain long tok save bilong kasino.

Ol wok i save wok gut

Askim ol sumatin long tingim hamas tanim pastaim long wanpela namba i kamap gen, na bihain ranim Demo Game ten taim (hevi bilong de yu kamap). Tokim ol long raitim wanpela “sistem” long edita bilong strateji na ranim 10,000 sesen (ol ekspektet velyu i bung stret wantaim). Tokim ol long kaunim sansmatematikSansSans bilong wanpela resal, long 0 i go 1 o 0% i go 100%. Wanpela namba: 1/37 = 2.70%.Ritim olgeta → bilong ran bilong 1913, na bihain sans bilong ran olsem i kamap long sampela taim insait long fifti yia bilong Monte Carlo (senis namel long wanpela samting stret na wanpela samting nating). Tokim ol long painim hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta → i “gat bias” long lista bilong stretpela tanim, na bihain miksim ol namba (planti tes).

Tingting bilong ol sumatin i rong kwik olsem wanem (ol klas i save tingim na tru)

tanim pastaim long namba i kamap gen: tingim ≈ 19, tru 8

8 na 19

p(≥1 win long 37 tanim): tingim 100%, tru 63.7%

63.7% na 100%

p(ret bihain long 10 ret): tingim “liklik moa”, tru 48.65%

48.65%

sesen i win, Martingale: tingim ≈ 95%, tru ≈ 78%

78% na 95%

avarej ansa, Martingale: tingim “i antap long siro”, tru i daunbilo long siro

daunbilo long siro

050100

Wan wan hul namel em wanpela skul. Las wan em olgeta kos.

Ritim Ol Lista bilong Tanim Ol i Bin Putim Ples Klia Statistik i Makim Samting Tru

Bilong wanem em i stap long tingting

Ol sumatin i save tingim 26 blakbetBlakBet wan-long-wan long 18 namba blak. Tok Frans: noir.Ritim olgeta →, wil bilong Jagger, na taim simulata i soim sistem bilong ol i lus. Ol i lusim tingting long sans long buk tasol pastaim long eksam; wil nogat. Lain bilong stretpela pasin i klia: skulim matematik i mekim pilai i kamap bet nogut, wantaim pilai yet, na ol sumatin bai gembling bihain bai save long pe bilong en liklik.

Ol Pleia bilong Rulet i Gat Nem

Ol askim

Em i stret long ol sumatin bilong skul?

Wantaim mani bilong pilai na tok klia olsem edj bilong kasinomatematikEdj bilong kasinoHap bilong olgeta mani bilong bet kasino i holim long avarej: 2.70% long rulet bilong Yurop.Ritim olgeta → em i skul, em i orait. Planti skul i yusim pinis das na loteri; rulet em i wankain samting tasol i gat moa long en.

Tisa i mas stat long wanem pes?

Edj bilong Kasino long Rulet, bihain Demo Game, bihain Simulata bilong Strateji long Rulet.

Demo Game i stap gut long klasrum?

Em i no gat mani tru, i no gat akaun na i no gat rot i go long ol kampani bilong gembling.

Liklik lap

Tritisevenpela ansa, wanpela edj, tupela handet yia bilong ol rong bilong lainim.

Ol As bilong Save

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gembla i lusim olgeta mani, sapta XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Sapta 13, rulet.

mipela i skelim gen long 2026-09-28model: Yurop, wanpela sirometodoloji ↗ol as bilong save ↗