Ɔda tin dɛn · Lanin · 7 minit

Rulɛt ɛn matematiks na skul

Q: I fit fɔ pikin dɛn we de go skul?

Wit mɔni fɔ tray ɛn if yu tɔk klia se di kasino advantej na di lɛsin, yɛs: bɔku skul silabɔs dɔn de yuz dayz ɛn lɔtri; rulɛt na rich vashɔn fɔ di sem tin.

Rulɛt wil de mek prɔbabiliti izi fɔ pikchɔ. Na so yu kin yuz am fɔ lan pikin dɛn, ɛn yu nɔ go ɛnkɔrej dɛn fɔ gambul.

Shɔt ansa

Tati-sɛvin rizɔlt we gɛt di sem chans, pe we nɔ de chenj, spin we nɔ dipen pan wan ɔda, wan nɛgativ wetin fɔ ɛkspɛkt we wi no, ɛn lɔng lɔng istri fɔ pipul we bin mek mistek. Rulɛt de sho wetin fɔ ɛkspɛkt, variansmatematiksVariansWan mɛzhɔ fɔ aw di rizɔlt dɛn sprɛd rawnd di valyu we fɔ ɛkspɛkt. I ay fɔ bɛt pan wan nɔmba, i lɔ fɔ ivin-mɔni bɛt.Rid ɔl →, di lɔ fɔ big nɔmbamatematiksLɔ fɔ big nɔmbaDi avrej fɔ rizɔlt dɛn we nɔ dipen pan wan ɔda de go nia di valyu we fɔ ɛkspɛkt as di nɔmba fɔ tray de bɔku.Rid ɔl →, gambula in mistek, ipɔtisis tɛst ɛn di bɔtde prɔblɛm bɛtɛ pas kɔpɔ ɔ dayz.

ɔl di rizɔlt dɛn we kin kam

37, ɔl gɛt di sem chans

tin dɛn we wi de lan

≥ 8

tul dɛn na dis sayt

fri, insay di brawza

lɛsin ziro

EV = −1/37, ɔltɛm

Wetin mek rulɛt

Kɔpɔ gɛt tu rizɔlt ɛn dayz gɛt siks; dɛn tu smɔl tumɔs fɔ sho di bɔtde prɔblɛmmatematiksBɔtde prɔblɛmƆmɔs pipul yu nid bifo tu pan dɛn go pɔsibul gɛt di sem bɔtde, ɔ ɔmɔs spin bifo wan nɔmba go pɔsibul kam bak. Pan wil wit 37 pɔkit, 8 spin dɔn du fɔ gɛt chans we pas af.Rid ɔl → ɔ chi-skwɛ tɛstlabChi-skwɛ tɛstStatistikal tɛst we de kɔmpia ɔmɔs tɛm ɛni pɔkit rili kam wit di n/37 we yu fɔ ɛkspɛkt. Dɛn de yuz am fɔ jɔj if wil gɛt bayas.Rid ɔl → wit ɛni dram. Kad de mɛmba wetin dɔn kɔmɔt. Rulɛt gɛt 37 rizɔlt we gɛt di sem chans, pemɔniPeWetin bɛt we win de gi yu, dɛn de tɔk am as “X to 1” ɔn tɔp di bɛt mɔni we kam bak.Rid ɔl → we nɔ de chenj ɛn we de mek wetin fɔ ɛkspɛkt na kalkuleshɔn pan wan lain, spin we nɔ dipen pan wan ɔda bikɔs na so dɛn mek di wil, ɛn advantej we smɔl so te i kin ayd insay wan sɛshɔn, bɔt i big so te i de rul wan ol ia. I gɛt bak tu ɔndrɛd ia mistek dɛn we dɛn dɔn rayt dɔŋ, fɔ kɔt opin ɛn stɔdi.

Kɔpɔ, dayz ɛn kad de gi we to rulɛt in 37 rizɔlt we gɛt di sem chans.

Chi-skwɛ tɛst

Lɛsin dɛn wan afta di ɔda

lɛsinaydiaɛgzampul pan rulɛttul na dis sayt

1prɔbabiliti lɛk kawntp(bɛt) = n/37Ɔds kalkuleta

2wetin fɔ ɛkspɛktEV = (n/37)(36/n − 1) − (37 − n)/37 = −1/37Fɔ bil bɛt

3spin we nɔ dipen pan wan ɔda ɛn di rul fɔ mɔltiplay(18/37)² fɔ tu rɛdPrɔbabiliti fɔ strik

4di ɔda pat ɛn “at list wan tɛm”1 − (36/37)³⁷ = 63.7%Rulɛt prɔbabiliti

5varians ɛn standad diviyeshɔnσ = 5.84 (bɛt pan wan nɔmba) agens 1.00 (rɛd), di sem EVVarians

6lɔ fɔ big nɔmba (ɛn wetin i nɔ de se)di avrej de kam nia; di tɔtal de go faWetin de apin if yu ple lɔng tɛm

7gambula in mistek26 blak, 1913Gambula in mistek

8rɛndɔm waka ɛn fɔ lɔs ɔlfɔmyula fɔ gambula we lɔs ɔlKalkuleta fɔ denja fɔ lɔs ɔl

9ipɔtisis tɛstchi-skwɛ pan 37 pɔkitAnalayza fɔ wil bayas

10di bɔtde prɔblɛmwan nɔmba de kam bak insay 8 spin, 56%Prɔblɛm: di bɔtde wil

11Monte Carlo simyuleshɔn10,000 sɛshɔn pan wan sɛkɔnStratɛji simulɛta

12wetin mek sistɛm dɛn de felwetin fɔ ɛkspɛkt de ad tugɛda strɛtYu kin bit rulɛt?

Lan pikin dɛn, bɔt nɔ lan dɛn fɔ gambul

Yuz mɔni fɔ tray ɛn di Tray gem, we nɔ gɛt rial bɛt mɔni. Bigin wit di valyu we fɔ ɛkspɛktmatematiksValyu we fɔ ɛkspɛktDi avrej rizɔlt fɔ ɛni bɛt if yu ple lɔng tɛm. −1/37 fɔ di bɛt mɔni fɔ ɛni nɔmal Yuropian bɛt.Rid ɔl → ɛn kɔntinyu fɔ kam bak to am: ɛni ɛksasayz de dɔn wit “ɛn di valyu we fɔ ɛkspɛkt na −1/37 pan di bɛt mɔni”. Yuz di sistɛm dɛn fɔ sho usay dɛn rɔng, nɔto lɛk we fɔ ple: di ɛksasayz na fɔ fɛn di mistek, ɛn di simulɛta de sho di mistek insay sɔm sɛkɔn. Tɔk bak bɔt di istri fɔ pipul we bin lɔs. Di lɛsin na se di kalkuleshɔn de win, ɛn dat na di ɔpozit fɔ advatayzmɛnt.

Ɛksasayz dɛn we de wok

Mek di stɔdɛnt dɛn gɛs ɔmɔs spin go pas bifo wan nɔmba kam bak, dɔn rɔn di Tray gem tɛn tɛm (bɔtde prɔblɛm). Mek dɛn rayt “sistɛm” na di stratɛji ɛdita ɛn rɔn 10,000 sɛshɔn (wetin fɔ ɛkspɛkt de ad tugɛda strɛt). Mek dɛn kalkul di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → fɔ di strik na 1913, dɔn di prɔbabiliti se da kayn strik go apin sɔmsay insay fifti ia na Monte Carlo (di difrɛns bitwin wan patikyula tin ɛn ɛni tin). Mek dɛn fɛn di pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl → we “gɛt bayas” insay spin istri we fɛr, dɔn mek dɛn mik di data (bɔku kɔmparizin).

Aw kwik di stɔdɛnt dɛn fil-fil de rɔng (wetin klas kin gɛs agens di tru)

spin te wan nɔmba kam bak: gɛs ≈ 19, tru 8

8 agens 19

p(≥1 win pan 37 spin): gɛs 100%, tru 63.7%

63.7% agens 100%

p(rɛd afta 10 rɛd): gɛs “smɔl pas”, tru 48.65%

48.65%

sɛshɔn wit prɔfit, Martingale: gɛs ≈ 95%, tru ≈ 78%

78% agens 95%

avrej rizɔlt, Martingale: gɛs “pɔsitiv”, tru nɛgativ

nɛgativ

050100

Ɛni ol na lɛsin. Di las wan na di ol kɔs.

Fɔ rid spin istri we dɛn dɔn pablish Statistikal signifikans

Wetin mek i de stik

Stɔdɛnt dɛn de mɛmba di 26 blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl →, Jagger in wil, ɛn di tɛm we di simulɛta sho dɛn sistɛm de lɔs. Prɔbabiliti we na jɔs tiori, dɛn de fɔgɛt am bifo di ɛgzam; wil, dɛn nɔ de fɔgɛt. Di rayt lain klia: tich di kalkuleshɔn we de mek di gem bad bɛt, wit di gem sɛf, ɛn di stɔdɛnt dɛn we go gambul leta go at list no di prayz.

Rulɛt pleya dɛn we gɛt nem

Kwɛstyɔn dɛn

I fit fɔ pikin dɛn we de go skul?

Wit mɔni fɔ tray ɛn if yu tɔk klia se di kasino advantejmatematiksKasino advantejDi pat pan ɛni bɛt mɔni we di kasino de kip pan avrej: 2.70% na Yuropian rulɛt.Rid ɔl → na di lɛsin, yɛs: bɔku skul silabɔs dɔn de yuz dayz ɛn lɔtri; rulɛt na rich vashɔn fɔ di sem tin.

Wish pej ticha fɔ bigin wit?

Kasino advantej, dɔn di Tray gem, dɔn di Stratɛji simulɛta.

Di Tray gem sef fɔ klasrum?

I nɔ gɛt rial mɔni, nɔ akawnt ɛn nɔ link to kasino kɔmpin dɛn.

Smɔl jok fɔ ɛz di maynd

Tati-sɛvin rizɔlt, wan advantej, tu ɔndrɛd ia mistek fɔ lan frɔm.

Usay wi gɛt am frɔm

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gambula we lɔs ɔl, chapta XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapta 13, rulɛt.

wi chɛk am 2026-09-28mɔdɛl: Yuropian, wan ziromɛtɔdɔlɔji ↗usay wi gɛt am frɔm ↗