Wetin de apin if yu ple lɔng tɛm: di lɔ fɔ big nɔmba na rulɛt
Aw di avrej de kam nia −2.70% smɔl smɔl, ɛn wetin mek i de tek lɔng pas aw yu go tink.
Di avrej lɔs fɔ ɛni spin de kam nia −1/37 as di spin dɛn de bɔku, ɛn di sprɛd de shɔnk lɛk 1/√N. Afta 1,000 spin pan rɛd, di avrej kin de insay ±3% fɔ wetin fɔ ɛkspɛkt.
Lɔ fɔ big nɔmba
Di avrej we yu de kɔnt as yu de go fɔ bɛt dɛn we nɔ dipen pan wan ɔda de go to 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 →. Afta N ivin-mɔni spin wit wan yunitmɔniYunitDi bes bɛt mɔni we sistɛm ɔ pleya de wok wit. Dɛn de ɛksplen prɔgrɛshɔn wit yunit so dat i go wok na ɛni tebul.Rid ɔl →, di avrej rizɔlt fɔ ɛni spin gɛt ɛkspɛkteshɔn −1/37 ɛn standad diviyeshɔnmatematiksStandad diviyeshɔnDi skwɛ rut fɔ varians; di nɔmal distans bitwin wan rizɔlt ɛn di valyu we fɔ ɛkspɛkt.Rid ɔl → 1/√N. Wen N na 100, dat sprɛd na 10% pan di bɛt mɔni, nia fɔ tɛm di 2.7% signal. Wen N na 1,000, i na 3.2%, lɛk di sem as di signal. Wen N na 10,000, i na 1%, ɛn yu go si di advantej klia. Insay wan sɛshɔn yu nɔ go si di advantej; insay wan ia yu nɔ go mis am.
Wetin de kam nia ɛn wetin nɔ de kam nia
Di avrej fɔ ɛni spin de kam nia. Di tɔtal nɔ de kam nia: i de go fa frɔm ziro as N de gro, pan avrej bay lɛk 2.7% pan N, wit sprɛd fɔ √N rawnd dat. Pleya we dɔn ple 10,000 spin wit $10 fɔ ɛkspɛkt fɔ dɔn lɔs $2,700, mɔ ɔ smɔl bay $1,000. Di pat fɔ rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → dɔn sɛtul nia 48.65% lɔng tɛm; di balans nɔ sɛtul ɛnisay.
- p10 −$440
- p25 −$280
- midul valyu −$140
- p75 +$0
- p90 +$140
Wetin mek wi fil kin rɔng
Pipul de ɛkspɛkt se di advantej go sho kwik bikɔs 2.70% de sawnd lɛk bɔku, ɛn dɛn de ɛkspɛkt se lɔng strik dɛn go “ivin” bikɔs 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 → se avrej dɛn de kam nia. Di tu fil dɛn rɔng pan di skel: di advantej smɔl if yu kɔmpia am wit di 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 → fɔ wan spin (σ = 1 yunit, EV = 0.027), so i de tek (1/0.027)² ≈ 1,400 spin bifo yu go si am pan wan sigma. Ɛn we di avrej de kam nia, dat nɔ de pul di tɔtal kam bak; i jɔs de mek di ɔl ɔp ɛn dɔn smɔl pas bifo.
Aw i de kam nia fɔ ɔda bɛt dɛn
Fɔ bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl →, σ = 5.84, so di sem kalkuleshɔn de gi (5.84/0.027)² ≈ 47,000 spin bifo di advantej rich wan sigma. Pleya we de bɛt pan wan nɔmba kin ple fɔ bɔku ia ɛn in yon rɛkɔd nɔ go sho di advantej difrɛn frɔm lɔk, ilɛk i de pe di sem 2.70% lɛk di pleya we de bɛt pan rɛd ɛn si am insay sɔm wik.
Wetin dis min fɔ tɛst sistɛm
Ɛnibɔdi we se sistɛm de wok fɔ ebul sho am ova 10,000 spin ɔ mɔ, wit pɔsitiv avrej we dɛn rayt dɔn. Na 1,000 spin, pɔsitiv avrej pan ivin mɔni de apin wan tɛm insay fayv ivin if di sistɛm nɔ de du natin; na 100 spin, i nia lɛk fɔ flip kɔyn. Di simulɛta dɛn na dis sayt de rɔn 2,000 sɛshɔn fɔ di lɔng we yu pik insay wan sɛkɔn, ɛn dat na mɔ pruf pas ɛni tɛstimoni.
Fɔmula
Kwɛstyɔn dɛn
Di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → se yu go ɛva de ɔp bak de fɔdɔm to ziro as yu de ple. Di tɔtal de go dɔŋ ɛn i nɔ gɛt ɛnd.
Nɔ. I min se di ɔl ɔp ɛn dɔn we dɔn pas de tɔn smɔl pat pan wan big sampul.
Fɔ ivin mɔni, lɛk 10,000 bifo di advantej klia. Fɔ bɛt pan wan nɔmba, lɛk 50,000.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Tu padi de ple 20 raund fɔ fɛr gemmatematiksFɛr gemGem usay nɔbɔdi nɔ gɛt advantej: ɛni bɛt gɛt valyu we fɔ ɛkspɛkt we na ziro.Rid ɔl →, lɛk fɔ trowe kɔyn ɔ rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → agens blakbɛtBlakIvin-mɔni bɛt pan di 18 blak nɔmba. Na Frɛnch: noir.Rid ɔl → we dɛn gi bak di zirowilZiroDi wan grin pɔkit we nɔ ivin-mɔni, dɔzin ɔ kɔlɔm bɛt nɔ kɔba; na usay di kasino advantej kɔmɔt. Dɛn kin kɔl am bak: wan ziro, 0.Rid ɔl → dɛn, ɛn dɛn de kip di skɔ as dɛn de go. Kɔnt di raund dɛn we ɛni wan de ɔp (if dɛn ivin, i de kɔnt fɔ di wan we bin de ɔp jɔs bifo). Wish wan gɛt mɔ chans: se dɛn sheb di lid 10 raund to 10, ɔ se wan padi lid ɔl 20?
Sho di ansa
Ansa Wan padi we lid ɔl 20 raund gɛt fa mɔ chans: 35.2%, if yu kɔnt ɛni wan pan di tu, ɛn ivin 10 to 10 na 6.1%.
Di chans se fɛr skɔ go ivin afta 2k raund na u = C(2k, k)/2²ᵏ: 0.246 afta 10 raund ɛn 0.176 afta 20. Wan klasik rizɔlt, di “arc-sine” lɔ, se di chans se wan padi we yu nem go lid fɔ 2k raund rayt rayt insay 2n raund na u(2k) × u(2n − 2k).
Fɔ lid ɔl 20: u(20) × u(0) = 0.176 fɔ ɛni padi, 35.2% fɔ ɛni wan pan di tu. Fɔ sheb ivin: u(10) × u(10) = 0.246² = 6.1%, di sheb we gɛt lɛs chans pas ɔl.
So insay fɛr gem di lid nɔ kin chenj an bɔku. Pleya we dɔn de ɔp ɔl di ivintɛm, ɔ dɔŋ ɔl di ivintɛm, nɔ si natin we nɔ nɔmal, ɛn i nɔ de tɔk natin bɔt di wil ɔ bɔt skil. Epstein (2013) gi di sem lɔ fɔ gem we lɔng pas: af pan di tɛm di say we gɛt lɔk pas de lid fɔ mɔ pas 85% pan di ple.
Smɔl jok fɔ ɛz di maynd
Di avrej de kam nia. Di tɔtal jɔs de kɔmɔt go.
Usay wi gɛt am frɔm
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.