Matimatiks · Big aydia · 7 minit

Rulɛt valyu we fɔ ɛkspɛkt

Rulɛt valyu we fɔ ɛkspɛkt na di avrej rizɔlt fɔ wan bɛt if yu bin go ebul fɔ du am bak ɛn bak sote go. Na Yuropian rulɛt i di sem fɔ ɛni nɔmal bɛt: yu de lɔs 1/37 pan ɛni bɛt mɔni, pan avrej, pan ɛni spin.

Insay izi tɔk

Imajin se yu put di sem $10 bɛt pan rɛd wan milyɔn tɛm. Sɔm spin go win $10, sɔm go lɔs $10. Ad ɔl di rizɔlt dɛn ɛn sheb am bay wan milyɔn: yu go gɛt lɛk −$0.27. Dat nɔmba na di valyu we fɔ ɛkspɛkt fɔ wan rulɛt bɛt. I nɔto wetin de apin pan ɛni wan spin; na di avrej pan ɛni spin if yu ple lɔng tɛm.

Shɔt ansaEV = prɔbabiliti fɔ win × di mɔni we yu win − prɔbabiliti fɔ lɔs × di mɔni we yu lɔs. Fɔ ɛni nɔmal rulɛt bɛt, dat de kam to −2.70% pan di bɛt mɔni.

Di fɔmula fɔ di EV fɔ wan rulɛt bɛt

EV = p · W − (1 − p) · S
p = n/37 · W = S·(36/n − 1) · n = nɔmba dɛn we yu kɔba · S = bɛt mɔni

Put di rulɛt rul fɔ pe, 36/n − 1, insay, ɛn n de kansɛl. Dat na di ɔl stori fɔ di kasino advantej insay wan lain:

EV = (n/37)·S·(36/n − 1) − ((37−n)/37)·S
   = S·(36 − n − 37 + n)/37
   = −S/37

Tray am: rulɛt kalkuleta fɔ valyu we fɔ ɛkspɛkt

Pik ɔmɔs nɔmba di bɛt kɔba. Di prɔbabiliti ɛn di pe de chenj; di valyu we fɔ ɛkspɛkt nɔ de chenj.

1 nɔmba we i kɔba · i de pe 35:1bɛt mɔni $10
p(win)1/37 = 2.70%
win de pe+$350
lɔs de kɔst−$10
EV = p·W − (1−p)·S0.0270·$350 − 0.9730·$10
valyu we fɔ ɛkspɛkt−$0.27 fɔ ɛni spin · −2.70%

Aw i de luk as tɛm de go

Avrej rizɔlt pan ɛni spin fɔ $10 bɛt pan rɛd, as di spin dɛn de bɔku. Na di bigin, lɔk de rul; di avrej we de rɔn de sidɔm nia −$0.27 as di sampul de big. Dis na di we aw di avrej de kam nia if yu ple lɔng tɛm, ɛn na dis di kasino de dipen pan.

EV −$0.27spin 1spin 2,000
Spin afta spin, di avrej we de rɔn de lɛf fɔ swing, ɛn i de sidɔm jɔs ɔnda ziro.

Lay-lay tɔk we pipul kin bilif

“If di EV nɛgativ, a go lɔs ɛni sɛshɔn.”
Nɔ. I min se di avrej ova bɔku sɛshɔn na lɔs. Wan wan sɛshɔn kin difrɛn bad bad wan, ɛn mɔ fɔ bɛt dɛn we gɛt ay varians lɛk bɛt pan wan nɔmba.
“Di kasino nid lɔng tɛm fɔ win.”
Di kasino in advantej de wok pan ɛni spin. Wetin lɔng tɛm de du na fɔ mek di rizɔlt izi fɔ si bifo. Insay wan sɛshɔn nɔmɔ, lɔk na di tin we pawa pas.
“Sɔm bɛt gɛt EV we bɛtɛ pas di ɔda wan dɛn.”
Nɔto na Yuropian rulɛt, pas wan tin: ɔnda la partage ɔ en prison, ivin-mɔni bɛt gɛt af di kasino advantej we i kin gɛt.

Smɔl jok fɔ ɛz di maynd

Nɔto wetin de apin pan wan spin. Na di avrej fɔ ɔl di spin dɛn.

Nɔto wetin de apin pan wan spin. Na di avrej fɔ ɔl di spin dɛn.