Rulɛt standad diviyeshɔn
Di rulɛt standad diviyeshɔn, we na di skwɛ rut fɔ 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 →, na di nɔmal distans bitwin wan rizɔlt ɛn wetin fɔ ɛkspɛkt.
Pan ɛni $1 we yu bɛt, σ na 5.84 fɔ bɛt pan wan nɔmba ɛn 1.00 fɔ rɛd. Fɔ wan sɛshɔn, mɔltipay am wit di bɛt mɔni ɛn wit di skwɛ rut fɔ di nɔmba fɔ spin.
Wan izi rul
Lɛk tu tɔd fɔ di sɛshɔn dɛn de lan insay wan σ frɔm wetin fɔ ɛkspɛkt, ɛn 95% insay tu. Fɔ 100 spin pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → wit $10 (wetin fɔ ɛkspɛkt na −$27, σ = $100), bɔku sɛshɔn de fɔdɔm bitwin −$127 ɛn +$73, ɛn ɔlmɔs ɔl bitwin −$227 ɛn +$173. Rizɔlt we de atsay da rɛnj nɔ de pruv natin, pas se wan sɛshɔn na twɛnti de du so.
Wetin mek √N
Lɔs we fɔ ɛkspɛktmatematiksLɔs we fɔ ɛkspɛktValyu we fɔ ɛkspɛkt tɛm ɔl di mɔni we yu bɛt; di avrej mɔni we yu de lɔs insay wan sɛshɔn ɔ wan tɛm.Rid ɔl → de gro wit N; di sprɛd de gro wit √N. If N smɔl, di sprɛd de win ɛn sɛshɔn dɛn na lɛk fɔ trowe kɔpɔ wit smɔl lin. If N big, di lɔs de rɔn pas di sprɛd. Di ples we dɛn kɔs, usay lɔs we fɔ ɛkspɛkt kwal wan standad diviyeshɔnmatematiksStandad diviyeshɔnDi skwɛ rut fɔ varians; di nɔmal distans bitwin wan rizɔlt ɛn di valyu we fɔ ɛkspɛkt.Rid ɔl →, na N = (σ/advantej)² = (1/0.027)² ≈ 1,370 spin fɔ ivin-mɔni ɛn (5.84/0.027)² ≈ 46,800 fɔ bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl →. Ɔnda dɛn nɔmba ya, na lɔk de disayd; ɔp dɛn, na di advantej.
Aw fɔ yuz am
Fɔ jɔj if wan sɛshɔn bin difrɛn, kalkul (rizɔlt − EV)/σ. Pɔsin we de bɛt $10 pan rɛd ɛn we dɔn 100 spin wit +$150 de na (150 + 27)/100 = 1.77σ, rizɔlt we de apin wan tɛm na 25: lɔk, nɔto sɔntin spɛshal. Pɔsin we de bɛt pan wan nɔmba wit di sem +$150 de na 0.3σ: nɔmal nɛt. Di sem dɔla rizɔlt min difrɛn tin pan difrɛn bɛt.
Standad ɛrɔ fɔ wan pat
Di sem kalkul de tɛl yu ɔmɔs spin yu nid fɔ si di advantej na di data. Di standad ɛrɔ fɔ di pat fɔ win we yu si na √(p(1 − p)/N). Fɔ rɛd wit N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Di gap bitwin fɛr kɔpɔ ɛn rɛd na 1.35%, so afta 1,000 spin yu stil nɔ go ebul fɔ sho di difrɛns wit kɔnfidɛns. Afta 10,000, di standad ɛrɔ na 0.5% ɛn yu kin du am. Na dat bak mek fɔ fɛn wil we gɛt bayas nid bɔku bɔku spin.
Wach yusɛf fɔ di bɛnt
Na shɔt sɛshɔn, di rizɔlt fɔ bɛt pan wan nɔmba fa frɔm nɔmal distribyushɔn: bɔku sɛshɔn na −$10 ɛni spin ɔltɛm, wit +$350 jɔmp wan wan tɛm. Di ±1σ rul de sho di sprɛd kɔrɛkt, bɔt i nɔ de sho di shep fayn te N rich ɔndrɛd ɔndrɛd. Fɔ ivin-mɔni bɛtbɛtIvin-mɔni bɛtRɛd/blak, ɔd/ivin, ay/lɔ. 18 nɔmba, i de pe 1:1.Rid ɔl →, di nɔmal apruksimeshɔn fayn frɔm lɛk 30 spin.
Fɔmula
Kwɛstyɔn dɛn
I de pruv se yu dɔn ple lɛk 40 sɛshɔn, ɔ yu bin de na di wan we gɛt lɔk na fɔti. Du am bak.
I de swing smɔl smɔl mɔ: di standad ɛrɔ fɔ di avrej na σ/√N. We N rich 10,000, i na 1% fɔ di bɛt mɔni.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Oba 100 spin pan Yuropian wil, 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 → pan rɛdbɛtRɛdIvin-mɔni bɛt pan di 18 rɛd nɔmba. Na Frɛnch: rouge.Rid ɔl → de ɔp if i gɛt 51 win ɔ mɔ, ɛn wan yunit pan bɛt pan wan nɔmbabɛtBɛt pan wan nɔmbaWan nɔmba nɔmɔ, i de pe 35:1.Rid ɔl → de ɔp if in nɔmba kam 3 tɛm ɔ mɔ. Yuz di bɛl kɔv fɔ gɛs di tu chans, dɔn kɔmpia dɛn wit di rayt rayt ansa dɛn.
Sho di ansa
Ansa Rɛd: di bɛl kɔv de gi 35.6% ɛn di rayt rayt ansa na 35.5%. Di bɛt pan wan nɔmba: di bɛl kɔv de gi 55.0% ɛn di rayt rayt ansa na 50.9%. Di shɔtkɔt de wok fɔ rɛd ɛn i de mis fɔ di wan nɔmba.
Rɛd: di win dɛn in avrej na 100 × 18/37 = 48.6, wit sprɛd fɔ √(100 × 18/37 × 19/37) = 5.0. Fɔ de ɔp min 51 ɔ mɔ; di af-we mak, 50.5, de 0.37 sprɛd ɔp di avrej, ɛn di bɛl kɔv put 35.6% ɔp dat. If yu ad di rayt rayt chans fɔ 51, 52 … 100 win, yu go gɛt 35.5%.
Bɛt pan wan nɔmba: di tɛm dɛn we i kam in avrej na 100/37 = 2.70, wit sprɛd fɔ √(100 × 1/37 × 36/37) = 1.62. Tri tɛm ɔ mɔ min ɔp 2.5, 0.12 sprɛd dɔŋ di avrej: 55.0% bay di bɛl kɔv. Rayt rayt, na 1 mayn di chans fɔ 0, 1 ɛn 2 tɛm, 6.5% + 17.9% + 24.7%, ɛn dat de lɛf 50.9%.
Di bɛl kɔv nid bɔku rizɔlt pan ɔl tu say fɔ di avrej. Rɛd gɛt dɛn afta 100 spin; nɔmba we de kam lɛs pas tri tɛm pan avrej nɔ gɛt dɛn. Di kɔv sɛf de gi 8.7% to “i nɔ kam atɔl”, ɛn di tru chans na 6.5%. Taylor (2021) put di binomial ɛn di bɛl kɔv sayd bay sayd di sem we.
Smɔl jok fɔ ɛz di maynd
Wan sɛshɔn na twɛnti de atsay tu sigma. Sɔmbɔdi de ɔltɛm na di tel.
Usay wi gɛt am frɔm
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.