Standet Diviesen long Rulet
Standet diviesen bilong rulet, em i skwea rut bilong 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 →, em i hamas samting i kamap i save stap longwe long avarej.
Long olgeta $1 yu betim, σ em i 5.84 long bet long wanpela namba na 1.00 long ret. Bilong wanpela sesen, taimsim long mani bilong bet na long skwea rut bilong hamas tanim.
Isi rot bilong tingim
Klostu tupela hap long tripela hap bilong ol sesen i pinis insait long wanpela σ long avarej, na 95% insait long tupela. Long 100 tanim long retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta → long $10 (avarej −$27, σ = $100), planti sesen i pinis namel long −$127 na +$73, na klostu olgeta namel long −$227 na +$173. Sapos samting i kamap ausait long dispela, em i no makim wanpela samting. Em i soim tasol olsem wanpela sesen long twentipela i save mekim olsem.
Bilong wanem √N
Avarej lusmatematikAvarej lusEkspektet velyu taims olgeta mani yu betim; avarej mani yu lusim long wanpela sesen o long wanpela taim.Ritim olgeta → i go antap wankain olsem N; spred i go antap olsem √N. Taim N i liklik, spred i strong moa, na ol sesen i olsem tromoi koin, wantaim liklik sait i hevi. Taim N i bikpela, lus i ran i go winim spred. Ples we avarej lus i kamap wankain olsem wanpela standet diviesenmatematikStandet diviesenSkwea rut bilong varians; hamas longwe resal i save stap long ekspektet velyu.Ritim olgeta → em i N = (σ/edj)² = (1/0.027)² ≈ 1,370 tanim long bet wan-long-wan, na (5.84/0.027)² ≈ 46,800 long ol bet long wanpela nambabetWanpela nambaWanpela namba tasol, pe em i 35:1.Ritim olgeta →. Aninit long ol dispela namba, gutpela luk i makim; antap long ol, edj i makim.
Olsem wanem long yusim
Long skelim sapos wanpela sesen i narakain, kaunim (samting i kamap − EV)/σ. Pleia i putim $10 long ret na i pinisim 100 tanim long +$150 i stap long (150 + 27)/100 = 1.77σ, samting i kamap wanpela taim long 25: em i gat gutpela luk, tasol em i no bikpela samting. Pleia i putim bet long wanpela namba na i kisim wankain +$150 i stap long 0.3σ: em i nait nating. Wankain namba bilong dola i makim narakain samting long narakain bet.
Standet rong bilong wanpela hap
Dispela kaunim yet i tokim yu hamas tanim yu nidim long lukim edj long ol namba. Standet rong bilong hap bilong win yu lukim em i √(p(1 − p)/N). Long ret wantaim N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Namel long stretpela koin na ret i gat 1.35%, olsem na bihain long 1,000 tanim yu no inap yet long tokaut strong olsem tupela i narakain. Bihain long 10,000, standet rong em i 0.5% na yu inap. Olsem na long painimaut bias bilong wil yu nidim planti tanim tru.
Lukaut long namba i go long wanpela sait
Long sotpela sesen, ol namba i kamap long bet long wanpela namba i no bihainim pasin bilong ol namba i stap namel: planti sesen i go daun isi isi −$10 long olgeta tanim, na sampela taim i kalap antap +$350. Lo ±1σ i tokaut stret long spred, tasol em i no soim gut pasin bilong en inap N i kamap planti handet. Long ol bet wan-long-wanbetBet wan-long-wanRet/blak, od/iven, antap/daunbilo. 18 namba, pe em i 1:1.Ritim olgeta →, dispela rot bilong kaunim klostu i gutpela stat long klostu 30 tanim.
Fomula
Ol askim
Em i soim olsem yu bin pilai klostu 40 sesen, o yu bin stap long dispela wanpela long foti i gat gutpela luk. Mekim gen.
Em i go antap na i go daun liklik moa na liklik moa: standet rong bilong avarej em i σ/√N. Taim N = 10,000, em i 1% bilong mani bilong bet.
Amamas wantaim Matematik
Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.
Long 100 tanim bilong wil bilong Yurop, wanpela yunitmaniYunitMani bilong bet bilong stat we wanpela sistem o wanpela pleia i wok long en. Ol i stori long ol progresen long yunit, olsem na ol i ken wok long wanem tebol.Ritim olgeta → long retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta → i stap antap wantaim 51 win o moa, na wanpela yunit long bet long wanpela nambabetWanpela nambaWanpela namba tasol, pe em i 35:1.Ritim olgeta → i stap antap sapos namba bilong en i kamap 3 taim o moa. Yusim bel kev long tingim tupela sans, na bihain skelim wantaim ol bekim stret.
Soim bekim
Bekim Ret: bel kev i givim 35.6% na bekim stret em 35.5%. Wanpela namba: bel kev i givim 55.0% na bekim stret em 50.9%. Sotpela rot i wok long ret na i no stret long wanpela namba.
Ret: ol win i gat avarej 100 × 18/37 = 48.6, wantaim senis bilong √(100 × 18/37 × 19/37) = 5.0. Stap antap i min 51 o moa; mak long namel, 50.5, em 0.37 senis antap long avarej, na bel kev i putim 35.6% antap long en. Bungim ol sans stret bilong 51, 52 … 100 win i givim 35.5%.
Wanpela namba: ol win i gat avarej 100/37 = 2.70, wantaim senis bilong √(100 × 1/37 × 36/37) = 1.62. Tripela win o moa i min antap long 2.5, 0.12 senis daunbilo long avarej: 55.0% long bel kev. Stret, em 1 rausim ol sans bilong 0, 1 na 2 win, 6.5% + 17.9% + 24.7%, na 50.9% i stap.
Bel kev i nidim planti risal long tupela sait bilong avarej. Ret i gat ol bihain long 100 tanim; namba i win liklik long tripela taim long avarej i no gat. Kev i givim 8.7% tu long “nogat win”, we sans tru em 6.5%. Taylor (2021) i putim binomial na bel kev klostu long narapela long wankain pasin.
Liklik lap
Wanpela sesen long twentipela i stap ausait long tupela sigma. Wanpela man i stap long tel oltaim.
Ol As bilong Save
- 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.