Varians
Bilong wanem bet long wanpela namba na bet long ret i gat wankain avarej lusmatematikAvarej lusEkspektet velyu taims olgeta mani yu betim; avarej mani yu lusim long wanpela sesen o long wanpela taim.Ritim olgeta →, tasol yu pilim olsem tupela narakain pilai.
Varians i makim hamas ol namba i kamap i go longwe long ekspektet velyu. Long wanpela yunit bilong bet, em i klostu 34 long bet long wanpela namba na klostu 1 long ret.
Fomula bilong wanpela bet
Long bet i pe W long 1 wantaim sansmatematikSansSans bilong wanpela resal, long 0 i go 1 o 0% i go 100%. Wanpela namba: 1/37 = 2.70%.Ritim olgeta → p, samting i kamap long 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 → em i +W wantaim sans p na −1 wantaim sans 1 − p. Ekspektet velyumatematikEkspektet velyuAvarej resal long wanpela bet long longpela taim. −1/37 bilong mani bilong bet long olgeta bet olpasin bilong Yurop.Ritim olgeta → em i pW − (1 − p) = −1/37. 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 E[X²] − EV² = pW² + (1 − p) − (1/37)². Long bet long wanpela nambabetWanpela nambaWanpela namba tasol, pe em i 35:1.Ritim olgeta →: (1/37)(1225) + 36/37 − 0.0007 ≈ 34.08. Long retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta →: 18/37 + 19/37 − 0.0007 ≈ 0.999.
Em i makim wanem long wanpela sesen
Ol varians i bung wantaim long ol tanim i no hangamap long narapelamatematikOl tanim i no hangamap long narapelaOlgeta tanim i gat wankain sans, maski wanem samting i kamap bipo. Olgeta kaunim long dispela sait i sanap long dispela.Ritim olgeta →, olsem na long N tanim wantaim wankain mani bilong bet, varians bilong olgeta em i N × mani bilong bet² × σ², na standet diviesenmatematikStandet diviesenSkwea rut bilong varians; hamas longwe resal i save stap long ekspektet velyu.Ritim olgeta → em i σ × mani bilong bet × √N. 100 tanim long $10: standet diviesen em i klostu $584 long ol bet long wanpela namba na $100 long ret, raun long wankain avarej −$27. Wanpela pleia i lukim ol namba i go antap na i go daun long ol handet dola; narapela i lukim i go isi isi tasol. Tupela i baim wankain pe.
Varians na ol sistem
ProgresenstratejiProgresenWanem lo i senisim mani bilong bet long ol resal i go pinis. Negative progresen i mekim bet i go antap bihain long lus, positive progresen bihain long win.Ritim olgeta → i no senisim EV long olgeta yunit yu betim, tasol em i senisim hamas mani yu betim na pasin bilong ol namba i kamap. MartingalestratejiMartingaleProgresen i mekim bet i dabel bihain long olgeta lus. Lukim hap Strateji long wanem samting em i mekim na i no mekim.Ritim olgeta → i daunim varians bilong planti sesen (planti liklik win) na i putim wanpela bikpela tel (bikpela lus i no save kamap planti). Long olgeta sesen wantaim, varians i antap moa long bet wankain oltaimstratejiBet wankain oltaimBetim wankain mani long olgeta tanim. Olgeta progresen ol i skelim wantaim dispela.Ritim olgeta → long wanem dispela tel. ParolistratejiParoliPositive progresen: dabel bihain long win, go bek long stat bihain long lus o bihain long tripela win wan bihain long narapela. Narapela nem: Martingale i go baksait.Ritim olgeta → i mekim narapela kain. Taim yu makim wanpela sistem, yu makim kain varians tasol; avarej i no stap long ol samting yu inap makim.
- p10 −$500
- p25 −$500
- namba long namel −$500
- p75 +$40
- p90 +$1,120
Strateji bilong Bet Wankain Oltaim long RuletStrateji Paroli bilong Rulet (Martingale i Go Baksait)
Bilong wanem em i bikpela samting long pleia
Varians i mekim na yu no inap save long ol sot sesen, tasol yu inap save long ol longpela sesen. Wantaim σ = $100 na EV = −$27 long 100 tanim, edj em i wanpela hap long fopela hap bilong nois, na sesen bilong win em i samting nating. Long 10,000 tanim, EV em i −$2,700 na σ em i $1,000; nau edj em i klostu tripela taim bilong nois, na ran bilong win em i samting bilong tripela sigma. Long sotpela taim varians em i pren bilong pleia, na long longpela taim em i pren bilong kasino.
Varians bilong planti bet wantaim
Long planti bet long wankain tanim, ol samting i kamap i save go wantaim (sapos 17 i win, blakbetBlakBet wan-long-wan long 18 namba blak. Tok Frans: noir.Ritim olgeta → na namba tu dosenbetDosen1–12, 13–24 o 25–36, pe em i 2:1.Ritim olgeta → tu i win), olsem na ol varians i no bung wantaim nating. Tul Bet Builder i kaunim stret ol namba inap kamap long wanem kain sipmaniSipSamting i makim wanpela namba mani i no save senis, yu putim long laiaut bilong mekim bet. Narapela nem: check.Ritim olgeta → yu putim, long rot bilong kaunim olgeta 37 samting inap kamap. Em tasol stretpela rot bilong mekim.
Fomula
Ol askim
Nogat. Olgeta bet i gat wankain ekspektet velyu. Varians i antap i makim olsem ol namba i go antap na i go daun bikpela moa raun long en.
Ol bet wan-long-wanbetBet wan-long-wanRet/blak, od/iven, antap/daunbilo. 18 namba, pe em i 1:1.Ritim olgeta →, wantaim σ ≈ 1 long wanpela yunit. I daun moa yet wantaim la partageloLa partageLo bilong Frans: taim siro i kamap, hap bilong mani bilong bet wan-long-wan i kam bek. Em i katim edj bilong kasino long ol dispela bet long hap, i go daun long 1.35%.Ritim olgeta →, na em i mekim avarej i kamap gutpela liklik tu.
Avarej win bilong kasino i wankain long olgeta dola; varians i senisim tasol olsem wanem mani bilong kasino i kam, sampela taim planti, sampela taim liklik, na kasino i gat planti tausen pleia long mekim em i stap isi.
Amamas wantaim Matematik
Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.
Tupela pleia wanwan i betim $1 long wanwan tanim long 100 tanim long wil bilong Yurop, wanpela oltaim long retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta →, narapela oltaim long 17. Husat i gat moa sans long stap antap long pinis?
Soim bekim
Bekim Pleia long 17: 50.9%, na 35.5% long ret. Tupela i lusim $2.70 long avarej.
Ret: pleia i stap antap wantaim 51 win o moa long 100, wanwan wantaim sansmatematikSansSans bilong wanpela resal, long 0 i go 1 o 0% i go 100%. Wanpela namba: 1/37 = 2.70%.Ritim olgeta → 18/37. Binomial distribution i givim 35.5%, na 50 win stret, no win no lus, narapela 7.7%.
Namba 17: wanwan win i givim bek $36, olsem na tupela win (−$28) i no inap na tripela (+$8) i inap. Sans bilong tripela o moa win long 100 tanim long 1/37 em 50.9%.
Pleia bilong wanpela namba i stap antap planti taim moa, tasol ol risal i kalap moa: wanpela win moa o liklik moa i muvim risal long $36, na ol pleia i stap daun planti taim i stap daun tru. Bollman (2024) i givim ol namba bilong Amerika, 26.5% na 49.2%.
Liklik lap
Wankain avarej lus. Wanpela bilong tupela i tokim yu long en long nek i strong.
Ol As bilong Save
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.