Spid i Go Daun
Dispela em i wanpela hap tasol bilong tanim we yu inap save tru long bihain.
Long rot, bal i go isi long wanpela lain i no gat kranki, we fraksen na win i makim. Long taim bilong sampela ful raun, yu inap tingim taim em bai i pundaun, klostu tru long hap sekon. Tasol taim bal i go nabaut bihain, planti bilong dispela save i lus.
Model
Ting olsem baltulBalLiklik bal dila i sutim long rot i go long narapela sait long rota. Ol nupela bal i ivorine o Teflon, 18–21 mm.Ritim olgeta → i go isi long tupela samting: hap a i no save senis (fraksen taim bal i ran), na hap b·v i bihainim spit (win na ol narapela lus i bihainim spit): dv/dt = −(a + bv). Ansa i soim olsem spit i go daun isi isi i go klostu long spit bilong pundaun. Olsem na taim bilong raun T = 2πr/v i go longpela moa long olgeta raun, na em i go longpela moa na moa. Painim a na b long ol namba wan sampela raun, na yu save long ol raun i stap yet na taim bal bai i pundaun. I no gat narakain samting hia; em i save bilong fisiks bilong namba wan yia long yunivesiti, long bal i ran long rot.
Dispela save i givim wanem
Sapos yu save long taim bilong pundaun inap 0.2 sekon, na rotatulRotaHap bilong wil i save tanim na i karim ol hul.Ritim olgeta → i tanim long 15 hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta → long wanpela sekon, yu inap painim hul i stap aninit long ples bal i pundaun inap klostu tripela hul. Em gutpela nius long man i laik save long bihain. Nogut nius em olsem: bihain bal i ran long hap i sliptulHap i slipHap i slip i stap namel long rot bilong bal na ol hul, we ol ston bilong sutim bal i stap.Ritim olgeta →, i paitim ston bilong sutim baltulSton bilong sutim balWanpela long ol ain i stap long hap i slip na i mekim bal i pundaun i kalap nabaut. Narapela nem: canoe, diamond, pin.Ritim olgeta → na i kalap long ol liklik banistulLiklik banisAin i banisim tupela hul long wil.Ritim olgeta →. Hul bal i sindaun long en inap stap long wanpela hap i brait 20 i go 30 hul. Bal i go nabaut long hap bilong pundaun, na dispela i kaikai planti bilong save yu kisim long hap bilong rot.
Wanem samting i stap yet
Sapos bal i save pundaun klostu long hul bilong pundaun planti moa long rendom, orait putim bet long seksenwilSeksenWanpela hap bilong wil we ol hul i stap wan bihain long narapela, i narakain long wanpela grup long laiaut.Ritim olgeta → raun long hul ol i tingim i givim liklik edj. Small na Tse (2012) i metaim dispela long laboratori wantaim kamera. Ol i painim olsem bal i pundaun long seksen ol i tingim planti taim inap long tanim edj bilong kasinomatematikEdj bilong kasinoHap bilong olgeta mani bilong bet kasino i holim long avarej: 2.70% long rulet bilong Yurop.Ritim olgeta → i kamap edj bilong pleia bilong sampela pesen. Long laboratori bilong ol, ol i lukim olgeta wil long antap, ol i save long wil, na ol i putim bet bihain long dila i sutim bal. Ol dispela samting i no stap long laiv tebol.
Wanem samting i senis long wan wan aua
Tupela namba a na b i no stap wankain oltaim long wanpela wil. Ol Eudaemon i bin taimim wanpela wil bilong kasino inap planti yia long ol yia 1970. Ol i painim olsem win i mekim bal i go isi moa long rot, na bal tu i bikpela samting: bal Teflon i lusim spit tupela taim hariap moa long bal ol i wokim olsem bal bilong biliat. Ol i lukim tu olsem save bilong ol long bihain i rong i go 5 i go 10% long wanpela aua, taim man i opim dua o win i senis. Long wanem, win i gat wara o win i hevi i mekim bal i go isi kwik moa. Olsem na program bilong ol i holim tupela kain seting: wanpela long hau kwik bal i go isi, na wanpela long spit we bal i lusim rot. Pleia i stretim gen tupela long olgeta tebol, na gen taim save long bihain i stat long rong.
Bilong wanem Laboratori i stori long dispela
I no bilong olgeta man i ken mekim. Em bilong soim wanem samting tru i mekim pilai i rendom: wanpela hap yu inap save long en, we kasino i lukautim long pasim bet kwik na long liklik tru namba bilong ful raun; na wanpela hap i paul olgeta, we kasino i lukautim long ol ston bilong sutim bal na ol liklik banis i daun. Pleia i save long dispela i save bilong wanem 2.70% i stap gut.
Mekim kaunting yu yet
Long wanpela strim, taimim bal taim em i go pas long ston bilong sutim bal long tripela raun, na tingim ol raun bihain. Planti taim, yu bai i stap insait long wanpela raun long pundaun. Dispela em hap yu inap save long en, i wok olsem mipela i tok. Bihain, lukim we bal i sindaun tru, long hul i stap aninit long ples em i pundaun, na raitim long faiv ten tanim. Dispela kaunting em i soim hau bal i go nabaut, na brait bilong en em i ansa long askim “bilong wanem man i no inap winim dispela?”.
Fomula
Ol askim
Nogat. Fraksen i senis wantaim das, wara long win na taim wil i bagarap liklik. Ol masin bilong save long bihain i stretim gen long olgeta tanim.
Tripela i givim save i no stret tumas; faivpela o sikispela i givim gutpela save. Long ol studio, liklik tru namba em fopela, na em i lusim liklik taim tasol bilong putim bet. Na taim bilong putim bet i pinis pinis.
Sampela tasol, long sotpela taim, wantaim masin, pastaim ol kasino i senisim pasin na ol lo i kamap. Lukim pilai bilong kisim edj.
Amamas wantaim Matematik
Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.
Long model bilong Thorp bilong soim baltulBalLiklik bal dila i sutim long rot i go long narapela sait long rota. Ol nupela bal i ivorine o Teflon, 18–21 mm.Ritim olgeta → i go isi, sapos wanpela raun long rot i kisim T sekon, bal i gat 1/(e^(3T/20) − 1) − 10/3 raun i stap pastaim long em i lusim rot. Hamas i stap bihain long raun bilong hap sekon, na bihain long raun bilong wanpela ful sekon? Liklik rong long kaunim taim bilong 0.012 sekon long T = 0.8 i muvim tok profet hamas?
Soim bekim
Bekim Klostu 9.5 raun bihain long raun bilong hap sekon na 2.85 bihain long raun bilong wanpela sekon. Liklik rong i muvim tok profet klostu 0.12 bilong wanpela raun, klostu 4½ hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta →.
T = 0.5: 3T/20 = 0.075 na e^0.075 ≈ 1.0779, olsem na 1/0.0779 ≈ 12.84, na 12.84 − 3.33 ≈ 9.51 raun. T = 1: e^0.15 ≈ 1.1618, 1/0.1618 ≈ 6.18, na 6.18 − 3.33 ≈ 2.85. Raun i hariap i min planti raun i stap yet, na raun i isi tupela taim i lusim i no inap wanpela hap long tri.
Long T = 0.8 fomula i givim 4.51 raun; long T = 0.812 em i givim 4.39. Liklik rong bilong 12 hap long tausen bilong sekon, klostu taim bal i kisim long ran long braitpela bilong em yet, i muvim tok profet 0.12 bilong wanpela raun: klostu 4½ hul bilong wil i gat 37 hul. Dispela wanpela liklik rong em planti bilong 5.5 hul Thorp i larim long kaunim taim bilong bal (lukim Pilai bilong Kisim Edj long Rulet), na em as na klok, i no kaunim, i pasim man i tok profet.
Liklik lap
Yu inap save inap long pundaun. Bihain, ol ston bilong sutim bal.
Ol As bilong Save
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Bass, T. A. The Eudaemonic Pie.
- Thorp, E. O. “Optimal gambling systems for favorable games.”