Ol Wil bilong Rulet i Narakain
Ol wil i gat 18, 25, 26, 31, 40, 49, 62, 73 o 105 hul. Wanpela lo i makim pe bilong klostu olgeta: hamas hul ol pe i no tingim.
Taim ol i makim ol pe olsem ol hul bilong kasino i no stap, edj bilong kasinomatematikEdj bilong kasinoHap bilong olgeta mani bilong bet kasino i holim long avarej: 2.70% long rulet bilong Yurop.Ritim olgeta → em namba bilong hul bilong kasino long namba bilong olgeta hul, maski wil i bikpela o liklik. Planti narakain wil i bihainim dispela lo. Ol wil i gat narapela pasin i brukim lo: pe ol i katim, bonus raun, o bet i stap long planti tanim.
Wanpela lo bilong olgeta wil
Yuropian ruletnarakain ruletRulet bilong YuropWil i gat wanpela siro, 37 hul, edj bilong kasino 2.70%. Em i wil mipela save yusim pastaim long dispela sait.Ritim olgeta → i givim 35 long 1 olsem wil i gat 36 hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta →. Em i gat 37, na hul i lus em edj bilong 2.70%. Wankain lo i wok long olgeta wil: sapos i gat N namba na Z hul bilong kasino, bet long n namba i givim (N − n)/n long 1 i gat edj Z/(N + Z). Ol i wokim o tingim ol wil bilong olgeta kain sais long dispela lo, na namba tebol i putim ol long lain bilong pe. Ol lain bilong en i soim tu ol as samting bilong pilai Royal Roulette, gem bilong Australia: ol namba bilong en em ol kas 2 i go inap king, tupela hul bilong kasino em es na joka, na wanpela kas i givim 47 long 1.
Wil i bikpela i ken i no dia tumas
Ol pleia i ting wil i gat 62 hul i hat moa long winim, olsem na ol i ting gem i nogut moa. Edj i hangamap long hamas hul bilong kasino tasol. Super 62 i gat tupela sirowilSiroWanpela grinpela hul we i no gat bet wan-long-wan, dosen o kolam i karamapim; em i as bilong edj bilong kasino. Narapela nem: wanpela siro, 0.Ritim olgeta →, olsem wil bilong Amerika, tasol ol i 2 long 62 hul, i no 2 long 38. Olsem na em i kostim 3.23%, na Amerika i kostim 5.26%. Roulette 73, i gat 72 namba na wanpela siro, bai i kostim 1.37%, klostu wankain long bet wan-long-wan bilong Frans. Long liklik wil, lo i wok long narapela sait. Bollman i stori long olpela wil i gat 18 hul, 1 inap 16 wantaim 0 na 00. Long lo, olgeta bet bai i kostim 2/18, 11.11%: tupela hul bilong kasino em bikpela hap bilong liklik wil.
We lo i bruk: ol i katim pe
PemaniPeMani bet i win i givim yu, ol i tok olsem “X long 1”, antap long mani bilong bet i kam bek.Ritim olgeta → i mas stret long namba bilong sipmaniSipSamting i makim wanpela namba mani i no save senis, yu putim long laiaut bilong mekim bet. Narapela nem: check.Ritim olgeta →, na taim lo i givim hap namba, kasino i katim i go daun. Avenue bet bilong 100 To 1 Roulette i karamapim 15 hul na i mas givim 5⅔ long 1; em i givim 11 long 2, na dispela i litimapim edj long 4.76% i go long 7.14%. Long Super 62, sevenpela namba i gat namba 6 insait (6, 16, 26, 36, 46, 56, 60), na bet long dispela namba i givim 7 long 1. Olsem na em i kamap 9.68%, tripela taim winim narapela hap bilong laiauttulLaiautGrid bilong bet ol i prinim long tebol. Narapela nem: table, felt, cloth.Ritim olgeta →. White bet bilong Riverboat Roulette i karamapim 8 namba long 7 long 2. Long tebol i nogat sip bilong 50 sen, man i winim $5 i kisim $17, i no $17.50, na dispela i litimapim edj long 5.26% i go long 7.37%. Bet long faivpela namba bilong Amerika, long 7.89%, em wankain samting yumi save pinis.
We lo i bruk: ol bonus
Fast Action Roulette, ol i statim long Marina Bay Sands long 2020, i yusim tru wil i gat fopela siro. Wil olsem em yet bai i kostim 10%. Long olgeta tanim, tenpela Bonus namba i lait long rendom we. Bet long wanpela nambabetWanpela nambaWanpela namba tasol, pe em i 35:1.Ritim olgeta → i givim 35 long 1, 40 long 1 sapos namba bilong en em Bonus namba, na 80 long 1 sapos olgeta lain bilong fopela namba bilong en em Bonus. Dispela i mekim em 6.65%. Ol narapela tripela bet bilong gem i kostim moa tumas. Double Bonus Spin bilong IGT i putim wanpela yelo Bonus hul, wanpela na hap hul i bikpela, long wil bilong Amerika. Taim 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 pundaun long en, olgeta bet i kisim tupela tanim fri. Long kalkulesen bilong mipela, dispela i mekim edj i go daun long namel long 1.94% (bet long wanpela namba) na 2.73% (wan-long-wan), daunbilo long wil bilong Amerika nating. Bollman (2021) i prinim 3% inap 16% bilong dispela gem. Fomula bilong em i gat wanpela rong long aljebra, na long bet wan-long-wanbetBet wan-long-wanRet/blak, od/iven, antap/daunbilo. 18 namba, pe em i 1:1.Ritim olgeta → em i soim olsem ol tanim fri i lusim winim mani bilong bet, na dispela i no inap kamap.
We lo i bruk: ol bet i stap
Riverboat Roulette (2012) i givim namba tu kala long 32 namba bilong wil bilong Amerika. White i makim fopela hul i raunim olgeta siro (1, 2, 9, 10, 13, 14, 27, 28). Bet long wanpela grup kala i win sapos wanpela namba bilong en i kamap pastaim long wanpela bilong etpela White namba. White namba em "White Out" i rausim olgeta bet long kala. Olgeta narapela namba i no win no lus: bet i stap yet, na namel long ol tanim yu ken kisim bek o litimapim. Teal i karamapim tripela namba na i givim 2 long 1. Long olgeta bet i pinis, em i lusim 2/11 bilong mani bilong bet, 18.18%. Long olgeta tanim em i lusim 2/38, 5.26% yumi save pinis, long wanem, long avarej bet i stap 38/11, klostu 3.5 tanim.
Wil Thorp i ken tok profet long en: Big Six
Big Six, o wil bilong gutpela sans, em bikpela wil i sanap i gat 54 hul: 24 i givim 1 long 1, 15 i givim 2 long 1, sevenpela 5 long 1, fopela 10 long 1, tupela 20 long 1, na tupela hul i gat mak bilong kampani i givim 40 long 1. I nogat siro; kasino i kisim hap bilong en long givim liklik pe, na edj i go long 11.1% long ol hul i givim 1 long 1 inap 24.1% long ol mak. Long 1961 Thorp i wokim wanpela masin liklik olsem boks masis bilong tok profet long en, na em i wokim long swis long pinga bilong lek. Long 1981, em i kaunim taim bilong wanpela ful raun bilong wil long kasino wantaim hanwas, na em i painim olsem planti taim em i ken tokaut ples wil bai i stop klostu long faivpela hul. Sapos em i betim tasol ol hul i givim bikpela pe klostu long ples em i tok profet, em bai i kisim bek klostu +211%, sapos ol i kisim bet bihain long wil i tanim pinis. Ol i no save mekim olsem, na wil i tanim isi na olgeta man i lukim, olsem na bet i kam las bai i ples klia; Thorp i raitim olsem gem i no gat inap pilai bilong haitim wanpela.
Bilong wanem planti i no kamap nambawan
Wil bilong kasino i kostim planti tausen dola, na ol i mas wokim spesel wil i gat narakain namba bilong hul. Olsem na planti nupela gem bilong rulet i holim wil nating na i putim ol nupela bet. Long dispela as, pes bilong sait bet i longpela moa long dispela pes. Wil i gat igel na 31 hul bilong Amerika long senturi 19, long 12.90% long wanpela namba na 9.68% long olgeta narapela bet, i dai long pe bilong en yet. Tingting bilong namba tri hul bilong kasino i kam bek gen long 2016 long wil i gat 39 hul, we em i kostim 7.69%.
Ol askim
Nogat, em yet i no makim. Edj em hamas hul bilong kasino: 1 long 73 i no dia tumas olsem 1 long 37.
Roulette 73, long 1.37%, tasol em i plen ol i prinim, i no tebol yu ken painim. Long ol wil ol i givim pinis long ol pleia, Super 62 long 3.23% i kam bihain long Yuropian na Frans.
Wanpela samting i mas baim bonus. Planti taim ol i katim pe bilong as bet, o ol i putim narapela bet i gat bikpela edj.
Amamas wantaim Matematik
Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.
Royal Roulette, ol i wokim long Australia, i gat 50 hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta →: 48 kas long 2 i go inap king, wantaim wanpela es na wanpela joka. Wanpela kas i pe 47 long 1, tupela kas 23 long 1, tripela 15 long 1, fopela 11 long 1, sikispela 7 long 1, etpela 5 long 1, twelpela 3 long 1, sikstinpela 2 long 1 na twentifo 1 long 1. Wanem lo i wokim ol dispela pemaniPeMani bet i win i givim yu, ol i tok olsem “X long 1”, antap long mani bilong bet i kam bek.Ritim olgeta →, na olgeta bet i kostim hamas?
Soim bekim
Bekim Olgeta bet long n kas i pe (48 − n)/n long 1, olsem na olgeta bet i kostim 2/50 = 4%.
Traim lo long sampela bet: 47/1 = 47, 36/12 = 3, 32/16 = 2, 24/24 = 1. Em i stret long olgeta nainpela. Lo i makim pe olsem wil i gat 48 hul, olsem na es na joka em tupela hul bilong kasino, stret olsem 0 na 00 long wil bilong Amerika.
Tupela hul bilong kasino long 50 i givim edj bilong 4%. Wanpela kain “bilong Yurop” i rausim joka na i holim ol pe: wanpela hul bilong kasino long 49, edj bilong 2.04%.
Super 62 i gat wanpela bet olsem wanpela dijit yu makim bai stap insait long namba i win. Wokim wankain bet long wil nating bilong Amerika. Hamas namba long 1 i go inap 36 i gat olgeta wan wan namba, na wanem ol pe bai holim 5.26% olsem oltaim?
Soim bekim
Bekim Ol namba i gat 3 o 4 namba tasol i kisim pe i stret gut (11 long 1 na 8 long 1). Ol namba 1, 2 na 3 i no inap kisim pe i stret long ol sipmaniSipSamting i makim wanpela namba mani i no save senis, yu putim long laiaut bilong mekim bet. Narapela nem: check.Ritim olgeta → olgeta.
Kaunim ol namba. Namba 1 i stap long 1, 10 i go inap 19, 21 na 31: 13 namba. Namba 2 tu i stap long 13 namba na namba 3 long 10. Ol namba 4, 5 na 6 i stap long fopela namba wan wan (4, 14, 24, 34), na 7, 8 na 9 long tripela wan wan.
Bet long n namba i holim edj bilong Amerika sapos em i pe (36 − n)/n long 1. Dispela i givim 8 long 1 long fopela namba na 11 long 1 long tripela, tupela i namba olgeta. Long 13 namba em i givim 23/13, klostu 1.77 long 1, na long 10 namba 2.6 long 1. Sapos yu raunim 1.77 i go daun long 7 long 4, bet i kostim 5.92%; sapos yu raunim i go antap long 2 long 1, pleia i gat edj bilong 2.63%. Sapos yu raunim 2.6 i go daun long 5 long 2, em i kamap 7.89%.
Namba 0 em i samting yu makim: 10, 20 na 30 tasol i pe 11 long 1 long 5.26%; sapos yu putim 0 na 00 tu, em i kamap bet long faivpela namba, 6 long 1 long 7.89%, olsem basket betbetBasket betLong wil i gat wanpela siro: 0, 1, 2, 3 wantaim wanpela sip, pe em i 8:1. Narapela nem: first four, quatre premiers.Ritim olgeta →.
nambaol nambalo i tokinap peedj bilong kasino1, 2131.77 long 17 long 45.92%3102.6 long 15 long 27.89%4, 5, 648 long 18 long 15.26%7, 8, 9311 long 111 long 15.26%100 To 1 Roulette i pe (100 − n)/n long 1 long planti bet, long wil i gat 100 namba na 5 mak bilong kasino. Ol bet bilong en i karamapim 1, 2, 3, 4, 5, 10, 15, 20 o 50 hul na i pe 100, 49, 32, 24, 19, 9, 11 long 2, 4 na 1 long 1. Bet long wanpela nambabetWanpela nambaWanpela namba tasol, pe em i 35:1.Ritim olgeta → na Avenue i gat 15 hul i brukim lo. Wanem narapela bet i brukim lo tu, na em i kostim hamas?
Soim bekim
Bekim Bet long tripela hul: lo i tok 32⅓ long 1, em i pe 32 long 1, na em i kostim 5.71%, i no 4.76%.
Sekim olgeta pe wantaim lo: 98/2 = 49, 96/4 = 24, 95/5 = 19, 90/10 = 9, 80/20 = 4 na 50/50 = 1 olgeta i stret. Long tripela hul, lo i givim 97/3 = 32⅓, na nogat sip i inap pe olsem, olsem na ol i raunim i go daun long 32.
Bet i win 3 taim long 105 tanim na i givim bek 33 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 → wantaim mani bilong bet: 3 × 33 = 99 yunit i kam bek long olgeta 105 yu betim, lus bilong 6/105 = 5.71%.
Roulette 73, wanpela plen ol i bin prinim, i gat 72 namba na wanpela sirowilSiroWanpela grinpela hul we i no gat bet wan-long-wan, dosen o kolam i karamapim; em i as bilong edj bilong kasino. Narapela nem: wanpela siro, 0.Ritim olgeta →, na olgeta bet i pe (72 − n)/n long 1. Yu ken karamapim 24 namba i gat kala gre long 14 sip: 4 bet long wanpela namba na 10 bet long tupela nambabetTupela nambaTupela namba i stap klostu, pe em i 17:1.Ritim olgeta →. Dispela bet long 14 sip i kostim hamas?
Soim bekim
Bekim 1.37% bilong 14 sip, olsem olgeta narapela bet long dispela wil.
Longpela rot: bet long wanpela namba i pe 71 long 1 na bet long tupela namba 35 long 1. Sapos wanpela bilong 4 namba bilong bet long wanpela namba i kamap, yu winim 71 na yu lusim ol arapela 13 sip: +58. Sapos wanpela bilong 20 namba bilong bet long tupela namba i kamap: +35 − 13 = +22. Long ol arapela 49 hul yu lusim olgeta 14. Long avarej long 73 tanim: 4 × 58 + 20 × 22 − 49 × 14 = 232 + 440 − 686 = −14 yunit, em i 1/73 bilong olgeta wan wan sip.
Sotpela rot: ol ekspektet velyumatematikEkspektet velyuAvarej resal long wanpela bet long longpela taim. −1/37 bilong mani bilong bet long olgeta bet olpasin bilong Yurop.Ritim olgeta → i ken bung wantaim. Olgeta wan wan sip em i bet nating i lusim 1/73 bilong em yet, olsem na 14 sip i lusim 14/73. Taim yu bungim ol bet, yu senisim pasin bilong ol ansa i stap nabaut, tasol yu no senisim kos bilong ol.
Super 62 i gat 60 namba, 0 na 00, na i pe (60 − n)/n long 1. Ol man i wokim tu i droim em wantaim wanpela, tripela na fopela hul bilong kasino. Alphabetic Roulette i pe (24 − n)/n long 1 long 25 hul, na i gat narapela kain i gat Y na Z long hul bilong ol yet. Makim kos bilong olgeta faivpela.
Soim bekim
Bekim Wantaim wanpela i go inap fopela siro: 1.64%, 3.23%, 4.76% na 6.25%. Alphabetic wantaim Y na Z i stap wan wan: 7.69%.
Olgeta bilong ol i holim ol pe bilong ol na i senisim namba bilong hul bilong kasino tasol, olsem na edj em hul bilong kasino ÷ olgeta hul.
Wanpela siro, 61 hul: 1/61 = 1.64%. Tupela, 62 hul: 2/62 = 3.23%. Tripela, 63 hul: 3/63 = 4.76%. Fopela, 64 hul: 4/64 = 6.25%. Olgeta siro yu putim i kostim klostu wanpela poin na hap.
Alphabetic i pe olsem em i gat 24 leta. Taim Y na Z i stap long wanpela hul, kasino i gat 1 long 25, 4%. Taim Y na Z i stap wan wan, em i gat 2 long 26, 7.69%, wankain olsem wil i gat tripela siro. Brukim wanpela hul i kamap tupela i mekim pe i go antap klostu tupela taim.
wilol hulhul bilong kasinoedj bilong kasino60 namba, wanpela siro6111.64%Super 626223.23%60 namba, tripela siro6334.76%Super 646446.25%Alphabetic2514.00%Alphabetic, Y na Z i stap wan wan2627.69%Wanpela wil bilong bipo tru i gat 18 hul: 1 i go inap 16, 0 na 00. Ol namba od na 0 em retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta →, ol namba iven na 00 em blakbetBlakBet wan-long-wan long 18 namba blak. Tok Frans: noir.Ritim olgeta →, na 16 namba i stap long laiauttulLaiautGrid bilong bet ol i prinim long tebol. Narapela nem: table, felt, cloth.Ritim olgeta → bilong 4 long 4. Wokim namba tebol bilong pemaniNamba tebol bilong peLista bilong hamas olgeta bet o resal i pe. Long ol masin na ol sait bet, em i ples we ol i makim edj bilong kasino.Ritim olgeta → i givim olgeta bet wankain edj. Na bilong wanem 0 i mas lusim bet long ret, maski em i ret?
Soim bekim
Bekim Pe (16 − n)/n long 1: 15 long 1 long wanpela namba, 7 long tupela, 3 long fopela, 1 long etpela. Olgeta bet i kostim 11.11%. Sapos 0 i winim bet long ret, ret bai kamap stretpela bet.
Makim pe bilong wil olsem 0 na 00 i no stap. Bet long n namba i win n taim long 18 na i pe (16 − n)/n long 1, olsem na em i bringim bek 16 yunit, wantaim mani bilong bet, long olgeta 18 yu betim. Olgeta bet i kostim 2/18, 11.11%.
Ol bet i save stap long laiaut i kamap namba olgeta: wanpela namba 15 long 1, tupela i stap klostu 7 long 1, wanpela lain o kolambetKolamTwelpela namba long wanpela lain i sanap long laiaut, pe em i 2:1.Ritim olgeta → bilong fopela 3 long 1, na tupela lain, o etpela od, iven, daunbilo o antap, 1 long 1. Bet long tripela namba bai nidim 4⅓ long 1; sapos yu raunim i go daun long 4 long 1, em i kostim 16.67%.
Ret i karamapim etpela namba od. Sapos 0, em i ret, i winim bet long ret tu, ret bai karamapim 9 long 18 hul long 1 long 1: pilai i stretmatematikPilai i stretPilai we i no gat wanpela sait i gat edj: olgeta bet i gat ekspektet velyu siro.Ritim olgeta → i nogat edj liklik. Ol hul bilong kasino i kisim edj bilong ol long rot bilong lusim olgeta bet tasol, i no bet long ol yet.
Liklik lap
Kaunim ol hul bilong kasino, na bihain lukim we ol i katim pe.
Ol As bilong Save
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”