Sans bilong Ol Ran long Rulet
Ol longpela ran bilong wanpela kala i save kamap planti taim. Na ol i no makim wanpela samting long tanim bihain.
Faivpela ret long lain: 2.7%. Tenpela: 0.074%. Long wanpela sesen bilong 200 tanim, ran bilong sikispela bilong wanpela kala i save kamap planti moa long taim em i no kamap.
Hamas taim ran bilong lus i save kamap
Bet wan-long-wan long wil i gat wanpela siro i save lus long 19 tanim long 37. Wanwan lain i soim sans olsem olgeta tanim long wanpela ran bai lus, na hamas mani pleia bilong Martingale, em i dabolim bet bihain long olgeta lus, i lusim inap long dispela taim.
| lus i bihainim lus | sans | klostu 1 long | lus inap nau | bet bihain |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Sans em 19/37 taim em yet wanpela taim long wanwan lus, i stat long wanpela tanim. Longpela sesen i gat planti tanim we kain ran inap stat, olsem na long wanpela nait em i kamap planti moa long wanpela lain i soim.
Wanpela ran
SansmatematikSansSans bilong wanpela resal, long 0 i go 1 o 0% i go 100%. Wanpela namba: 1/37 = 2.70%.Ritim olgeta → olsem olgeta k tanim bihain i retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta → em i (18/37)ᵏ. Tupela: 23.7%. Faivpela: 2.7%. Tenpela: 0.074%, klostu 1 long 1,350. Twentipela: 1 long 1.8 milion. Twenti sikis, rekot bilong Monte Carlo: 1 long 137 milion. Ol dispela em i sans bilong wanpela stretpela ran i stat long wanpela stretpela tanim. Klostu i no gat wanpela man i askim dispela askim tru.
Long wanpela sesen
Askim ol man i laik askim tru em i “ran bilong k bai kamap long wanpela hap long sesen bilong mi?”, na bekim i bikpela moa tru long (18/37)ᵏ, long wanem sesen bilong 200 tanim i gat klostu 200 ples we ran inap stat. Ran bilong sikispela o moa bilong wankain kala, ret o blakbetBlakBet wan-long-wan long 18 namba blak. Tok Frans: noir.Ritim olgeta →, i save kamap long sesen bilong 200 tanim klostu 94% bilong ol taim; eitpela o moa klostu 47%; tenpela o moa klostu 14%. Sapos yu kolim kala pastaim, ol sans i go daun, i kamap klostu 75%, 27% na 7%. Pleia i sindaun inap wanpela nait bai lukim ol longpela ran long olgeta nait.
Bilong wanem Martingale i tingim dispela
Olgeta 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 go antap bihain long lus i gat wanpela longpela ran we em i bruk: sikispela lus long bet bilong stat $10 wantaim mak $500, tenpela long FibonaccistratejiFibonacciProgresen i bihainim lain namba 1, 1, 2, 3, 5, 8, 13…: wanpela step i go pas bihain long lus, tupela step i go bek bihain long win.Ritim olgeta →, faivpela long taimsim long tripela long ol dosenbetDosen1–12, 13–24 o 25–36, pe em i 2:1.Ritim olgeta →. Sans bilong ran bilong sikispela lus long bet wan-long-wan em i (19/37)⁶ ≈ 1.8% long wanpela traim, na sesen bilong 200 tanim i gat ating 100 traim, olsem na bruk i save kamap klostu long fopela sesen long faivpela bilong dispela longpela. Sans bilong ol ran long rulet em i as na dispela bikpela pundaun i no samting i kamap liklik taim tasol.
Hat na kol namba
Wankain kaunim i wok long ol bet long wanpela nambabetWanpela nambaWanpela namba tasol, pe em i 35:1.Ritim olgeta →. Long 300 tanim, avarej hamas taim wanpela namba i kamap em i 8.1; standet diviesenmatematikStandet diviesenSkwea rut bilong varians; hamas longwe resal i save stap long ekspektet velyu.Ritim olgeta → em i klostu 2.8. Wanpela namba bai kamap 15 taim na wanpela 2 taim long sans tasol, olgeta taim. Bod bilong ol namba i kamap i makim ol “hat” namba, em i makim antap bilong pasin bilong ol namba i stap namel. Laboratori i tokaut hamas tanim yu nidim pastaim long hat nambatingting i no truHat nambaNamba i bin kamap planti moa long yu ting long taim i no longpela i go pinis. Long stretpela wil, em i no tokaut long wanpela samting.Ritim olgeta → i makim wanpela samting (planti tausen, long wanpela wil yu save long en).
I no hangamap long narapela: em tasol as tingting
Ran bilong tenpela ret i no mekim blak i gat sans moa, na em i no mekim ret i gat sans moa tu. Tupela i 18/37. Ol ran em i pasin bilong ol lain namba i rendom, na sapos ol i no kamap, em bai samting yu mas tingting long en: lain bilong 200 tanim i no gat ran i longpela moa long fopela bai soim strong moa olsem man i bagarapim wil, winim lain i gat ran bilong twelvpela.
Fomula
Ol askim
26 blak long Monte Carlo long 18 Ogas 1913 em i dispela ol man i save long en. Ol i tok 32 ret long lain i kamap long wanpela kasino long Amerika long 1943. Tupela i stret wantaim sans tasol, long wanem ol kasino i save ranim planti tanim tru.
Em i 18/37 long tupela sait. Putim bet olsem plen bilong yu i tok, o no ken putim.
Nogat. Bias i save kamap ples klia taim sampela hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta → i kamap planti moa long planti tausen tanim, i no long ol ran bilong wanpela kala.
Amamas wantaim Matematik
Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.
Long avarej, hamas tanim bilong wil bilong Yurop i mas kamap pastaim long olgeta 37 namba i kamap wanpela taim o moa?
Soim bekim
Bekim Klostu 155 tanim long avarej; namba long namel em 147.
Kaunim taim bilong wet long wanpela nupela namba wanpela taim. Tanim namba wan oltaim i soim nupela namba. Taim yu lukim 1 namba pinis, 36 hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta → long 37 i nupela, olsem na nupela namba bihain i kisim 37/36 tanim long avarej. Taim yu lukim k namba pinis, em i kisim 37/(37 − k).
Bungim ol taim bilong wet: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = 155.5 tanim.
Planti bilong dispela em long las. Las namba yet i kisim 37 tanim long avarej, na las faivpela klostu 85. Long wil bilong Amerika, wankain kaunim i givim klostu 161. Em i hevi bilong man i bungim kupon (coupon collector); wankain avarej i kam long kaunim nomol.
Long 37 tanim bilong wil bilong Yurop, wanpela tanim long wanwan hul, hamas narakain namba yu ken ting long lukim?
Soim bekim
Bekim Klostu 23.6. Klostu wanpela hap long tri bilong ol namba, klostu 13, i no kamap liklik.
Kisim wanpela namba, olsem 17. Long wanwan tanim em i no kamap wantaim sans 36/37, olsem na em i no kamap long olgeta 37 tanim wantaim sans (36/37)³⁷ ≈ 0.363.
Olgeta namba i gat wankain sans, olsem na long avarej 37 × 0.363 ≈ 13.4 namba i no kamap na 37 − 13.4 ≈ 23.6 i kamap, planti bilong ol tupela taim o moa.
Ol pleia bilong rulet i kolim dispela lo bilong hap long tri (law of thirds). Em i no lo, em i kaunim bilong ol namba i kamap gen tasol: long ran i longpela olsem wil, klostu wanpela hap long tri bilong ol namba i no kamap, long stretpela wil olsem long olgeta narapela. Long 38 hul hap em (37/38)³⁸ ≈ 0.363 tu; long bikpela wil em i sindaun klostu long 1/e ≈ 0.368.
Pren i soim yu tupela lista bilong 50 kala, retbetRetBet wan-long-wan long 18 namba ret. Tok Frans: rouge.Ritim olgeta → o blakbetBlakBet wan-long-wan long 18 namba blak. Tok Frans: noir.Ritim olgeta →, na i tok tupela i kam long wil i nogat ol 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 →. Wanpela i senisim kala 25 taim na ran i longpela tru em sikis. Narapela i senis 35 taim na ran i no winim tri. Wanem wanpela em man i giaman wokim?
Soim bekim
Bekim Namba tu. Lista tru i senis klostu 24 o 25 taim. Lista i gat 35 senis i kamap klostu wanpela taim long 500 lista, na lista i nogat ran i longpela moa long tri klostu tupela taim long 100.
Wanwan nupela kala i kamap gen o i senis, hap na hap, olsem na 49 sans long senis i givim 24.5 senis long avarej, antap o daun klostu 3.5. Tripela ten faiv em tripela step bilong dispela antap long avarej; stretpela wil i kamapim kain namba bilong senis klostu wanpela taim long 500 lista.
Ol ran i tokim wankain stori. Lista tru bilong 50 i gat ran bilong foa o moa klostu 98% bilong taim, na ran i longpela tru planti taim em faiv o sikis.
Ol manmeri i wokim lista rendom long tingting bilong ol i senis planti tumas, long wanem ran bilong foa o faiv i luk olsem wanpela pasin long ai bilong ol. Taylor (2021) i soim wankain mak long ol lista bilong tromoi koin ol sumatin i giaman wokim: rendom tru i gat ran planti moa long ol manmeri i ting.
Wanpela buk bilong ol stori bilong kasino i stori long wanpela pleia we namba bilong em i kamap faivpela taim i bihainim narapela na i kolim olsem rekot. Long wil bilong Yurop dispela i no save kamap olsem wanem? Na hamas taim em i mas kamap long wanpela hap insait long wanpela kasino i gat 20 tebol, wanwan i tanim 40 taim long wanpela aua, de na nait?
Soim bekim
Bekim Namba yu kolim i kamap faivpela taim i bihainim narapela: 1 long 69 milion. Wanem namba i kamap fopela taim moa bihain long em i kamap pastaim: 1 long 1.87 milion. Dispela kasino i tanim klostu 7 milion taim long wanpela yia, olsem na em i mas lukim ran bilong faiv tripela o fopela taim long wanpela yia.
Namba yu kolim i kamap wantaim sans 1/37 long wanwan tanim, olsem na faivpela i bihainim narapela i gat sans (1/37)⁵ = 1 long 69,343,957. Tasol nogat man i kolim namba pastaim. Wanem namba i kamap pastaim, fopela tanim bihain i mas kamapim em gen: (1/37)⁴ = 1 long 1,874,161.
20 tebol × 40 tanim × 24 aua × 365 de = 7,008,000 tanim long wanpela yia. Wanwan tanim inap statim ran, olsem na kasino i ting long 7,008,000/1,874,161 ≈ 3.7 ran bilong faiv long wanpela yia.
Nogat ofisel rekot bilong dispela kain samting, na i no nidim: samting i no save kamap long wanpela tebol em i nomol samting long olgeta hap bilong kasino, na ol i stori long tebol we em i kamap. Stori, long Goldman (2007), i stap long wil i gat dabel siro, we ol namba em 1 long 79 milion na 1 long 2.09 milion.
Liklik lap
Ol longpela ran em i pasin bilong samting i rendom.
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.