Matematik bilong Rulet · Hevi bilong matematik · 7 min

Hevi: Wil bilong De Yu Kamap

Hamas tanim bipo wanpela namba i kamap gen? Liklik moa tru long planti manmeri i ges.

Sotpela bekim

Hevi bilong de yu kamap long wil i gat 37 hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta →: bihain long 8 tanim tasol, sans em i winim hap olsem wanpela namba i kamap pinis tupela taim. Ol pleia i ting ol namba i kamap gen em i makim wanpela pasin. Tasol em samting yu ken wetim long stretpela wil.

50% sans bilong namba i kamap gen
8 tanim
90% sans
14 tanim
99% sans
20 tanim
avarej tanim inap namba i kamap gen pastaim
≈ 8.3

Hevi

Tanim wanpela stretpela wil bilong Yurop. Hamas tanim inap sansmatematikSansSans bilong wanpela resal, long 0 i go 1 o 0% i go 100%. Wanpela namba: 1/37 = 2.70%.Ritim olgeta → olsem tupela tanim o moa i soim wankain namba i winim hap? Planti pleia i ges klostu 18 o 19, hap bilong 37. Bekim em 8.

Bekim

Kaunim sans olsem nogat namba i kamap gen, na rausim long wan. Bihain long k tanim, p(olgeta i narakain) = (37/37)(36/37)(35/37)…((38 − k)/37). Bilong k = 8: 1 × 0.973 × 0.946 × 0.919 × 0.892 × 0.865 × 0.838 × 0.811 ≈ 0.44. Olsem na p(wanpela i kamap gen) ≈ 0.56. Bilong k = 14 em 0.93; bilong k = 20 em 0.996. Tingting bilong yu i rong, long wanem namba bilong ol pea bilong tanim i go antap olsem k², na wanem pea i ken kamap wankain.

tanim kp(olgeta i narakain)p(wanpela o moa i kamap gen)
575.7%24.3%
843.8%56.2%
1026.4%73.6%
147.1%92.9%
200.4%99.6%
37≈ 0%≈ 100%
p(nogat i kamap gen) = 37! / ((37 − k)! · 37ᵏ).

Bilong wanem em i bikpela samting long tebol

Bod bilong risalt i soim 20 namba i kamap laspela i save soim wanpela namba i kamap gen klostu oltaim, na planti taim tupela o tripela. Ol pleia i lukim “17 i kamap tupela taim long ten tanim” na i ting 17 em i hat namba. Matematik bilong de yu kamap i tok olsem namba i kamap gen insait long ten tanim i save kamap 74% bilong taim, na namba i kamap gen em i rendom. Pasin em i tru; mining em i no tru.

Sans olsem wanpela namba i kamap gen bihain long k tanim%
4 tanim
16%
6 tanim
36%
8 tanim
56%
10 tanim
74%
14 tanim
93%
20 tanim
99.6%
%
049.8099.6%

Ol Resal bilong Rulet: Ritim Bod

Hevi i kam bihain

Hamas tanim inap wanpela namba yu makim, olsem 17, i kamap tupela taim? Em narakain askim, na bekim i bikpela moa tru: avarej wet em 74 tanim, na sans bilong tupela 17 insait long 20 tanim em klostu 10%. Namel long “wanpela namba i kamap gen” (8 tanim) na “dispela namba i kamap gen” (74 tanim) em olgeta narakain namel long wanpela pasin yu lukim bihain na wanpela tok profet yu mekim paslain.

Traim

Ranim Demo Game long ten tanim na lukim ol risalt bilong bipo. Planti taim wanpela namba bai kamap gen. Ranim gen. Namba i kamap gen bai narakain. Mekim ten taim na yu lukim pinis hevi bilong de yu kamapmatematikHevi bilong de yu kamapHamas manmeri i mas i stap paslain long tupela i gat wankain de bilong kamap, o hamas tanim paslain long wanpela namba i kamap gen. Long wil i gat 37 hul, 8 tanim i inap long givim sans i winim hap.Ritim olgeta →. Mekim wan tausen taim (ol simulata i ken) na yu mesarim pinis.

Fomula

p(nogat i kamap gen long k) = Π (38 − i)/37 bilong i = 1…k
p(i kamap gen) = 1 − p(nogat i kamap gen)

Ol askim

Em i wankain olsem hevi bilong de yu kamap long ol manmeri?

Stret, wantaim 37 hul i no 365 de. 23 manmeri i givim 50% bilong de bilong kamap; 8 tanim i givim 56% bilong wil.

Na tripela bilong wankain namba?

50% bihain long klostu 19 tanim. Em i samting nambawan yet.

Namba i kamap gen i makim bias?

Nogat. Ol tausen tanim long wanpela wil i ken makim; wanpela namba i kamap gen i no save makim.

Amamas wantaim Matematik

Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.

  1. Wanpela bot bilong ol ansa long sait bilong wil bilong Amerika i soim 16 tanim i go pinis. Wanem sans olsem nogat wanpela namba i kamap tupela taim long en?

    Soim bekim

    Bekim Klostu 2.5%: klostu 39 bot long 40 i soim wanpela namba i kamap gen.

    Go wan wan tanim. Namba wan tanim inap kamap wanem namba. Namba tu i mas misim em: 37 sans long 38. Namba tri i mas misim tupela: 36 long 38. Namba sikstin i mas misim fiftinpela namba: 23 long 38.

    Mekim taim: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0.0246.

    Bot i nogat namba i kamap gen em i samting i no save kamap planti. Bot i gat namba i kamap gen i no tok wanpela samting long wil.

  2. Long tenpela tanim bilong wil bilong Yurop, wanem sans olsem 17 i kamap stret faivpela taim? Olsem wanpela namba, maski wanem namba, i kamap faivpela taim o moa? Na olsem wanpela namba i kamap tripela taim o moa long fopela tanim?

    Soim bekim

    Bekim 17 stret faivpela taim: 1 long 315,576. Wanpela namba faivpela taim o moa: klostu 1 long 8,333. Wanpela namba tripela taim o moa long fopela tanim: 1 long 349.

    17 faivpela taim: makim wanem faivpela tanim bilong tenpela, 252 rot, na olgeta i gat sans (1/37)⁵ × (36/37)⁵. Wantaim, 1 long 315,576.

    Wanpela namba: olgeta wan wan bilong 37 namba i gat sans bilong 1 long 308,325 long kamap faivpela taim o moa, na dispela i givim 37 long 308,325, o 1 long 8,333. Taim tupela namba i kamap faivpela taim wan wan, em i no save kamap planti, ol i kaunim tupela taim, tasol sapos yu rausim, em i no senisim wanpela samting long dispela mak.

    Tripela taim long fopela tanim: long wanpela namba, 4 × 36 + 1 = 145 bilong 37⁴ ansa inap kamap; long wanpela bilong 37 namba, 145/37³ = 1 long 349.

    Long wil i gat dabel 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 →, ol namba i makim wankain samting em 1 long 359,275, 1 long 9,243 na 1 long 368. Namel long “17” na “wanpela namba” em hevi bilong de bilong mama karimmatematikHevi bilong de yu kamapHamas manmeri i mas i stap paslain long tupela i gat wankain de bilong kamap, o hamas tanim paslain long wanpela namba i kamap gen. Long wil i gat 37 hul, 8 tanim i inap long givim sans i winim hap.Ritim olgeta → gen: i gat 37 rot bilong kirap nogut.

Liklik lap

Wanpela samting i kamap gen kwik. Dispela samting em i rendom.

Wanpela samting i kamap gen kwik. Dispela samting em i rendom.

Ol As bilong Save

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3rd ed., 1968. Gambler’s ruin, sapta XIV.
  2. Wizard of Odds. “Ask the Wizard”, askim bilong rulet. Ol i nupim long 3 Ogas 2026.
mipela i skelim gen long 2026-09-28model: Yurop, wanpela sirometodoloji ↗ol as bilong save ↗