Matematik bilong Rulet · Hevi bilong matematik · 7 min

Hevi: Tupela Dosen na Wanpela Sip

Tupela dosen i karamapim 24 namba. Putim wanpela sip long siro na yu karamapim 25. Dispela insurens i givim win?

Sotpela bekim

Nogat. Wanwan hap em −2.70% bilong mani bilong bet bilong en, olsem na olgeta wantaim em −2.70% bilong olgeta mani. Dispela hevi i soim bilong wanem, i kaunim stret ol risalt na sans bilong ol, na i soim wanem i senis (pasin bilong en) na wanem i no senis (pe).

tupela dosen
24/37 · win tru +1 o −2
wantaim siro
25/37 i karamap
EV long wanpela yunit
−1/37 oltaim
skul
ol EV i bung

Hevi

Yu putim $10 long namba wan dosenbetDosen1–12, 13–24 o 25–36, pe em i 2:1.Ritim olgeta →, $10 long namba tu dosen na $1 long 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 →. (a) Wanem ol risalt i ken kamap na wanem sans bilong ol? (b) Wanem ekspektet velyumatematikEkspektet velyuAvarej resal long wanpela bet long longpela taim. −1/37 bilong mani bilong bet long olgeta bet olpasin bilong Yurop.Ritim olgeta →? (c) SipmaniSipSamting i makim wanpela namba mani i no save senis, yu putim long laiaut bilong mekim bet. Narapela nem: check.Ritim olgeta → long siro i mekim bet i kamap gutpela moa?

Bekim (a) na (b)

Ol risalt: 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 → long 1–24 (24 hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta →): wanpela dosen i pe $20, narapela i lusim $10, siro i lusim $1: win tru +$9. Bal long 25–36 (12 hul): tupela dosen i lus, siro i lus: −$21. Bal long siro (1 hul): ol dosen i lusim $20, siro i pe $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57 long wanpela tanim long $21 yu betim: 2.70%.

risalthulsanswin o lus
1–242464.9%+$9
25–361232.4%−$21
012.7%+$15
avarej−$0.57 = 2.70% bilong $21

Bekim (c)

Sapos nogat sip long siro: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54 long $20 yu betim. Em tu 2.70%. Sip long siro i senisim risalt bilong siro long −$20 i kamap +$15. Em i gutpela moa long $35 wanpela taim long 37, olsem $0.95 long wanpela tanim. Tasol em i kostim $1 long ol narapela 36 tanim, olsem $0.97 long wanpela tanim. Senis tru: −$0.03 long wanpela tanim, em 2.70% bilong dispela wanpela dola i kam antap. Insurens i gat pe stret olsem olgeta narapela samting.

Bilong wanem em i stret long olgeta hap

Ol ekspektet velyu i save bung. Wanem lain bet yu putim wantaim i gat EV i wankain olsem ol EV bilong ol hap i bung wantaim, na wanwan em −1/37 bilong mani bilong bet bilong en. Olsem na wanem bung em −1/37 bilong olgeta mani bilong bet. I no gat wanpela rot bilong putim ol sip long laiauttulLaiautGrid bilong bet ol i prinim long tebol. Narapela nem: table, felt, cloth.Ritim olgeta →, maski hamas, bilong abrusim dispela. Tul Bet Builder bai soim yu long wanem lain bet yu ken putim. Wanem samting ol bung i senisim em pasin bilong ol risalt: hamas taim yu win, hamas mani, na hamas nogut moa i ken kamap.

Wankain $21 long tripela rot: sans bilong win na nogut moa i ken kamap
$21 long ret: p(win)
48.6% · nogut moa −$21
tupela dosen + siro: p(win)
67.6% · nogut moa −$21
$21 long 17: p(win)
2.7% · nogut moa −$21
033.8067.6% · nogut moa −$21
Olgeta tripela i gat EV −$0.57 long wanpela tanim. Ol i narakain long pasin bilong ol tasol.

Askim i hat moa

Painim wanpela bung bilong ol nambawan bet i karamapim olgeta 37 namba. Tripela dosen ($10 wanwan) wantaim $1 long siro: wanem namba long 1–36 i givim −$1 (wanpela dosen i pe $20, tupela narapela i lusim $20, siro i lusim $1), na siro i givim +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 long $31 yu betim: 2.70%. Yu ken mekim sua olsem yu no inap kirap nogut, tasol yu baim wankain pe yet bilong dispela.

Fomula

EV(bung) = Σ EV(ol hap) = −(olgeta mani bilong bet)/37

Ol askim

I gat wanpela bung bilong bet i gat edj i liklik moa?

Nogat, long tebol bilong Yurop. Long tebol bilong Frans, ol bet wan-long-wanbetBet wan-long-wanRet/blak, od/iven, antap/daunbilo. 18 namba, pe em i 1:1.Ritim olgeta → tasol i gat 1.35%. Sapos yu putim narapela samting wantaim, edj bilong olgeta i go antap.

Na sapos mi betim ret na blak wantaim?

Yu lusim $1 long wanwan $1 long siro tasol, na i no win long narapela taim. EV −2.70% na nogat gutpela samting: em dispela wanpela bung i no gat as tru.

Orait bilong wanem putim ol bet wantaim?

Bilong makim pasin bilong sesen yu laikim. Em i stretpela as, na em wanpela as tasol.

Liklik lap

Insurens long tebol bilong rulet i kostim stret olsem em i seivim.

Insurens long tebol bilong rulet i kostim stret olsem em i seivim.

Ol As bilong Save

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Sapta 13, rulet.
mipela i skelim gen long 2026-09-28model: Yurop, wanpela sirometodoloji ↗ol as bilong save ↗