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?

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).
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%.
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.
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
Ol askim
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.
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.
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.
Ol As bilong Save
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.