Ekspektet Velyu bilong Ol Bet Yu Singautim
Voisins, tiers, orphelinsFR · seksenOrphelins“Ol pikinini i no gat papamama”: eitpela namba i stap yet bihain long voisins na tiers: 17, 34, 6 na 1, 20, 14, 31, 9.Ritim olgeta →, ol namba klostu na jeu zéro. Mipela i wokim wanwan inap long −1/37 long wanpela sip.

Ol bet yu singautim i bung bilong ol nambawan bet, tasol ol sip i no stap wankain. Olsem na pe bilong ol i senis long wanwan hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta →. Wanwan i stap −2.70% bilong olgeta mani bilong bet yet, long wanem ol ekspektet velyu i save bung wantaim. Dispela pes i soim matematik bilong olgeta faivpela.
Bilong wanem ol i luk narakain
Bet long wanpela nambabetWanpela nambaWanpela namba tasol, pe em i 35:1.Ritim olgeta → i gat wanpela risalt tasol i save pe. Voisins du zéroFR · seksenVoisins du zéro“Ol namba klostu long siro”: sevintinpela namba long 22 i go 25 long wil, yu betim wantaim nainpela sip.Ritim olgeta → i gat tripela narakain pemaniPeMani bet i win i givim yu, ol i tok olsem “X long 1”, antap long mani bilong bet i kam bek.Ritim olgeta →. Em i makim sapos 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 bet long tripela nambabetBet long tripela nambaTripela namba long wanpela lain bilong laiaut, pe em i 11:1. Tok Frans: transversale.Ritim olgeta → i gat tupela sip, long bet long fopela nambabetFopela nambaFopela namba i bung long wanpela kona long laiaut, pe em i 8:1.Ritim olgeta → i gat tupela sip, o long wanpela bet long tupela nambabetTupela nambaTupela namba i stap klostu, pe em i 17:1.Ritim olgeta →. Ol narakain pe i haitim wanpela samting i no save senis. Olgeta sipmaniSipSamting i makim wanpela namba mani i no save senis, yu putim long laiaut bilong mekim bet. Narapela nem: check.Ritim olgeta → insait long bet em wanpela nambawan bet, wantaim EV −1/37 bilong em yet. Na olgeta bet em ol dispela i bung wantaim.
Voisins du zéro (9 sip, 17 namba)
2 long 0-2-3 (tripela namba, i pe 11), 2 long 25-26-28-29 (fopela namba, i pe 8), 1 wanwan long tupela namba 4-7, 12-15, 18-21, 19-22, 32-35 (i pe 17). Win long tripela namba: +22 − 7 = +15. Win long fopela namba: +16 − 7 = +9. Win long tupela namba: +17 − 8 = +9. Nogat win: −9. EV = (3 × 15 + 4 × 9 + 10 × 9 − 20 × 9)/37 = (45 + 36 + 90 − 180)/37 = −9/37. Nainpela sip, −9/37: −1/37 long wanpela sip.
Tiers du cylindre (6 sip, 12 namba)
Sikispela bet long tupela namba, wanwan i pe 17. Wanpela i win: +17 − 5 = +12. Nogat win: −6. EV = (12 × 12 − 25 × 6)/37 = (144 − 150)/37 = −6/37. Em bet yu singautimtebolBet yu singautimBet yu tokim dila long en, yu no putim long han bilong yu. Planti taim em i bet long wanpela seksen bilong wil olsem voisins o tiers. Narapela nem: “bet yu tokaut”.Ritim olgeta → i stap isi moa: wanpela pe, wanpela lus.
Orphelins (5 sip, 8 namba)
1 bet long wanpela namba long 1 (i pe 35), tupela namba 6-9, 14-17, 17-20, 31-34 (i pe 17). Win long 1: +35 − 4 = +31. Win long 17 (tupela bet long tupela namba): +34 − 3 = +31. Win long 6, 9, 14, 20, 31, 34: +17 − 4 = +13. Nogat win: −5. EV = (31 + 31 + 6 × 13 − 29 × 5)/37 = (62 + 78 − 145)/37 = −5/37.
Ol namba klostu na jeu zéro
Ol namba klostubetOl namba klostuWanpela namba na tupela hul long tupela sait bilong en long wil, faivpela sip long wan wan namba.Ritim olgeta →: faivpela bet long wanpela namba; wanpela i win +35 − 4 = +31; EV = (5 × 31 − 32 × 5)/37 = (155 − 160)/37 = −5/37. Jeu zéroFR · seksenJeu zéro“Pilai bilong siro”: sevenpela namba i stap klostu tru long siro (12, 35, 3, 26, 0, 32, 15), yu betim wantaim fopela sip.Ritim olgeta →: tupela namba 0-3, 12-15, 32-35 na wanpela namba long 26; win long 26: +35 − 3 = +32; win long tupela namba: +17 − 3 = +14; EV = (32 + 6 × 14 − 30 × 4)/37 = (32 + 84 − 120)/37 = −4/37.
Long wil bilong elektronik
Roulette Evolution bilong IGT, olsem Bollman (2021) i tokaut long en, i givim ol dispela bet yu singautim long wanpela wil bilong elektronik i gat 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 →. Matematik i no senis: wanwan i stap −1/37 long wanpela sip yet. Wanem i senis em dispela wanpela tok ol pleia i save mekim bilong ol bet long seksenwilSeksenWanpela hap bilong wil we ol hul i stap wan bihain long narapela, i narakain long wanpela grup long laiaut.Ritim olgeta →. Long tebol tru, sampela i bilip olsem ol i ken ritim pasin bilong dila na spit bilong tanim gut inap long ges long hap bal bai pundaun long en. Ol i kolim dispela wheel clocking, na bet yu singautim em rot i stret bilong betim wanpela hap. Wil bilong elektronik i no gat dila bilong ritim. Olsem na dispela tok, we i no strong long tebol tru, i lus olgeta.

Skul bilong en
Ol bet yu singautim i bilong mekim isi, i no bilong matematik. Ol i rot i kwik tru bilong betim wanpela seksen bilong wil, na wanpela rot tasol bilong mekim long wanpela tok. Ekspektet velyumatematikEkspektet velyuAvarej resal long wanpela bet long longpela taim. −1/37 bilong mani bilong bet long olgeta bet olpasin bilong Yurop.Ritim olgeta → bilong ol long wanpela sip em i wankain olsem bet long wanpela namba i isi tru. Ol narakain pe em ol namba bilong buk tasol, i no edj.
Fomula
Ol askim
Nogat. Wanwan em −1/37 long wanpela sip. Ol i narakain long hamas namba ol i karamapim na long pe bilong ol.
Tupela bet long tupela namba i gat 17 insait, olsem na win i pe 17 tupela taim na i lusim tripela sip tasol.
18 sip, olgeta pe i kamap dabel, EV −18/37. Mekim i kamap bikpela i no senisim wanpela samting.
Amamas wantaim Matematik
Traim ol dispela yu yet pastaim. Bekim bilong wanwan i hait; opim taim yu redi.
Wanpela wil bilong elektronik i givim ol bet yu singautimtebolBet yu singautimBet yu tokim dila long en, yu no putim long han bilong yu. Planti taim em i bet long wanpela seksen bilong wil olsem voisins o tiers. Narapela nem: “bet yu tokaut”.Ritim olgeta → bilong Frans: tiers (6 sipmaniSipSamting i makim wanpela namba mani i no save senis, yu putim long laiaut bilong mekim bet. Narapela nem: check.Ritim olgeta →), jeu zéroFR · seksenJeu zéro“Pilai bilong siro”: sevenpela namba i stap klostu tru long siro (12, 35, 3, 26, 0, 32, 15), yu betim wantaim fopela sip.Ritim olgeta → (4), orphelinsFR · seksenOrphelins“Ol pikinini i no gat papamama”: eitpela namba i stap yet bihain long voisins na tiers: 17, 34, 6 na 1, 20, 14, 31, 9.Ritim olgeta → (5), voisins (9) na ol namba klostubetOl namba klostuWanpela namba na tupela hul long tupela sait bilong en long wil, faivpela sip long wan wan namba.Ritim olgeta → (5). Long olgeta wan wan, hamas taim em i winim sampela samting, na em i kostim hamas?
Soim bekim
Bekim Olgeta i kostim 2.70%. Ol i winim sampela samting long 12, 7, 8, 17 na 5 tanim long 37.
Kos i kam long lo long dispela pes: olgeta wan wan sip em i bet nating i lusim 1/37 bilong em yet, na 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.
Sans bilong winim sampela samting em namba bilong hultulHulWanpela long ol 37 hul i gat namba long rota. Narapela nem: slot, cup.Ritim olgeta → bet i karamapim, long 37. Tiers i karamapim 12, jeu zéro 7, orphelins 8 na voisins 17. Ol namba klostu i karamapim wanpela namba na tupela hul long tupela sait bilong en long wil: 5.
Bollman (2021) i tok jeu zéro i gat fopela sip long 26, i no wanpela. Dispela i wokim bet bilong 7 sip na i senisim ol pemaniPeMani bet i win i givim yu, ol i tok olsem “X long 1”, antap long mani bilong bet i kam bek.Ritim olgeta → bilong en, i no kos bilong en: em i stap yet long 2.70%.
betol siphul i karamapi winim sampela samtingedj bilong kasinotiers61232.4%2.70%jeu zéro4718.9%2.70%orphelins5821.6%2.70%voisins91745.9%2.70%ol namba klostu5513.5%2.70%
Liklik lap

Nainpela sip, nainpela hap long tetisevenpela. Matematik em ol sip yet.
Ol As bilong Save
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Wykes, A. The Complete Illustrated Guide to Gambling.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.