Matematik bilong Rulet · Yusim long pilai · 7 min

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.

Sotpela bekim

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.

ol bet yu singautim
5 nambawan
sip
4 i go 9
EV long wanpela sip
−1/37
pe i senis long wanwan hul
yes

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.

bet yu singautimsipi karamapimol risalt (win tru long yunit, ol hul)EV (yunit)
Voisins du zéro917+15 × 3 · +9 × 14 · −9 × 20−9/37
Tiers du cylindre612+12 × 12 · −6 × 25−6/37
Orphelins (en cheval)58+31 × 2 · +13 × 6 · −5 × 29−5/37
Ol namba klostu (5)55+31 × 5 · −5 × 32−5/37
Jeu zéro47+32 × 1 · +14 × 6 · −4 × 30−4/37
Olgeta tripela seksen wantaim2037+15/+9/+12/+31/+13 long wanwan hul; i no save mis−20/37
Brukim EV long namba bilong sip, na olgeta lain i kamap −1/37.

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.

Sans bilong wanpela win, ol bet yu singautim% bilong ol tanim
Jeu zéro (7)
18.9%
Ol namba klostu (5)
13.5%
Orphelins (8)
21.6%
Tiers (12)
32.4%
Voisins (17)
45.9%
Olgeta tripela (37)
100%
% bilong ol tanim
050100%
Sapos yu karamapim olgeta wantaim 20 sip, risalt bai stap namel long −2 na +16 yunit, na EV em −20/37. Dispela promis i kostim 2.70% olsem olgeta narapela samting.

Bet Jeu Zéro long Rulet

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.

Long wil bilong elektronik i no gat dila bilong ritim, na tok bilong betim wanpela hap bilong wil i go wantaim.

Ol Masin Rulet bilong Elektronik

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

EV(bet yu singautim) = Σ EV(ol sip) = −(ol sip)/37
win tru taim i win = pe long sip i win − ol sip i lus

Ol askim

I gat wanpela bet yu singautim i gutpela moa?

Nogat. Wanwan em −1/37 long wanpela sip. Ol i narakain long hamas namba ol i karamapim na long pe bilong ol.

Bilong wanem orphelins i pe +31 long 17?

Tupela bet long tupela namba i gat 17 insait, olsem na win i pe 17 tupela taim na i lusim tripela sip tasol.

Olsem wanem sapos mi betim voisins wantaim 2 sip long wanwan ples?

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.

  1. 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 kasino
    tiers61232.4%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.

Nainpela sip, nainpela hap long tetisevenpela. Matematik em ol sip yet.

Ol As bilong Save

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Sapta 13, rulet.
  2. Wykes, A. The Complete Illustrated Guide to Gambling. Doubleday, 1964.
  3. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021. Sapta 2, rulet.
mipela i skelim gen long 2026-09-28model: Yurop, wanpela sirometodoloji ↗ol as bilong save ↗