Roulette ka Math · Applied · 7 min

Call Bets ki Expected Value

Voisins, tiers, orphelinsFR · sectorOrphelins“Anaath”: voisins aur tiers ke baad bache aath numbers: 17, 34, 6 aur 1, 20, 14, 31, 9.Poora padhein →, neighbours aur jeu zéro, har ek ko har chip par −1/37 tak hisaab karke dikhaya gaya.

Chhota jawab

Call bets asamaan weights wali standard bets ke combinations hain, isliye unke payouts pocketsaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → ke hisaab se badalte hain. Phir bhi har ek total stake ka −2.70% hai, kyunki expected values jud jaati hain. Yeh page paanchon ka hisaab dikhata hai.

call bets
5 standard
chips
4 se 9
EV har chip par
−1/37
payout pocket ke hisaab se badalta hai
haan

Yeh alag kyun dikhti hain

Straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → ka ek hi nateeja payout deta hai. Voisins du zéroFR · sectorVoisins du zéro“Zero ke padosi”: wheel par 22 se 25 tak ke satrah numbers, nau chips se bet.Poora padhein → ke teen alag payoutspaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → hain, is par nirbhar ki ballsaamanBallChhoti ball jo rotor ki ulti disha mein track par chhodi jaati hai. Aaj ki balls ivorine ya Teflon ki hoti hain, 18–21 mm.Poora padhein → double-weighted streetbetStreetLayout ki ek row ke teen numbers, payout 11:1. French mein: transversale.Poora padhein → mein giri, double-weighted cornerbetCornerLayout par ek corner share karne wale chaar numbers, payout 8:1.Poora padhein → mein ya kisi single splitbetSplitDo saath wale numbers, payout 17:1.Poora padhein → par. Yeh vividhta ek sthir cheez chhupaati hai: bet ki har chippaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → ek aam bet hai jiska EV khud ka −1/37 hai, aur poori bet unka jod hai.

Voisins du zéro (9 chips, 17 numbers cover)

0-2-3 par 2 (street, 11 deta hai), 25-26-28-29 par 2 (corner, 8 deta hai), splits 4-7, 12-15, 18-21, 19-22, 32-35 mein se har ek par 1 (17 dete hain). Street mein hit: +22 − 7 = +15. Corner mein hit: +16 − 7 = +9. Split par hit: +17 − 8 = +9. Miss: −9. EV = (3 × 15 + 4 × 9 + 10 × 9 − 20 × 9)/37 = (45 + 36 + 90 − 180)/37 = −9/37. Nau chips, −9/37: har chip par −1/37.

call betchipscover karti hainateeje (net units, pockets)EV (units)
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
Neighbours (5)55+31 × 5 · −5 × 32−5/37
Jeu zéro47+32 × 1 · +14 × 6 · −4 × 30−4/37
Teeno sectors ek saath2037pocket ke hisaab se +15/+9/+12/+31/+13; miss kabhi nahi−20/37
EV ko chips se bhaag dijiye aur har row −1/37 hai.

Tiers du cylindre (6 chips, 12 numbers cover)

Chhe splits, har ek 17 deta hai. Koi bhi hit: +17 − 5 = +12. Miss: −6. EV = (12 × 12 − 25 × 6)/37 = (144 − 150)/37 = −6/37. Sabse sapaat call bettableCall betHaath se lagane ke bajaye dealer ko bola gaya bet, aam taur par voisins ya tiers jaisa wheel-sector bet. Doosra naam: “announced bet”.Poora padhein →: ek payout, ek haar.

Orphelins (5 chips, 8 numbers cover)

1 par 1 straight-up (35 deta hai), splits 6-9, 14-17, 17-20, 31-34 (17 dete hain). 1 par hit: +35 − 4 = +31. 17 par hit (do splits): +34 − 3 = +31. 6, 9, 14, 20, 31, 34 par hit: +17 − 4 = +13. Miss: −5. EV = (31 + 31 + 6 × 13 − 29 × 5)/37 = (62 + 78 − 145)/37 = −5/37.

Neighbours aur jeu zéro

NeighboursbetNeighborsWheel par ek number aur uske dono taraf ke do-do pockets, paanch straight-up chips.Poora padhein →: paanch straight-ups; koi bhi hit +35 − 4 = +31; EV = (5 × 31 − 32 × 5)/37 = (155 − 160)/37 = −5/37. Jeu zéroFR · sectorJeu zéro“Zero game”: zero ke sabse paas ke saat numbers (12, 35, 3, 26, 0, 32, 15), chaar chips se bet.Poora padhein →: splits 0-3, 12-15, 32-35 aur 26 par ek straight-up; 26 par hit: +35 − 3 = +32; split hit: +17 − 3 = +14; EV = (32 + 6 × 14 − 30 × 4)/37 = (32 + 84 − 120)/37 = −4/37.

Koi bhi hit ki probability, call betsspins ka %
Jeu zéro (7)
18.9%
Neighbours (5)
13.5%
Orphelins (8)
21.6%
Tiers (12)
32.4%
Voisins (17)
45.9%
Teeno (37)
100%
spins ka %
050100%
20 chips se sab kuch cover karna −2 aur +16 units ke beech result aur −20/37 ka EV pakka karta hai. Is guarantee ki keemat bhi baaki sab ki tarah 2.70% hai.

Jeu Zéro Roulette Bet

Electronic wheel par

IGT ka Roulette Evolution, jaisa Bollman (2021) batate hain, yeh call bets electronic single-zerowheelZeroAkela green pocket jise koi even-money, dozen ya column bet cover nahi karta; house edge ka source. Doosre naam: single zero, 0.Poora padhein → wheel par deta hai. Arithmetic nahi badalta: har ek ab bhi har chip par −1/37 hai. Jo badalta hai woh sectorwheelSectorWheel par pockets ka lagatar ek hissa (arc), layout ke kisi group se alag cheez.Poora padhein → bets ke paksh mein players ka ek tark hai. Asli table par kuch log maante hain ki woh dealer ki aadaton aur spin ki speed ko itna achha padh sakte hain ki andaaza laga lein ball kis hisse mein giregi, ise wheel clocking kehte hain, aur call bet kisi hisse par bet lagaane ka swabhaavik tareeka hai. Electronic wheel par padhne ke liye koi dealer nahi, aur woh tark, jo asli table par bhi kamzor hai, khatam ho jaata hai.

Electronic wheel par padhne ke liye koi dealer nahi, aur wheel ke kisi hisse par bet lagaane ka tark bhi saath chala jaata hai.

Electronic Roulette Terminals

Seekh

Call bets suvidha hain, ganit nahi. Wheel ke kisi sector par bet lagaane ka yeh sabse tez tareeka hai aur ek hi announcement mein aisa karne ka akela tareeka. Inki expected valueganitExpected valueLambe samay mein har bet ka ausat nateeja. Har standard European bet ke liye stake ka −1/37.Poora padhein → har chip par utni hi hai jitni sabse saade straight-up ki, aur payouts ki vividhta bas hisaab-kitaab hai, edge nahi.

Formula

EV(call bet) = Σ EV(chips) = −(chips)/37
hit par net = jeetne wali chip(s) ka payout − haarne wali chips

Sawaal

Kya koi call bet behtar value hai?

Nahi. Har ek har chip par −1/37 hai. Fark coverage aur payout ke roop mein hai.

Orphelins 17 par +31 kyun deta hai?

Do splits mein 17 shaamil hai, isliye hit par 17 do baar milta hai aur sirf teen chips haarti hain.

Agar main har position par 2 chips ke saath voisins lagaaun toh?

18 chips, har payout double, EV −18/37. Scale karne se kuch nahi badalta.

Maths ke saath mazaa

Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.

  1. Ek electronic wheel French call betstableCall betHaath se lagane ke bajaye dealer ko bola gaya bet, aam taur par voisins ya tiers jaisa wheel-sector bet. Doosra naam: “announced bet”.Poora padhein → offer karta hai: tiers (6 chipspaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein →), jeu zéroFR · sectorJeu zéro“Zero game”: zero ke sabse paas ke saat numbers (12, 35, 3, 26, 0, 32, 15), chaar chips se bet.Poora padhein → (4), orphelinsFR · sectorOrphelins“Anaath”: voisins aur tiers ke baad bache aath numbers: 17, 34, 6 aur 1, 20, 14, 31, 9.Poora padhein → (5), voisins (9) aur neighborsbetNeighborsWheel par ek number aur uske dono taraf ke do-do pockets, paanch straight-up chips.Poora padhein → (5). Har ek kitni baar kuch na kuch jeetti hai, aur uski keemat kya hai?

    Solution dikhaiye

    Jawab Har ek ki keemat 2.70% hai. Yeh 37 mein se kramashah 12, 7, 8, 17 aur 5 spins par kuch na kuch jeetti hain.

    Keemat is page ke rule se nikalti hai: har chip ek aam bet hai jo apna 1/37 haarti hai, aur expected valuesganitExpected valueLambe samay mein har bet ka ausat nateeja. Har standard European bet ke liye stake ka −1/37.Poora padhein → jud jaati hain.

    Kuch jeetne ka chance utne pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → hai jitne bet cover karti hai, 37 mein se. Tiers 12 cover karti hai, jeu zéro 7, orphelins 8 aur voisins 17. Neighbors ek number aur wheel par uske dono taraf ke do-do pockets cover karti hai: 5.

    Bollman (2021) jeu zéro ko 26 par ek ki jagah chaar chips ke saath describe karte hain. Isse yeh 7-chip bet ban jaati hai aur uske payoutspaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → badalte hain, keemat nahi: ab bhi 2.70%.

    betchipscover kiye pocketskuch jeetti haihouse edge
    tiers61232.4%2.70%
    jeu zéro4718.9%2.70%
    orphelins5821.6%2.70%
    voisins91745.9%2.70%
    neighbors5513.5%2.70%

Thodi hansi

Nau chips, nau baata saintees. Arithmetic chips hi hain.

Nau chips, nau baata saintees. Arithmetic chips hi hain.

Sources

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapter 13, roulette.
  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. Chapter 2, roulette.
2026-09-28 ko review kiyamodel: European, single zero walamethodology ↗sources ↗