Sawaal: Do Dozen aur Ek Chip

Sawaal

Aap pehle dozenbetDozen1–12, 13–24 ya 25–36, payout 2:1.Poora padhein → par $10, doosre dozen par $10 aur 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 → par $1 lagaate hain. (a) Kaun se outcomes possible hain aur unki probabilities kya hain? (b) Expected valueganitExpected valueLambe samay mein har bet ka ausat nateeja. Har standard European bet ke liye stake ka −1/37.Poora padhein → kya hai? (c) Kya zero wali chippaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → bet ko behtar banati hai?

Hal (a) aur (b)

Outcomes: 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 → 1–24 mein (24 pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein →): ek dozen $20 deta hai, doosra $10 haarta hai, zero $1 haarta hai: net +$9. Ball 25–36 mein (12 pockets): dono dozens haarte hain, zero bhi haarta hai: −$21. Ball zero par (1 pocket): dozens $20 haarte hain, zero $35 deta hai: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ $21 ke stake par har spin −$0.57: 2.70%.

Hal (c)

Zero chip ke bina: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ $20 ke stake par −$0.54, yeh bhi 2.70%. Zero chip ne zero wale −$20 outcome ko +$15 mein badal diya (37 mein ek baar $35 ka sudhaar, har spin $0.95 ke barabar) aur baaki 36 spins par $1 ka kharcha kiya (har spin $0.97 ke barabar). Net badlaav: har spin −$0.03, jo extra dollar ka 2.70% hai. Insurance ki keemat bhi bilkul baaki sab ki tarah tay hai.

Yeh har jagah kyun laagu hota hai

Expected values jud jaati hain. Ek saath lagi kisi bhi bets ke set ka EV uske hisson ke EVs ka jod hota hai, aur har hissa apne stake ka −1/37 hai. Isliye koi bhi combination total stake ka −1/37 hai. Betting layoutsaamanLayoutTable par chhapa betting grid. Doosre naam: table, felt, cloth.Poora padhein → par chips ka koi bhi arrangement, chahe kitni bhi chips hon, isse bach nahi sakta; Bet Builder tool aapke lagaaye ja sakne wale kisi bhi set ke liye iski pushti karega. Combinations jo badalte hain woh distribution hai: aap kitni baar jeette hain, kitna jeette hain, aur sabse bura case kitna bura hai.

Ek mushkil follow-up sawaal

Standard bets ka aisa combination dhoondhiye jo saare 37 numbers cover kare. Teen dozens ($10 har ek) aur zero par $1: 1–36 mein se kisi par bhi net −$1 (ek dozen $20 deta hai, baaki do $20 haarte hain, zero $1 haarta hai), aur zero par net +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = $31 ke stake par −31/37: 2.70%. Aap pakka kar sakte hain ki aap kabhi chaunkenge nahi, aur is suvidha ke liye phir bhi wahi keemat chukaate hain.

Formula

Sawaal