Roulette House Edge
Har stake ka woh hissa jo casino average mein rakh leta hai.
European roulette: har standard bet par 2.70%, kyunki payouts aise calculate hote hain jaise 36 pockets hon, jabki pockets 37 hain.
Derivation
Straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → ke fair odds 36 to 1 hone chahiye, kyunki jeetne ke har ek tareeke ke muqable haarne ke 36 tareeke hain. Casino 35 to 1 deta hai. Woh missing unitpaisaUnitBase stake jismein koi system ya player kaam karta hai. Progressions units mein batayi jaati hain taaki kisi bhi table par laagu hon.Poora padhein →, 37 barabar-chance wale outcomes par baanta jaaye, to har spin par stake ka 1/37 = 2.70% hai. Yahi kami har payoutpaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → mein dikhti hai kyunki har payout 36/n − 1 rule use karta hai: splitbetSplitDo saath wale numbers, payout 17:1.Poora padhein → 17.5 ki jagah 17 deta hai, dozenbetDozen1–12, 13–24 ya 25–36, payout 2:1.Poora padhein → 2.083 ki jagah 2, redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → 1.056 ki jagah 1. Fark hamesha har jeet par 1/n units hai, aur har spin par n/37 jeet, isliye hamesha har spin par 1/37.
Edge vs hold
Edge har lagaye gaye unit par expected lossganitExpected lossExpected value guna kul lagayi gayi raqam; ek session ya ek muddat mein ausat nuksaan.Poora padhein → hai: har spin 2.70%. HoldpaisaHoldPlayers table par jo paisa laate hain uska woh hissa jo casino asal mein rakh leta hai. Yeh house edge se zyada hota hai kyunki jeet ka paisa dobara lagaya jaata hai.Poora padhein → woh hai jo casino asal mein aapke table par laaye paise mein se rakhta hai, aur yeh kahin zyada hota hai kyunki aap apni jeet dobara laga dete hain. $100 ka buy-intableBuy-inTable par cash dekar chips lena. Yeh spins ke beech hota hai, aur cash dealer ke haath mein dene ke bajaye layout par rakha jaata hai.Poora padhein → jo 200 spins mein $10 karke lagaya gaya, usne $2,000 ka turnover kiya aur lagbhag $54 edge mein diye; us buy-in par hold 54% hai. Casinos hold report karte hain; players ko edge mein sochna chahiye.
Har bet ka edge same kyun hai
Yeh design ka faisla hai, sanyog nahi. 36/n − 1 rule 18vi sadi mein fix hua aur double zerovariantDouble zeroAmerican wheel ka 00 pocket. Iske hone se house edge 2.70% se badhkar 5.26% ho jaata hai.Poora padhein → baad mein payouts chhuye bina hataya gaya. Agar payouts 37 pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → ke liye fair hote, to straight-up 36 to 1 deta aur casino ki koi kamaai na hoti. Ek jaisa edge suvidhajanak hai: koi bhi roulette bet doosre ke muqable “sucker bet” nahi hai, sirf ek apvaad ke saath, 7.89% wala American five-number bet.
Roulette edge kya nahi hai
Yeh session haarne ki probabilityganitProbabilityKisi outcome ka chance, 0 se 1 tak ya 0% se 100% tak. Ek number: 1/37 = 2.70%.Poora padhein → nahi hai; zyadatar chhote sessions varianceganitVarianceYeh naap ki results expected value ke aas-paas kitna faile hue hain. Straight-up ke liye zyada, even-money bets ke liye kam.Poora padhein → se tay hote hain, aur 100-spin even-money sessions mein se lagbhag 42% plus mein khatam hote hain. Yeh har session ki fee nahi hai; yeh turnoverpaisaTurnoverSession ya muddat mein lagayi gayi kul raqam, dobara lagayi gayi jeet milakar. Doosre naam: handle, action.Poora padhein → ke saath badhta hai, isliye jo progressionstrategyProgressionKoi bhi rule jo pichhle results ke hisaab se stake badalta hai. Negative progressions haar ke baad ise badhati hain, positive jeet ke baad.Poora padhein → zyada lagati hai woh zyada chukati hai. Koi bet pattern ise patla nahi kar sakta, kyunki ek saath lage bets ke edges unke stakes ke anupaat mein jud jaate hain.
Paise mein
Har $1,000 wager par expected loss European roulettevariantEuropean rouletteSingle-zero wheel, 37 pockets, house edge 2.70%. Is site ka standard model.Poora padhein → mein $27.03, American mein $52.63, aur la partageniyamLa partageFrench rule: zero aane par even-money stake ka aadha wapas milta hai. In bets par house edge aadha hokar 1.35% ho jaata hai.Poora padhein → ke saath even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, payout 1:1.Poora padhein → par $13.51 hai. Ek regular jo hafte mein do baar, har shaam $500 lagata hai, saal bhar mein $52,000 ka turnover karta hai aur European wheel par lagbhag $1,400 edge mein deta hai. Har spin par figure chhota hai aur saal bhar mein lagatar.
Har spin ya har resolved bet
Lagbhag har roulette bet ek spin mein settle hota hai, isliye uska har spin edge aur har bet edge ek hi number hai. Jo bet push hokar layoutsaamanLayoutTable par chhapa betting grid. Doosre naam: table, felt, cloth.Poora padhein → par reh sakta hai, uske do hote hain. Riverboat Roulette ka teal bet American wheel ke 3 numbers cover karta hai, agar 8 White numbers mein se kisi se pehle inmein se koi aaye to 2 to 1 jeetta hai, aur baaki sab par push hota hai. Har resolved bet par yeh stake ka 2/11, yaani 18.18% haarta hai. Har spin par 2/38, yaani 5.26%, kyunki average mein bet 38/11 spins, lagbhag 3.5, tak laga rehta hai. Dono figures sahi hain. Per-spin figure bet ko baaki table se compare karta hai aur batata hai ki ek ghanta kitne ka padta hai; per-resolved figure batata hai ki bet aakhir mein settle hone par har stake ka kitna wapas aata hai.
Jab casino daam galat laga de
Is page ka har edge us arithmetic se aata hai jo casinos aam taur par sahi karte hain. Kabhi-kabhi nahi karte. October 1994 mein Biloxi, Mississippi ke Grand Casino ne teen dice ka total 4 aane par 80 to 1 offer kiya, aur 17 par bhi wahi. Teen dice 216 tarah se girte hain aur unmein se sirf 3 ka total 4 hota hai, isliye bet har lagaye unit par 81 × 3/216 = 1.125 lautata tha: player ke liye 12.5% edge. Players ne dhyaan diya. Casino ek din mein lagbhag $1,80,000 haara, bet band kiya, aur use 60 to 1 par dobara khola, jo wahi 216 mein 3 chances house ke liye 15.3% edge bana deta hai. Hunacek (2025), Bollman ka hawala dete hue, yeh kahani batate hain. Roulette ke standard payouts itne seedhe hain ki unmein is tarah galti nahi hoti; uske anokhe side betsbetSide betMain game ke saath juda ek optional extra wager, aam taur par kisi streak, bonus event ya jackpot par. Lagbhag hamesha standard bets se mehnga.Poora padhein → mein arithmetic check karna faayde ka hai.
Doosre table games mein side bets
Bollman (2021) blackjack, baccarat, craps aur roulette ke main bets ko unhi tables ke aam side bets ke saath rakhte hain. Pehle teen games mein side bet main bet se mehnga padta hai, aksar kai guna. Apvaad table ka aakhri game hai: American roulettevariantAmerican roulette0 aur 00 wala wheel, 38 pockets, house edge 5.26%. Is site ka default model nahi hai.Poora padhein → ka edge main bets par 5.26% hai, itna zyada ki Colors ya WINGO jaisa side bet sasta pad sakta hai.
Formula
Sawaal
Nahi. Yeh aap jitna wager karte hain uska 2.70% hai. Wahi paisa dobara lagane se woh phir se wager hota hai.
Nahi. Yeh ek anupaat hai. Dollars mein expected loss stake ke saath badhta hai.
Edge se naapein to saare standard European bets barabar hain; fark sirf itna hai ki woh kitni baar jeette hain aur kitna dete hain. La partage ke saath even-money bets ka edge baakiyon ka aadha hai.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
European wheel par ek straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → aur redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → par bet, dono ki keemat 2.70% hai, jabki ek sirf ek number cover karti hai aur doosri atharah. Har bet ka house edgeganitHouse edgeHar stake ka woh hissa jo casino average mein rakh leta hai: European roulette mein 2.70%.Poora padhein → ek jaisa kyun hota hai?
Solution dikhaiye
Jawab Har payoutpaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → aise tay kiya jaata hai jaise 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 → wahan ho hi nahi, isliye har bet 37 spins mein ek unitpaisaUnitBase stake jismein koi system ya player kaam karta hai. Progressions units mein batayi jaati hain taaki kisi bhi table par laagu hon.Poora padhein → haarti hai, chahe woh kuch bhi cover kare.
n numbers par ek bet lijiye. Woh (36 − n)/n to 1 deti hai. 37 spins mein woh average mein n baar jeetti hai aur 37 − n baar haarti hai.
Jeet se n × (36 − n)/n = 36 − n units aate hain. Haar mein 37 − n units jaate hain. Fark har 37 spins mein −1 unit hai, aur n cancel ho gaya: nateeja straight-up, cornerbetCornerLayout par ek corner share karne wale chaar numbers, payout 8:1.Poora padhein → ya dozenbetDozen1–12, 13–24 ya 25–36, payout 2:1.Poora padhein → ke liye ek hi hai. 37 mein ek unit ka nuksaan 2.70% hai.
N pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → wale wheel par yahi hisaab (36 − N)/N deta hai, yaani American wheel par −2/38 = 5.26%. Sirf ek bet is pattern ko todti hai, American five-number bet: rule ke hisaab se use 6.2 to 1 dena chahiye, woh 6 deti hai, aur uski keemat 7.89% hai.
Keno, lottery jaisa game, bet ki gayi raqam ka 25% ya usse zyada rakh leta hai. Agar koi casino roulette wheel mein zeros jod de aur payouts waise hi chhod de, toh roulette ko keno jitna mehenga banane ke liye kitne zeros lagenge?
Solution dikhaiye
Jawab Baarah zeros: 48 pockets wala wheel.
z zeros ke saath wheel mein 36 + z pockets hote hain, aur payouts ab bhi 36 maan kar chalte hain. Upar wale puzzle ke rule se, har bet 36 + z spins mein z units haarti hai, isliye house edge z/(36 + z) hai.
Ise ek chauthai ke barabar rakhiye: 4z = 36 + z, toh z = 12. 48 pockets wale wheel par baarah zeros 25% ki keemat lenge.
Las Vegas Strip ka triple-zero wheel, jo zyadatar players ko milne wala sabse mehenga roulette hai, usmein iske ek chauthai zeros hain.
zerospocketshouse edge1372.70%2385.26%3397.69%44010.00%124825.00%Massachusetts Lottery ne 2023 mein 36 numbers wala aur bina zero ka ek wheel launch kiya. Ek single number 25 for 1 deta hai, aur red, blackbetBlack18 black numbers par even-money bet. French mein: noir.Poora padhein →, odd ya even 3 for 2 dete hain. Zero na hone par kya yeh roulette se sasta hai?
Solution dikhaiye
Jawab Nahi, kahin zyada mehenga: number par 30.56% aur red ya black par 25%, jabki European wheel par 2.70%.
“For” mein stake shamil hai. $1 ki number bet average mein 36 draws mein ek baar $25 lautati hai: $36 lagane par $25 wapas, yaani 36 mein $11 ka nuksaan, 30.56%.
Red par $2 ki bet aadhe samay $3 lautati hai: har $4 lagane par $3 wapas, yaani 25% ka nuksaan.
Zero keemat tay karne ka sirf ek tareeka hai. Roulette aise payout deta hai jaise 36 pockets hon aur ek 37th jod deta hai; is wheel mein 36 pockets hain aur yeh seedha kam deta hai. Bollman (2024) ise exercise ke roop mein deta hai.
Ek casino 1 se 36 tak ke gyarah prime numbersganitPrime number1 se bada poora number jise sirf 1 aur woh khud poori tarah bhaag dete hain: 2, 3, 5, 7, 11, 13 aur aage.Poora padhein → par nayi bet chahta hai: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 aur 31. European wheel par baaki har bet jitni, yaani 2.70%, keemat rakhne ke liye ise kitna dena chahiye? 2 to 1 par iski keemat kitni hogi?
Solution dikhaiye
Jawab 25 to 11, lagbhag 2.27 to 1. 2 to 1 par iski keemat 10.81% hogi.
Pehle puzzle ka rule lagaiye: n numbers par bet (36 − n)/n to 1 deti hai. n = 11 par yeh 25/11 to 1 hai, ek ajeeb payout, kyunki $10 ki chippaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → $22.73 jeetegi.
2 to 1 par, $1 ki bet 37 mein se 11 spins par $2 jeetti hai aur baaki 26 par $1 haarti hai: har 37 spins mein 22 − 26 = −4 units, 10.81%.
Isiliye roulette 1, 2, 3, 4, 6, 12 aur 18 numbers par bets bechta hai: 36 in sab se poora divide hota hai, isliye fair payout poora number aata hai. Taylor (2021) yeh exercise das primes ke saath deta hai; asal mein gyarah hain.
Thodi hansi
Har stake ka 1/37, har bet par, har spin.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Hunacek, M. Quantitative Literacy Through Games and Gambling.