Anokhe Roulette Wheels
18, 25, 26, 31, 40, 49, 62, 73 ya 105 pockets wale wheels. Ek hi rule lagbhag sabki keemat batata hai: pockets ka woh hissa jise payouts ignore karte hain.
Jab payouts aise tay hote hain jaise house pockets hain hi nahi, toh house edgeganitHouse edgeHar stake ka woh hissa jo casino average mein rakh leta hai: European roulette mein 2.70%.Poora padhein → house pockets ko total pockets se divide karne par milta hai, wheel chahe kitna bhi bada ho. Zyadatar unusual wheels is rule ko follow karte hain. Interesting woh hain jo ise todte hain: round kiya gaya payout, bonus round, ya aisa bet jo kai spins tak laga rehta hai.
Har wheel ke liye ek rule
European roulettevariantEuropean rouletteSingle-zero wheel, 37 pockets, house edge 2.70%. Is site ka standard model.Poora padhein → 35 to 1 aise deta hai jaise wheel mein 36 pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → hon. Usme 37 hain, aur woh missing pocket hi 2.70% ka edge hai. Yahi rule kisi bhi wheel par kaam karta hai: N numbers aur Z house pockets ke saath, n numbers par bet jo (N − n)/n to 1 deta hai, uska edge Z/(N + Z) hota hai. Har size ke wheels isi rule par banaye ya propose kiye gaye hain, aur table unhe keemat ke order mein rakhti hai. Iski rows Australian game Royal Roulette khelne ki basics bhi batati hain: iske numbers 2 se king tak ke cards hain, iske do house pockets ace aur joker hain, aur ek card 47 to 1 deta hai.
Bada wheel sasta bhi ho sakta hai
Players 62-pocket wheel ko lamba shot samajhte hain aur maan lete hain ki game bura hai. Edge sirf house pockets ke hisse par depend karta hai. Super 62 mein American wheel ki tarah do zeroswheelZeroAkela green pocket jise koi even-money, dozen ya column bet cover nahi karta; house edge ka source. Doosre naam: single zero, 0.Poora padhein → hain, par woh 38 mein se 2 nahi balki 62 mein se 2 pockets hain, isliye yeh 5.26% ke muqable 3.23% leta hai. Roulette 73, 72 numbers aur ek zero ke saath, 1.37% leta, lagbhag French even money jitna. Chhote wheel par rule ulta kaam karta hai. Bollman 18 pockets ka ek purana wheel imagine karte hain, 1 se 16 plus 0 aur 00. Rule ke hisaab se har bet 2/18, yaani 11.11% leta: chhote wheel mein do house pockets bada hissa hote hain.
Jahan rule tootta hai: rounding
PayoutpaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → ek sensible chippaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → amount hona chahiye, aur jab rule fraction deta hai toh casino neeche round kar deta hai. 100 To 1 Roulette ka Avenue bet 15 pockets cover karta hai aur use 5⅔ to 1 dena chahiye; woh 11 to 2 deta hai, jisse uska edge 4.76% se 7.14% ho jaata hai. Super 62 par saat numbers mein digit 6 hai (6, 16, 26, 36, 46, 56, 60) aur us digit par bet 7 to 1 deta hai, jisse woh 9.68% ho jaata hai, baaki layoutsaamanLayoutTable par chhapa betting grid. Doosre naam: table, felt, cloth.Poora padhein → ka teen guna. Riverboat Roulette ka White bet 8 numbers 7 to 2 par cover karta hai; jis table par 50-cent chips nahi hain, wahan $5 ke winner ko $17.50 ki jagah $17 milte hain, jisse edge 5.26% se 7.37% ho jaata hai. American five-number bet, 7.89% par, isi cheez ka jaana-pehchana case hai.
Jahan rule tootta hai: bonuses
Fast Action Roulette, jo 2020 mein Marina Bay Sands mein launch hua, chaar zeros wala ek real wheel chalata hai, jo akele 10% leta. Har spin par das Bonus numbers random tarike se light up hote hain. Straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → 35 to 1 deta hai, agar uska number Bonus number ho toh 40 to 1, aur agar chaar ki poori row Bonus ho toh 80 to 1, jisse woh 6.65% par aa jaata hai. Game ke baaki teen bets kahin zyada lete hain. IGT ka Double Bonus Spin American wheel mein ek yellow Bonus pocket jodta hai, jo dedh pocket chauda hai; jab 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 → wahan girti hai, har bet ko do free spins milte hain. Hamare calculation se isse edge 1.94% (straight-up) aur 2.73% (even money) ke beech aa jaata hai, plain American wheel se kam. Bollman (2021) is game ke liye 3% se 16% chhapte hain; unke simplified formula mein ek algebra galti hai, aur even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, payout 1:1.Poora padhein → ke liye woh yeh matlab nikalta hai ki free spins stake se zyada haarte hain, jo ho hi nahi sakta.
Jahan rule tootta hai: bets jo lage rehte hain
Riverboat Roulette (2012) ne American wheel ke 32 numbers ko ek doosra color diya. White har zero ke aas-paas ke chaar pockets ko mark karta hai (1, 2, 9, 10, 13, 14, 27, 28). Color group par bet tab jeetta hai jab uske numbers mein se koi aath White numbers mein se kisi se pehle aaye. White number ek “White Out” hai jo har color bet saaf kar deta hai. Baaki har number push hai: bet laga rehta hai, aur spins ke beech use hataya ya badhaya ja sakta hai. Teal teen numbers cover karta hai aur 2 to 1 deta hai. Har resolved bet par yeh stake ka 2/11, yaani 18.18% haarta hai. Har spin par yeh 2/38 haarta hai, wahi jaana-pehchana 5.26%, kyunki average bet 38/11, lagbhag 3.5 spins tak laga rehta hai.
Ek wheel jise Thorp predict kar sakte the: Big Six
Big Six, ya wheel of fortune, 54 slots wala ek bada khada wheel hai: 24 slots 1 to 1 dete hain, 15 slots 2 to 1, saat 5 to 1, chaar 10 to 1, do 20 to 1, aur do logo slots 40 to 1. Isme koi zero nahi hai; house kam payment karke apna hissa leta hai, aur edge 1 to 1 wale slots par 11.1% se logos par 24.1% tak jaata hai. 1961 mein Thorp ne iske liye matchbox ke size ka ek predictor banaya, jo pair ke angoothe ke switch se chalta tha, aur 1981 mein, wristwatch se casino wheel ke ek chakkar ka time naap kar, unhone paaya ki woh aksar rukne ki jagah paanch slots ke andar bata sakte the. Prediction ke paas sirf zyada dene wale slots par bet lagane se lagbhag +211% milta, agar wheel ghumane ke baad bets liye jaate. Aisa nahi hota, aur wheel dheere aur sabke saamne ghoomta hai, isliye late bet saaf dikh jaata; Thorp ne likha ki game mein itna action nahi tha ki ek bhi chhup sake.
Itne kam kyun chalte hain
Ek professional wheel hazaron dollars ka hota hai, aur unusual number of pockets wala wheel order par banwana padta hai. Isliye zyadatar naye roulette games standard wheel rakhte hain aur bets jodte hain, isi wajah se side-bet page is page se lamba hai. 19vi sadi ke America ka 31-pocket eagle wheel, single number par 12.90% aur baaki sab par 9.68% ke saath, apni hi keemat se khatam ho gaya. Teesre house pocket ka idea 2016 mein 39-pocket wheel par wapas aaya, jahan yeh 7.69% leta hai.
Sawaal
Apne aap nahi. Edge house pockets ka hissa hai: 73 mein 1, 37 mein 1 se sasta hai.
Roulette 73, 1.37% par, lekin yeh ek published design hai, aisi table nahi jo aapko milne ki sambhavna ho. Players ko offer kiye gaye wheels mein European aur French ke baad Super 62, 3.23% par, aata hai.
Bonus ki keemat chukani padti hai, aksar base payout mein cut se ya high edge wale alag bet se.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
Australia mein bane Royal Roulette mein 50 pocketssaamanPocketRotor ke 37 numbered khaanon mein se ek. Doosre naam: slot, cup.Poora padhein → hain: 2 se king tak ke 48 cards, plus ek ace aur ek joker. Single card 47 to 1 deta hai, do cards 23 to 1, teen 15 to 1, chaar 11 to 1, chhah 7 to 1, aath 5 to 1, baarah 3 to 1, solah 2 to 1 aur chaubees 1 to 1. Kaunsa rule yeh payoutspaisaPayoutJeetne wala bet kya lautata hai, “X to 1” ke roop mein bataya jaata hai, wapas mile stake ke upar.Poora padhein → banata hai, aur har bet ki keemat kya hai?
Solution dikhaiye
Jawab n cards par har bet (48 − n)/n to 1 deti hai, isliye har bet ki keemat 2/50 = 4% hai.
Rule ko kuch bets par aazmaiye: 47/1 = 47, 36/12 = 3, 32/16 = 2, 24/24 = 1. Yeh naun mein fit hota hai. Rule wheel ki keemat aise lagata hai jaise usmein 48 pockets hon, isliye ace aur joker do house pockets hain, bilkul jaise American wheel par 0 aur 00.
50 mein se do house pockets 4% ka edge dete hain. Ek “European” version joker hata deta hai aur payouts wahi rakhta hai: 49 mein ek house pocket, 2.04% ka edge.
Super 62 mein ek bet hai ki chuna hua digit jeetne wale number mein aayega. Yahi bet ek aam American wheel ke liye design kijiye. 1 se 36 tak ke kitne numbers mein har digit aata hai, aur kaun se payouts aam 5.26% banaye rakhenge?
Solution dikhaiye
Jawab Sirf un digits ko saaf payouts milte hain jo 3 ya 4 numbers mein hain (11 to 1 aur 8 to 1). Digits 1, 2 aur 3 ko poore chipspaisaChipEk fixed raqam ka token, jise bet lagane ke liye layout par rakha jaata hai. Doosra naam: check.Poora padhein → mein fair tareeke se pay nahi kiya ja sakta.
Numbers giniye. Digit 1 aata hai 1, 10 se 19, 21 aur 31 mein: 13 numbers. Digit 2 bhi 13 numbers mein hai aur digit 3, 10 mein. Digits 4, 5 aur 6 chaar-chaar numbers mein hain (4, 14, 24, 34), aur 7, 8 aur 9 teen-teen mein.
n numbers par bet American edge tab rakhti hai jab woh (36 − n)/n to 1 de. Isse chaar numbers ke liye 8 to 1 aur teen ke liye 11 to 1 aata hai, dono poore. 13 numbers ke liye 23/13 aata hai, lagbhag 1.77 to 1, aur 10 numbers ke liye 2.6 to 1. 1.77 ko neeche 7 to 4 kar dijiye toh bet ki keemat 5.92% hai; upar 2 to 1 kar dijiye toh player ke paas 2.63% ka edge hai. 2.6 ko neeche 5 to 2 karne par 7.89% banta hai.
Digit 0 ek choice hai: sirf 10, 20 aur 30 hon toh 11 to 1 par 5.26%; 0 aur 00 jod dijiye toh yeh five-number bet ban jaati hai, 6 to 1 par 7.89%, basketbetBasketSingle-zero wheel par: ek chip se 0, 1, 2, 3, payout 8:1. Doosre naam: first four, quatre premiers.Poora padhein → ki tarah.
digitnumbersrule kehta haide sakta haihouse edge1, 2131.77 to 17 to 45.92%3102.6 to 15 to 27.89%4, 5, 648 to 18 to 15.26%7, 8, 9311 to 111 to 15.26%100 To 1 Roulette, 100 numbers aur 5 house symbols wale wheel par, zyadatar bets par (100 − n)/n to 1 deta hai. Uski bets 1, 2, 3, 4, 5, 10, 15, 20 ya 50 pockets cover karti hain aur 100, 49, 32, 24, 19, 9, 11 to 2, 4 aur 1 to 1 deti hain. Straight-upbetStraight-upEk single number, payout 35:1.Poora padhein → aur 15-pocket wali Avenue rule todti hain. Aur kaunsi bet todti hai, aur uski keemat kya hai?
Solution dikhaiye
Jawab Teen-pocket wali bet: rule 32⅓ to 1 kehta hai, woh 32 to 1 deti hai, aur uski keemat 4.76% ki jagah 5.71% hai.
Har payout ko rule se milaiye: 98/2 = 49, 96/4 = 24, 95/5 = 19, 90/10 = 9, 80/20 = 4 aur 50/50 = 1 sab fit hote hain. Teen pockets ke liye rule 97/3 = 32⅓ deta hai, jo koi chip pay nahi kar sakti, isliye ise neeche 32 kar diya jaata hai.
Bet 105 spins mein 3 baar jeetti hai aur tab stake samet 33 unitspaisaUnitBase stake jismein koi system ya player kaam karta hai. Progressions units mein batayi jaati hain taaki kisi bhi table par laagu hon.Poora padhein → lautati hai: har 105 lagane par 3 × 33 = 99 units wapas, yaani 6/105 = 5.71% ka nuksaan.
Roulette 73, ek published design, mein 72 numbers aur ek 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 → hai, aur har bet (72 − n)/n to 1 deti hai. Uske 24 gray numbers 14 chips se cover kiye ja sakte hain: 4 straight ups aur 10 splitsbetSplitDo saath wale numbers, payout 17:1.Poora padhein →. Us 14-chip bet ki keemat kya hai?
Solution dikhaiye
Jawab 14 chips ka 1.37%, us wheel ki baaki har bet ki tarah.
Lamba tareeka: straight-up 71 to 1 deta hai aur split 35 to 1. Agar 4 straight-up numbers mein se ek aata hai, toh aap 71 jeette hain aur baaki 13 chips haarte hain: +58. Agar 20 split numbers mein se ek aata hai: +35 − 13 = +22. Baaki 49 pockets par aap saare 14 haarte hain. 73 spins mein average: 4 × 58 + 20 × 22 − 49 × 14 = 232 + 440 − 686 = −14 units, jo har chip ka 1/73 hai.
Chhota tareeka: 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. Har chip ek aam bet hai jo apna 1/73 haarti hai, isliye 14 chips 14/73 haarti hain. Bets ko jodne se results ka bikhraav badalta hai, unki keemat kabhi nahi.
Super 62 mein 60 numbers, 0 aur 00 hain, aur yeh (60 − n)/n to 1 deta hai. Iske designers ne ise ek, teen aur chaar house pockets ke saath bhi banaya. Alphabetic Roulette 25 pockets par (24 − n)/n to 1 deta hai, aur iska ek variant hai jismein Y aur Z ke apne alag pockets hain. Paanchon ki keemat nikaliye.
Solution dikhaiye
Jawab Ek se chaar zeros ke saath: 1.64%, 3.23%, 4.76% aur 6.25%. Y aur Z alag wala Alphabetic: 7.69%.
In sab mein payouts wahi rehte hain aur sirf house pockets ki ginti badalti hai, isliye edge = house pockets ÷ saare pockets.
Ek zero, 61 pockets: 1/61 = 1.64%. Do, 62 pockets: 2/62 = 3.23%. Teen, 63 pockets: 3/63 = 4.76%. Chaar, 64 pockets: 4/64 = 6.25%. Har joda gaya zero lagbhag dedh point ki keemat badhata hai.
Alphabetic aise pay karta hai jaise usmein 24 letters hon. Y aur Z ek pocket share karein toh house ke paas 25 mein 1 hai, 4%. Y aur Z alag hon toh 26 mein 2 hain, 7.69%, utna hi jitna triple-zero wheel. Ek pocket ko do mein baantne se keemat lagbhag doguni ho gayi.
wheelpocketshouse pocketshouse edge60 numbers, ek zero6111.64%Super 626223.23%60 numbers, teen zeros6334.76%Super 646446.25%Alphabetic2514.00%Alphabetic, Y aur Z alag2627.69%Ek antique wheel mein 18 pockets hain: 1 se 16, 0 aur 00. Odd numbers aur 0 redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → hain, even numbers aur 00 blackbetBlack18 black numbers par even-money bet. French mein: noir.Poora padhein →, aur 16 numbers 4-by-4 layoutsaamanLayoutTable par chhapa betting grid. Doosre naam: table, felt, cloth.Poora padhein → par hain. Aisi pay tablepaisaPay tableList ki har bet ya result kya pay karta hai. Machines aur side bets mein house edge yahin tay hota hai.Poora padhein → design kijiye jo har bet ko ek jaisa edge de. Aur 0 red hote hue bhi red ki bet ko kyun haarna chahiye?
Solution dikhaiye
Jawab (16 − n)/n to 1 dijiye: ek number par 15 to 1, do par 7, chaar par 3, aath par 1. Har bet ki keemat 11.11% hai. Agar 0 red ki bet jeetta, toh red ek fair bet ban jaati.
Wheel ki keemat aise lagaiye jaise 0 aur 00 wahan hon hi nahi. n numbers par bet 18 mein n baar jeetti hai aur (16 − n)/n to 1 deti hai, isliye har 18 lagane par stake samet 16 units wapas laati hai. Har bet ki keemat 2/18, yaani 11.11% hai.
Layout ki natural bets poore numbers mein aati hain: ek number 15 to 1, bagal-bagal ke do 7 to 1, chaar ki ek row ya columnbetColumnLayout ke ek vertical column ke barah numbers, payout 2:1.Poora padhein → 3 to 1, aur do rows, ya odd, even, low ya high aath, 1 to 1. Teen-number bet ko 4⅓ to 1 chahiye; neeche 4 to 1 karne par uski keemat 16.67% hai.
Red aath odd numbers cover karta hai. Agar 0, red hone ke naate, red ki bet bhi jeetta, toh red 18 mein se 9 pockets 1 to 1 par cover karta: bina kisi edge ka fair gameganitFair gameAisa game jismein kisi bhi side ka edge nahi: har bet ki expected value zero hai.Poora padhein →. House pockets apna edge sirf isliye kamaate hain kyunki woh khud par lagi bet ke alawa har bet haarte hain.
Thodi hansi
House pockets giniye, phir rounding dhoondhiye.
Sources
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”