Roulette Systems ka Itihaas
Do sadiyon se log apna stake badalne ke rules likhte aa rahe hain.

Martingale 18vi sadi ka hai; D’Alembert ka naam ek aise mathematician par hai jise yeh pasand nahi tha; Labouchère ek Victorian politician ka shauk tha. Tab bhi inmein se koi kaam nahi karta tha.
Martingale
Yeh naam Provençal jue ki slang se aaya hai (à la martegalo, “Martigues ke logon ki tarah”, jo laaparwahi ke liye mashhoor the), jo doubling bet ke liye bola jaata tha aur 1760 ke dashak se French dictionaries mein milta hai. Thorp (1984), American Heritage Dictionary ke hisaab se, ek doosri lok-vyakhya deta hai: Martigues ke logon ka ajeeb aadaton ke liye mazaak udaya jaata tha, jaise patloon ko peeche se baandhna, isliye is phrase ka matlab ho gaya “bewakoofi bhare tareeke se”. 18vi sadi ke Paris mein yeh pehle se ek chetavni wali kahani thi: Casanova batata hai ki 1750 ke dashak mein Venice mein faro par double karte hue usne ek fortune ganwa diya. Yeh fail kyun hota hai, iska math, yaani table limittableTable limitAllowed minimum aur maximum bet. Maximum hi doubling progressions ko rokta hai.Poora padhein → aur seemit bankrollpaisaBankrollKhelne ke liye alag rakhi gayi kul raqam. Bankroll management ka matlab hai tay karna ki har bet aur har session mein iska kitna hissa risk karna hai.Poora padhein →, 1770 ke dashak tak samajh liya gaya tha. ProbabilityganitProbabilityKisi outcome ka chance, 0 se 1 tak ya 0% se 100% tak. Ek number: 1/37 = 2.70%.Poora padhein → theory mein “martingalestrategyMartingaleProgression jo har haar ke baad bet double karti hai. Yeh kya karti hai aur kya nahi, iske liye Strategy section dekhiye.Poora padhein →” 1930 ke dashak mein ek fair gameganitFair gameAisa game jismein kisi bhi side ka edge nahi: har bet ki expected value zero hai.Poora padhein → ka technical term ban gaya, aur roulette ka Martingale theek yahi cheez nahi hai.

D’Alembert
Jean le Rond d’Alembert ne Encyclopédie (1754) mein tark diya ki heads ki ek streak ke baad tails ki probability badh jaati hai, yaani ek bade mathematician ki taraf se gambler’s fallacy ka shuruaati roop. Haar ke baad 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 → jodne aur jeet ke baad ek ghatane wala betting system unke naam par baad ke juaariyon ne rakha jo yahi maante the. Unhone ise propose nahi kiya tha, aur apne achhe dinon mein woh ise reject hi karte.
Labouchère
Henry LabouchèrestrategyLabouchèreCancellation system: numbers ki ek line likhiye, dono siron ka jod bet kijiye, jeet ke baad unhe kaat dijiye, haar ke baad haara hua stake jod dijiye.Poora padhein → (1831–1912), journalist, theatre owner aur Liberal MP, ne 1870 ke dashak mein London society mein cancellation system ko popular kiya aur kehte hain ki Monte Carlo mein iska istemal bhi kiya. Yeh tareeka, numbers ki ek line likhna aur dono sire ka jod bet karna, unse purana hai. Naam unka isliye chipak gaya kyunki woh doosri cheezon ke liye mashhoor the, aur kyunki yeh system aksar kaam karta dikhta hai, jisse dinner par yeh baatcheet ka mudda ban gaya.
Casanova faro par double karke haarta hai. Martingale tab bhi purana hai.
D’Alembert woh fallacy publish karte hain jo baad mein unke naam ka system banti hai.
“Martingale” jue ki slang ke roop mein French dictionaries mein aata hai.
Labouchère London mein cancellation ko popular karte hain.
Fibonacci aur Paroli progressions jue ki manuals mein dikhne lagte hain.
Wheel layout par based “sector” systems mail order se bikte hain.
Doob ke student Halmos sabit karte hain ki koi bhi betting system ek nuksaan wale game ko faayde wala nahi bana sakta.
Computers har system ko simulate karte hain. Sab mein turnover ka −1/37 aata hai.
Wahi systems online bikte hain, wahi results ke saath, aur is site par browser mein simulate kiye jaate hain.
20vi sadi
FibonaccistrategyFibonacciProgression jo sequence 1, 1, 2, 3, 5, 8, 13… follow karti hai: haar ke baad ek kadam aage, jeet ke baad do kadam peeche.Poora padhein → aur ParolistrategyParoliPositive progression: jeet ke baad double, haar ke baad ya lagatar teen jeet ke baad reset. Doosra naam: reverse Martingale.Poora padhein → lagbhag 1900 ke aas-paas jue ki manuals mein aaye. Sadi ke beech mein mail-order systems aaye, har ek ke saath testimonial aur money-back guarantee, aur pehle computer simulations bhi, jinhone wahi dikhaya jo math pehle se keh raha tha. Koi system kaam nahi kar sakta, iska proof pehle se maujood tha: Joseph Doob (1936) aur Paul Halmos (1939) ne dikhaya ki kab aur kitna bet lagana hai, iska koi bhi rule ek fair ya nuksaan wale game ka expected result nahi badalta, aur Thorp ke 1969 ke survey ne yeh shartein usi roop mein rakhi jaise juaari unse milte hain. Tab se systems nahi badle; marketing pamphlets se video par chali gayi hai.

Myth: Hamesha Jeetne Wali Roulette StrategyFibonacci Roulette Strategy
Yeh tike kyun rehte hain
System khiladi ko karne ke liye kuch aur sunane ke liye ek kahani deta hai. Zyadatar systems mein zyadatar sessions ek chhoti jeet par khatam hote hain, jo hisaab-kitaab se behtar kahani hai. Haarne wale sessions kam hote hain aur badkismati ke roop mein yaad rakhe jaate hain. Marketing ko odds ke baare mein jhooth bolne ki zaroorat nahi; use bas ek jeetne wala session dikhana hota hai, aur aise bahut hain. Iska jawab, turnoverpaisaTurnoverSession ya muddat mein lagayi gayi kul raqam, dobara lagayi gayi jeet milakar. Doosre naam: handle, action.Poora padhein → ka 2.70%, 1796 se maujood hai aur kabhi bhi ek lucky raat jitna asardaar nahi raha.
Bikne wale systems
20vi sadi ke dhande ne apni schemes bhi jodi, har ek wahi negative bets ki nayi vyavastha. Phase One $25 plus kharidar ki jeet ka 10% mein becha gaya, $500 dene ke baad Phase Two ka vaada tha aur $5,000 mein ek “Inner Circle”. Inmein se koi bhi hisaab nahi badalta: bets ki ek series ki expected valueganitExpected valueLambe samay mein har bet ka ausat nateeja. Har standard European bet ke liye stake ka −1/37.Poora padhein → unki expected values ka jod hoti hai.
Woh jo system nahi hai
Stop rules: pehle se tay karna ki kitna haarna ya jeetna hai aur phir uth jaana. Inhe aksar kisi system ke hisse ke roop mein becha jaata hai aur yahi akela hissa hai jo kuch karta hai, kyunki yeh turnover kam karte hain. Inka koi naam nahi hai, jo theek hi hai.
Sawaal
Martingale, ek sadi ya usse bhi zyada se. Haar ke baad double karna har kisi ka pehla idea hota hai.
D’Alembert sabse kareeb aaye, anjaane mein. Pascal, Fermat, Huygens, Bernoulli aur Laplace sabne samjhaya ki yeh fail kyun hote hain.
Kyunki zyadatar sessions jeet jaate hain, aur jeetne wale session ka video banana sasta hai.
Thodi hansi

Do sadiyon ke naam. Ek number.
Sources
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- d’Alembert, J. “Croix ou pile.”
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.