D'Alembert Roulette Strategy
D’Alembert roulette strategy haar ke baad ek unit jodti hai aur jeet ke baad ek ghatati hai.
Yeh wheel ko beat nahi karti. Yeh sabse flat common 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 → hai: stakes dheere upar khiskte hain, drawdowns medium hote hain, aur edge ko koi farak nahi padta.
System par chaliye
Haar par ek step upar. Jeet par ek step peeche.
Stakes aur results base bet ke units mein hain.
D’Alembert roulette system, step by step
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 → bet kijiye. Haare, toh agli bet ek unit badi. Jeete, toh ek unit chhoti, lekin ek se kam kabhi nahi. Bas itna hi. Ek jhoola socho: har haar stake ko ek notch upar karti hai aur har jeet wapas neeche. Iske peeche ki maanyata yeh hai ki jeet aur haar barabar ho jaayengi, toh stake wapas base par aa jaayega. Attraction yeh hai ki aas-paas ke stakes par ek jeet aur ek haar ka har joda +1 unit deta hai: 3 haaro, 4 jeeto, net +1.
Ek session kaisa dikhta hai?
Narm, aur stake dheere-dheere upar chadhta hai. Even money par haar jeet se 19 ke muqable 18 zyada hoti hain, isliye lambe session mein stake upar khiskta hai. Kyunki stake tab sabse zyada hota hai jab aap haar rahe hote hain, aur jeetne par kam, losing stretches ka average stake winning wale se zyada hota hai. Sessions MartingalestrategyMartingaleProgression jo har haar ke baad bet double karti hai. Yeh kya karti hai aur kya nahi, iske liye Strategy section dekhiye.Poora padhein → se smooth hote hain, medium drawdownspaisaDrawdownSession ke andar bankroll ke peak se baad ke low tak ki giraawat. Maximum drawdown aisi sabse badi giraawat hai.Poora padhein → ke saath aur bina khaai ke, aur average mein flat bettingstrategyFlat bettingHar spin par same raqam lagana. Har progression ko isi baseline se compare kiya jaata hai.Poora padhein → se thoda zyada haarte hain kyunki average stake zyada hai.
- p10 −$500
- p25 −$500
- median −$500
- p75 −$500
- p90 −$500
Kya D’Alembert system kaam karta hai?
Nahi. Balanced session jeetta hai, aur sessions balanced nahi rehte. Aas-paas ke stakes par w jeet aur l haar ke baad net result w − l units hai, plus ek correction ki aap ladder mein kahan the. Agar w = l ho toh result theek +w units hai, jo guaranteed profit jaisa lagta hai. Pakad yeh hai ki w = l expected case nahi hai: 37 spins mein aap 18 jeet aur 19 haar expect karte hain. Ek extra haar aise stake par jo chadhkar maan lo 8 units tak pahunch gaya ho, aath +1 jodon se zyada le jaati hai. Expectation total turnoverpaisaTurnoverSession ya muddat mein lagayi gayi kul raqam, dobara lagayi gayi jeet milakar. Doosre naam: handle, action.Poora padhein → ka −1/37 hi nikalta hai, jaisa nikalna chahiye.
Chhote sessions aksar kyun jeette hain?
Balanced case ek aise rule ka hissa hai jo har session par lagta hai. D ko haar minus jeet ki ginti maan lijiye. N spins ka session jo ek unit se shuru hota hai, (N − D²)/2 − D units par khatam hota hai, jab tak ek unit ki koi bet nahi jeetti (aisi jeet ke baad stake ke paas neeche jaane ki jagah nahi). D = 0 par yeh +N/2 hai, yaani upar wale section ka +w. Har extra haar square hokar gini jaati hai: 100 spins ke baad D 4 ho toh bhi +38 units bachte hain, D 8 par +10, aur D 10 par −10. Sirf chance D ko lagbhag √N tak phaila deta hai, 100 spins ke baad das, aur bina 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 → wale game mein bahut saare balanced sessions ke gain aur kuch tedhe sessions ke loss bilkul cancel ho jaate hain. Zero average mein har 37 spins par ek extra haar jodta hai, aur kyunki D square hota hai, iski keemat session se tez badhti hai. 100 spins tak ke zyadatar sessions aage khatam hote hain; average kabhi nahi, aur kuch sau spins ke baad zyadatar sessions bhi haarte hain.
Agar ise ulta kar dein toh?
Contra-D’Alembert, jise reverse D’Alembert bhi kehte hain, jeet ke baad ek unit jodta hai aur haar ke baad ek ghatata hai. Yeh original ka bilkul ulta aaina hai. Jab tak ek unit ki koi bet nahi haarti, N spins ka session (D² − N)/2 + D units par khatam hota hai, jahan D ab jeet minus haar hai. Balanced session har spin aadha unit haarta hai, aur sirf haar se kaafi aage nikli jeet ki run profit deti hai. Toh zyadatar sessions thoda haarte hain aur kuch bahut jeette hain, original ke shape ka ulta, aur average wahi lagaye gaye paise ka 2.70% hai.
d’Alembert kaun the?
Jean le Rond d’Alembert, mathematician aur Encyclopédie ke co-editor, ne 1754 ke ek article mein kaha ki heads ki run ke baad tails ki sambhavna badh jaati hai. Woh galat the, aur unke naam wala fallacy gambler’s fallacy ka ek roop hai. Roulette mein D’Alembert system ka naam baad mein unke naam par un gamblers ne rakha jo yahi maante the. Unhone ise design nahi kiya tha aur shayad woh iska samarthan bhi nahi karte.
Kya iske aur versions hain?
Upar wala Contra-D’Alembert ek narm ParolistrategyParoliPositive progression: jeet ke baad double, haar ke baad ya lagatar teen jeet ke baad reset. Doosra naam: reverse Martingale.Poora padhein → jaisa behave karta hai. Kuch players haar ke baad do units jodte hain aur jeet ke baad ek ghatate hain, jisse ladder Martingale ki taraf steep ho jaati hai. Sab versions mein har lagaye gaye unit par expected lossganitExpected lossExpected value guna kul lagayi gayi raqam; ek session ya ek muddat mein ausat nuksaan.Poora padhein → same hai.
Simulator · D'Alembert
$1,000 bankroll se even-money bets ke 2,000 sessions.
Base bet $10 · table limit $500 · har session 100 spins
Haar ki streak kitni baar aati hai
Single-zero wheel par even-money bet 37 mein se 19 spins haarti hai. Har row woh chance hai ki spins ka ek diya hua silsila poora haar jaaye, aur tab tak ek D’Alembert player, jo har haar ke baad ek base bet jodta hai, kitna haar chuka hota hai.
| lagatar haar | chance | lagbhag 1 in | ab tak ki haar | agli bet |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $3 |
| 3 | 13.5% | 7 | $6 | $4 |
| 4 | 7.0% | 14 | $10 | $5 |
| 5 | 3.6% | 28 | $15 | $6 |
| 6 | 1.8% | 55 | $21 | $7 |
| 7 | 0.94% | 106 | $28 | $8 |
| 8 | 0.48% | 207 | $36 | $9 |
| 9 | 0.25% | 403 | $45 | $10 |
| 10 | 0.13% | 784 | $55 | $11 |
| 11 | 0.065% | 1527 | $66 | $12 |
| 12 | 0.034% | 2974 | $78 | $13 |
| 13 | 0.017% | 5792 | $91 | $14 |
| 14 | 0.0089% | 11279 | $105 | $15 |
| 15 | 0.0046% | 21965 | $120 | $16 |
Chance 19/37 ko har haar par ek baar khud se guna karke aata hai, ek diye hue spin se gina hua. Lambe session mein aise kai spins hote hain jahan aisa silsila shuru ho sakta hai, isliye ek shaam mein yeh ek row ke andaaze se kahin zyada mumkin hai.
Sawaal
Ismein koi khaai nahi, isliye yeh sabse narm negative progression hai. Yeh flat betting se sasta nahi; thoda mehnga hai.
Sirf table limittableTable limitAllowed minimum aur maximum bet. Maximum hi doubling progressions ko rokta hai.Poora padhein → ya aapka 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 →. Lambe losing session mein yeh lagataar chadhta hai.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
Aap redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → par 50 spins tak D’Alembert khelte hain, 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 → se shuru karke, aur ek unit ki bet kabhi nahi jeette (aisi jeet ke baad stake ke neeche jaane ki jagah nahi hoti). Aap 27 haar aur 23 jeet ke saath khatam karte hain. Aap kitne units upar ya neeche hain? Aur 29 haar aur 21 jeet ke saath?
Solution dikhaiye
Jawab 27 haar ke saath +13 units, 29 ke saath −15 units. Pachaas mein se do spins ulte jaane ki keemat 28 units hai.
D ko haar minus jeet kahiye. N spins ka result (N − D²)/2 − D hai. 27 haar aur 23 jeet ke saath D = 4: (50 − 16)/2 − 4 = 17 − 4 = +13. 29 aur 21 ke saath D = 8: (50 − 64)/2 − 8 = −7 − 8 = −15.
Rule kyun chalta hai: stake hamesha ek unit plus ab tak ki haar minus ab tak ki jeet hota hai. Har haar jise baad ki jeet cancel karti hai ek pair banati hai, s haaro aur phir s + 1 jeeto, jo net +1 unit deta hai, jaisa upar ki table dikhati hai. N spins mein aise (N − D)/2 pairs bante hain, jinki keemat +(N − D)/2 hai. Bachi hui D haarein upar jaate hue stakes 1, 2 … D par lagi thi aur kabhi cancel nahi hui; unki keemat 1 + 2 + … + D = D(D + 1)/2 hai. Milakar: (N − D)/2 − D(D + 1)/2 = (N − D²)/2 − D.
Square hi poori kahani hai. Balanced session har spin aadha unit deta hai, aur balance se har kadam door pichhle se zyada mehnga padta hai.
Aap red par 100 spins tak reverse D’Alembert khelte hain, ek unit se shuru karke, aur ek unit ki koi bet kabhi nahi haarti. Aap 52 jeet aur 48 haar ke saath khatam karte hain. Aap kahan khade hain? Aur 60 jeet aur 40 haar ke saath?
Solution dikhaiye
Jawab 52 jeet ke saath −38 units, 60 ke saath +170. Jeet mein chhoti badhat phir bhi haarti hai; sirf badi badhat faayda deti hai.
D ko jeet minus haar kahiye. N spins ka result (D² − N)/2 + D hai.
52 jeet aur 48 haar: D = 4, isliye (16 − 100)/2 + 4 = −42 + 4 = −38.
60 jeet aur 40 haar: D = 20, isliye (400 − 100)/2 + 20 = 150 + 20 = +170.
Kyun: har jeet jise baad ki haar cancel karti hai ek pair banati hai, s par jeeto aur phir s + 1 par haaro, jo net −1 deta hai. Bachi hui D jeetein upar jaate hue stakes 1, 2 … D par lagi thi aur kabhi cancel nahi hoti; woh D(D + 1)/2 laati hain. N spins mein (N − D)/2 pairs bante hain, isliye total D(D + 1)/2 − (N − D)/2 = (D² − N)/2 + D hai.
Yeh original D’Alembert ka rule hai ulte signs ke saath: wahan balance har spin aadha unit jeetta hai aur imbalance ki saza milti hai; yahan balance har spin aadha unit ka padta hai aur imbalance ka inaam milta hai.
Thodi hansi
Ek aise mathematician ke naam par jinhone coin ko galat samjha.
Sources
- RouletteDoc. Strategy ka description aur examples.
- Roulette77. Strategy ka description aur examples.
- d’Alembert, J. “Croix ou pile.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed.