Walkthrough: Ek Martingale Session
Red par das dollar, har haar ke baad double, $500 ki table par. Spin dar spin, us spin samet jo sab khatam kar deta hai.
$1,000 ke bankroll se ek simulated Martingale session. Iktalees chhoti jeet, phir lagatar chhe haar aur saatvaan bet refuse. +$410 tak upar hone ke baad session $220 neeche khatam hota hai, aur system yahi karta hai.
Plan
RedbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → par $10 lagaiye. Haar ke baad double kijiye. Jeet ke baad wapas $10. Table limittableTable limitAllowed minimum aur maximum bet. Maximum hi doubling progressions ko rokta hai.Poora padhein → $500 hai, isliye stakes hain 10, 20, 40, 80, 160, 320 aur phir $640 ka bet jo table refuse kar degi. Lagatar chhe haar system tod deti hain; har attempt mein aisa hone ka chance (19/37)⁶ ≈ 1.8% hai, aur 100 spin ke session mein lagbhag 50 attempts hote hain. Expected: 100 spin ke andar tootne ka lagbhag 60% chance, aur tootne par $630 ka nuksaan.
Spin 1–30
Aam MartingalestrategyMartingaleProgression jo har haar ke baad bet double karti hai. Yeh kya karti hai aur kya nahi, iske liye Strategy section dekhiye.Poora padhein →: ek se teen haar ki strings, har ek ek jeet par khatam jo net +$10 deti hai. Spin 30 tak humare 17 jeet ho chuke hain, har ek ek cycle band karti hai, aur hum $170 upar hain. Ab tak ka sabse bada stake teen haar ke baad $80 tha. Lagta hai jaise $10 ke note chhapne ki machine ho.
Spin 31–60
Wahi sab, ek chaar-haar wale cycle ke saath (stakes $160 tak, phir jeet), jisne thodi der ke liye table par $310 rakh diye aur himmat jaisa laga. 60 spin ke baad: 41 cycles poore, $410 upar, aur 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 → ka sabse neecha point $1,040 tha. Har Martingale session ka histogram apni zyadatar lambai tak aisa hi dikhta hai.
Spin 61–66
L L L L L L. Stakes 10, 20, 40, 80, 160, 320: $630 gaye. Agla bet $640 hota; limit $500 hai. System toot gaya. Hum $500 laga sakte hain (aur jeetne par bhi cycle par $130 neeche rahenge) ya wapas $10 par reset karke nuksaan maan sakte hain. Lagatar chhe blackbetBlack18 black numbers par even-money bet. French mein: noir.Poora padhein → ya 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 → ki probabilityganitProbabilityKisi outcome ka chance, 0 se 1 tak ya 0% se 100% tak. Ek number: 1/37 = 2.70%.Poora padhein → har cycle par 1.8% hai. Humne lagbhag 45 cycles chalaye the. 45 cycles mein kahin na kahin is point tak pahunchne ka chance lagbhag 55% tha. Yeh bad luck nahi tha; yeh median tha.
- p10 −$1,000
- p25 −$1,000
- median −$1,000
- p75 +$790
- p90 +$1,690
Hisaab
60 spin ke baad $410 upar, 66 ke baad $220 neeche. Kul lagaya: 66 spin mein lagbhag $2,100, jabki flat $10 bettor ka $660. $2,100 ke turnoverpaisaTurnoverSession ya muddat mein lagayi gayi kul raqam, dobara lagayi gayi jeet milakar. Doosre naam: handle, action.Poora padhein → par expected lossganitExpected lossExpected value guna kul lagayi gayi raqam; ek session ya ek muddat mein ausat nuksaan.Poora padhein → $57 hai; humara asal −$220 usse lagbhag ek-tihaai standard deviationganitStandard deviationVariance ka square root; expected value se kisi result ki aam doori.Poora padhein → neeche hai, jo aise system ke liye aam baat hai jiske distribution ki left tail lambi hai. Agar hum $400 ke stop-winstrategyStop-winMunafe ka pehle se tay target, jis par aap session khatam kar dete hain.Poora padhein → ke saath spin 60 par ruk jaate, toh $410 upar nikalte, aur agla session phir wahi 1.8% per cycle lekar aata.
Session kya dikhata hai
Martingale 48.65% wale bet ko ek aise sequence mein badal deta hai jo apne 98% cycles jeetta hai aur baaki 2% par 63 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 → haarta hai. Yeh per dollar expected loss nahi badalta; yeh dollars ko guna kar deta hai. Humare bagal wale flat bettor ne ek-tihaai lagaya aur average mein ek-tihaai haara. Jo player yeh system saal bhar chalayega, woh zyadatar shaamein jeetega aur saal haar jaayega.
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 Martingale player, jo har haar ke baad double karta 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 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
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
Chhe ki jagah nau haar ise todti: 0.25% per cycle, aur aisa hone par $5,110 jaate. Kam aane wali khaai, gehri khaai, wahi −2.70%.
Woh 48.65% baar jeetta aur phir bhi cycle ko −$130 par chhodta. Toote hue Martingale ke baad koi achhi chaal nahi hoti; bas woh stake hota hai jo aap aage chunte hain.
Haan, us session ke liye. Saare sessions ke mean ke liye nahi.
Maths ke saath mazaa
Pehle khud try kijiye. Har solution chhupa hua hai; jab taiyaar hon tab kholiye.
$1 se $500 wali table par ek MartingalestrategyMartingaleProgression jo har haar ke baad bet double karti hai. Yeh kya karti hai aur kya nahi, iske liye Strategy section dekhiye.Poora padhein → player single-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 → wheel par redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → par $1 se shuru karta hai. Lagatar kitni haar doubling ko rok deti hain, tab tak kitna haara ja chuka hota hai, aur aisa kitni baar hota hai?
Solution dikhaiye
Jawab Naun haar: $511 gaye, aur agli bet $512 ki hoti. Aisa lagbhag 403 sequences mein ek baar hota hai.
Stakes hain 1, 2, 4, 8, 16, 32, 64, 128 aur 256: kul $511. Dasvi $512 hoti, limit se upar. $500 ki bet jeet bhi jaaye toh player $11 neeche rehta hai; haar jaaye toh $1,011 neeche.
Red 19/37 chance se haarta hai, isliye lagatar naun haar ka chance (19/37)⁹ ≈ 0.25% hai, lagbhag 403 sequences mein ek baar. Har poora sequence $1 jeetta hai, isliye player us ek $511 ki haar se pehle lagbhag $402 ki chhoti jeet ki ummeed karta hai, aur lagayi gayi har raqam ka 2.70% average mein phir bhi haara jaata hai.
Double-zero wheel par chance (20/38)⁹ hai, lagbhag 323 mein ek baar. Bollman (2021) “lagbhag 833 mein 1” chhaapte hain, jo (18/38)⁹ hai, yaani lagatar naun jeet ka chance.
Thodi hansi
Iktalees chhoti jeet aur ek badi haar. Poora system bas yahi hai.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”