Walkthrough: D’Alembert ki Ek Dopahar
Haar ke baad ek unit upar, jeet ke baad ek unit neeche, sau spin tak har spin par red. Sabse naram system, aur naram hone ki keemat.
$5 per unit par 100 spin ka ek simulated D’Alembert session. Stake paanch baar wapas $5 par aaya, bure daur mein badhkar $80 tak gaya, aur $55 par khatam hua jab session $40 neeche tha. Woh system jo santulan jaisa lagta hai, par hai nahi.
System par chaliye
Haar par ek step upar. Jeet par ek step peeche.
Stakes aur results base bet ke units mein hain.
Plan
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 →, $5, redbetRed18 red numbers par even-money bet. French mein: rouge.Poora padhein → par shuru kijiye. Haar ke baad ek unit jodiye; jeet ke baad ek hataiye, kabhi ek se neeche nahi. Theory, jo d’Alembert ne nahi di thi par ilzaam unhi par aata hai, yeh hai ki jeet aur haar barabar ho jaati hain, isliye har ek haar aur ek jeet ki jodi par hum ek unit upar rehte hain. Hisaab kehta hai ki red 48.65% spin jeetta hai, isliye haar jeet se lagbhag chaalees mein ek zyada hoti hai, aur stake waqt ke saath upar khisakta jaata hai.
Spin 1–30
Chaudah red, pandrah blackbetBlack18 black numbers par even-money bet. French mein: noir.Poora padhein →, 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 →. Teen haar ke silsile mein stake $20 tak gaya, spin 18 tak wapas $5 par aaya, aur is daur ke ant tak $25 tak pahunch gaya. Net +$20. Har haar-jeet jodi ne waade ke mutabik ek unit diya; extra haar unhe kha gayi. Yeh ek dheemi pump jaisa lagta hai jo zyadatar kaam karta hai.
Spin 31–65
Bura daur. Baaees non-red ke muqable terah red, jismein saat haar ka ek silsila bhi tha. Spin 41 par $5 se stake ek-ek unit karke $80 tak chadha, aur har $75 ki haar ne pehle ki pandrah $5 wali jeet mita di. Is daur ka net −$485; ab tak kul −$465. Kisi ek spin par kuch dramatic nahi hua; yeh sab dheere khisakne ne kiya.
- p10 −$500
- p25 −$500
- median −$500
- p75 −$500
- p90 +$885
Spin 66–100
Pandrah non-red ke muqable bees red, stake $5 ke steps mein $80 se $55 ki taraf utarta hua. Bade stake par har jeet ne asli paisa wapas laaya: $70 ki haar ke baad $75 ki jeet jodi ko +$5 deti hai, lekin jodi badi hai. Is daur ka net +$425; final −$40.
Hisaab-kitaab
Average stake lagbhag $37, toh kul lagaya gaya paisa lagbhag $3,670, jabki flat $5 lagane wale ka $500. $3,670 par expected lossganitExpected lossExpected value guna kul lagayi gayi raqam; ek session ya ek muddat mein ausat nuksaan.Poora padhein → $99 hai; asal mein −$40, ek standard deviationganitStandard deviationVariance ka square root; expected value se kisi result ki aam doori.Poora padhein → se kam. Stake ke size ka khisakna hi system ka poora asar hai: table par zyada paisa, har dollar se wahi 2.70% kat, nateejon ka zyada chauda phailav.
Session kya dikhata hai
D’Alembert staking rule ke roop mein likha gaya gambler’s fallacy hai: yeh maan leta hai ki jeet aur haar itni jaldi barabar ho jaayengi ki stake wapas neeche aa jaaye. Lambe samay mein woh dilution se barabar hoti hain, correction se nahi, aur stake ke paas ek unit par lautne ki koi wajah nahi hai. Yeh bina cliff ka dheema system hai, aur yahi dheemapan wajah hai ki players us par bharosa karte hain.
Sawaal
Kabhi-kabhaar. Stake har haar par ek unit badhta hai, double nahi hota, isliye limit tak pahunchne mein bahut lamba bura silsila chahiye.
Haan, aur bure silsile ke baad cap ise cap par flat bettingstrategyFlat bettingHar spin par same raqam lagana. Har progression ko isi baseline se compare kiya jaata hai.Poora padhein → bana deta hai. Koi bhi cap theek hai; koi bhi edge nahi badalta.
Unhone 1754 mein tark diya ki heads ke silsile ke baad tails ki sambhavna badh jaati hai. Jo gamblers sehmat the, unhone system ka naam unke naam par rakh diya. Unhe sharmindagi hoti.
Thodi hansi
Sabse naram system. Yeh cliff se girta nahi, dheere khisakta hai.
Sources
- d’Alembert, J. “Croix ou pile.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.