Blaise Pascal: Roulette Wheel ki Kahani
Woh mathematician jise aksar wheel ka credit diya jaata hai, jo asal mein kuch aur banane ki koshish kar rahe the.
Pascal (1623–1662) ne 1650 ke dashak mein perpetual-motion devices par experiments kiye. Unke naam se juda lagbhag bina friction ghoomne wala wheel roulette rotor ka mumkin poorvaj hai; yeh credit parampara se hai, documents se nahi.
Mathematician
Blaise Pascal ne unees saal ki umar mein mechanical calculator banaya, teenager rehte projective geometry mein results saabit kiye, pressure aur vacuum par buniyaadi kaam kiya, aur 1654 mein Pierre de Fermat ke saath letters mein “problem of points” hal kiya: beech mein ruke game of chance ke stakes ko fair tarike se kaise baantein. Unka jawab, ki game chalta rehta toh har player ki jeet ki probabilityganitProbabilityKisi outcome ka chance, 0 se 1 tak ya 0% se 100% tak. Ek number: 1/37 = 2.70%.Poora padhein → ke hisaab se baanto, expected valueganitExpected valueLambe samay mein har bet ka ausat nateeja. Har standard European bet ke liye stake ka −1/37.Poora padhein → ki shuruaat hai. Is site ka har EV calculation unhi letters se nikla hai.
Kya Blaise Pascal ki koi roulette machine thi?
1650 ke dashak ke beech Pascal ne perpetual-motion machine par kaam kiya, aur kaha jaata hai ki unhone ek bahut balanced wheel banaya jo kam friction ke saath der tak ghoomta tha. Yeh kahani ki yahi wheel roulette ka rotorsaamanRotorWheel ka ghoomne wala hissa jismein pockets hote hain.Poora padhein → bana, kai histories mein dohrai jaati hai aur kisi primary source mein documented nahi hai. Mumkin hai ki 18vi sadi mein spa towns ke operators ne yeh naam selling point ki tarah use kiya ho. Lab is saboot par ise maanega nahi.
Probability, unke shabdon mein aur hamare
1654 ke letters mein roulette ka zikr nahi hai, kyunki tab woh tha hi nahi. Sawaal yeh hai: do players ko pot jeetne ke liye teen points chahiye; woh 2–1 par ruk jaate hain; pot kaise baanta jaaye? Pascal ka jawab woh use karta hai jise aaj hum conditional expectation kehte hain, aur mumkin aage ke raaston ke tree par neeche jaata recursive argument. Huygens ne yeh letters padhe aur 1657 mein expectation par pehli textbook chhaapi. “Expectation” shabd unka hai.
Pascal aur Fermat problem of points hal karte hain: expected value ek position ki fair keemat ke roop mein.
Huygens, De Ratiociniis in Ludo Aleae: expectation par pehla chhapa hua kaam.
Jakob Bernoulli, Ars Conjectandi: law of large numbers.
Paris mein roulette ka vivaran. Har payout 36/n − 1 hai: EV = −1/37 (ya −2/38).
Pearson ka chi-square test, roulette spins par dikhaya gaya.
Upar ka sab kuch, is site par, browser mein.
Wager
Betting par Pascal ka sabse mashhoor argument roulette par nahi, Bhagwan par hai: Pensées ka “wager”, jo vishwas ko infinite payoff wale bet ki tarah dekhta hai. Yeh expected-value argument hai, aur pehli baar kisi ne kisi baat ke paksh mein decision theory use ki. Jo roulette players wheel ke liye Pascal ka naam lete hain woh galat Pascal ka naam le rahe hain; jo matter karta hai woh hai jisne dikhaya ki jua ki keemat kaise lagayein.
Vidambana
Pascal ne pehla roulette wheel banaya ho ya nahi, yeh game unke asli kaam ki badhiya misaal hai: us aadmi ka device jisne saabit kiya ki muft mein kuch nahi milta (perpetual motion fail hoti hai; expectation bani rehti hai), aur jo har saal kuch million players ko yahi baat dikhane ke kaam aata hai.
Sawaal
1650 ke shuru mein woh Paris ke gambling circles mein uthte-baithte the, isi tarah problem of points Chevalier de Méré ke zariye unke paas pahuncha. Unke paison ke liye seriously khelne ka koi record nahi hai.
Kyunki yeh achhi kahani hai aur 19vi sadi ke casino promoters ko pasand thi. Dohrayein toh footnote ke saath.
Thodi hansi
Unhone saabit kiya ki muft mein kuch nahi milta. Phir kisi ne usi par casino bana diya.
Sources
- Pascal, B. & Fermat, P. Correspondence on the problem of points.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.