It should not have been since in reality there is no paradox. In addition to contributing to science, Daniel Bernoulli economics and statistics are also held in high regard.In 1738, he published a book titled Exposition of a New Theory on the Measurement of Risk. In the history of statistics, economy and decision theory, the St. Petersburg paradox plays a key role. Inilah yang dikenal sebagai Paradoks St. Petersburg, dinamai berdasarkan publikasi Daniel Bernoulli Commentaries of the Imperial Academy of Science of Saint Petersburg pada tahun 1738 . Before Daniel Bernoulli published, in 1728, a mathematician from Geneva, Gabriel Cramer, had already found parts of this idea (also motivated by the St. Petersburg Paradox) in stating that the mathematicians estimate money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it. Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox to show that expected value theory must be normatively wrong. 1000 is a fair game. This article demonstrates if two fundamental precepts of Austrian economics are applied this becomes clear. Before Daniel Bernoulli published, in 1728, a mathematician from Geneva, Gabriel Cramer, had already found parts of this idea (also motivated by the St. Petersburg Paradox) in stating that . We all caught up to explain. prompting two Swiss mathematicians to develop expected utility theory as a solution. … The game consists of tossing a coin. Daniel Bernoulli evinced great interest in the problem known as St. Petersburg paradox and tried to resolve this. St. Petersburg Paradox, and applies the expected utility theory to solve it, as Daniel Bernoulli did. Bernoulli's principal work in mathematics was his treatise on fluid mechanics, Hydrodynamica. 1713: Bernoulli stated the problem in a letter to Réymond de Montmort. Bernoulli proposes a coin ip game where one ips until the coin lands tails. A friend of mine recently told me about the St. Petersburg Paradox, a puzzle presented by Daniel Bernoulli to the Imperial Academy of Sciences in St. Petersburg, Russia, in 1738. Daniel Bernoulli and the St. Petersburg Paradox . The St. Petersburg paradox is a simple game of chance played with a fair coin where a player must buy in at a certain price in order to place $2 in a pot that doubles each time the coin lands heads, and pays out the pot at the first tail. Paul would simply respond, 'How many times am I. Loading... Home Other. He considered lotteries of the following type: A fair coin is tossed. Let's begin by calculating probabilities associated with this game. Bernoulli was living in St. Petersburg, Russia, at the time when he developed this, and that’s why it’s called the St. Petersburg Paradox. The Saint Petersburg paradox, is a theoretical game used in economics, to represent a classical example were, by taking into account only the expected value as the only decision criterion, the decision maker will be misguided into an irrational decision. Since the individual behaves on the basis of expected utility from the extra money if he wins a game and the marginal utility of money to him declines as he has extra money, most individuals will not ‘play the game’, that is, will not make a bet. It is in this way that Bernoulli resolved ‘St. Petersburg paradox’. 2 k;k = 1;2;::: x : 2 4 8 16 32 ::: p(x) : 1 2 1 4 1 8 1 16 1 32::: Pay c. Receive X. 다니엘 베르누이 (Daniel Bernoulli)는 상트 페테르부르크 역설 (St. Petersburg paradox)으로 알려진 문제에 큰 관심을 갖고이를 해결하려고 노력했습니다. für das eine Teilnahmegebühr verlangt wird, wird eine faire Münze so lange geworfen, bis zum ersten Mal „Kopf“ fällt. article Daniel Bernoulli also proposed a solution to the paradox and, although the paradox was rst announced to the world by Montmort (1713), the problem has come to be known as the St. Petersburg paradox. In: Nieuw Archief voor Wiskunde, 1998, p. 223 - 227. Some Probabilities . The St. Petersburg Paradox—first described by Daniel Bernoulli in 1738—describes a game of chance with infinite expected value. SAJEMS NS Vol 6 (2003) No 2 332 necessary to repeat it here in any detail. Imagine that you’re asked to pay some amount of money to participate in a bet. The payouts double for each toss that lands heads, and an in nite expected value is obtained. Although a theoretically rational person should pay dearly to play such a game, few people will pay more than a trivial sum. 상트 페테르부르크 역설은 대부분의 사람들이 공정한 게임이나 내기에 참여하지 않는 문제를 말합니다. He agrees to give Paul one ducat if he gets "heads" on the very first throw, two ducats if he gets it on the second, four if on the third, By Robert William Vivian. 设定掷出正面或者反面为成功，游戏者如果第一次投掷成功，得奖金2元，游戏结束；第一次若不成功，继续投掷，第二次成功得奖金4元，游戏结束；这样，游戏者如果投掷不成功就反复继续投掷，直到… Le paradoxe de Saint-Pétersbourg fait référence au problème qui explique pourquoi la plupart des gens ne souhaitent pas participer à un jeu ou à un pari équitable. Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was . Bernoulli's Hypothesis: Hypothesis proposed by mathematician Daniel Bernoulli that expands on the nature of investment risk and the return earned on an investment. We end discussing the implications of the boundedness hypothesis and how we obtain new paradoxes. Probabilitas koin yang adil mendarat adalah 1/2. 1738: Daniel Bernoulli presented the problem to the Imperial Academy of Sciences in St. Petersburg, Russia. Show that the expected monetary value of this game is infinite. Daniel Bernoulli's [ 1 ] response to the paradox is presented in §4, followed by a reminder of the more recent concept of ergodicity in §5, which leads to an alternative resolution in §6 with the key theorem 6.2. Daniel Bernoulli, a swiss mathematician, found that Russians were unwilling to make bets even at better than 50-50 odds knowing fully that their mathematical expectations of winning money in a particular kind of gamble were greater the more money they bet. This lottery problem goes back a full three centuries to the mathematician Nicolas Bernoulli who first formulated the problem in 1713. This oddity was a thought experiment that was developed in 1738 by this Swiss mathematician named Daniel Bernoulli. Ce paradoxe de Saint-Pétersbourg avait été soulevé par Pierre Raymond de Montmort auprès de Nicolas Bernoulli en 1713. contradiction, which nowadays is called the St. Petersburg Paradox (SPP). How much would you be willing to pay to play this game? The purpose of this article is to demonstrate that contrary to the accepted view, the St Petersburg game does not lead to a paradox at all. Doomsday argument-Wikipedia. Ciononostante, ragionevolmente, si considera adeguata solo una minima somma, da pagare per partecipare al gioco. In economics, Bernoulli is best known for his 1738 article resolving the St. Petersburg paradox, a probability problem set by his cousin Nicholas Bernoulli in 1713, involving the solution to a game of chance with an infinite expected return. It is clear that the series beyond the Tk term is once again the same - "Solving Daniel Bernoulli's St Petersburg paradox : the paradox which is not and never was" Twenty five years later, in 1738, his nephew Daniel Bernoulli presented the problem to the Imperial Academy of Sciences in St. Petersburg. which the agent is fullycompensated for her decreasing marginal utility of money T1 - Daniel Bernoulli and the St. Petersburg paradox. This is a very interesting thing because Savage wrote the book from the viewpoint of Bayesian. SAJEMS NS Vol 6 (2003) No 2 332 necessary to repeat it here in any detail. Although the problem is phrased di erently today, this was the birth of the St. Petersburg paradox. If a head occurs for the rst time on the nth toss then you will be paid 2ndollars. Someone offers you the following opportunity: he will toss a fair coin. Daniel (I) Bernoulli [1] propounded what later came to be known as the St. Petersburg paradox in 1738: Peter tosses a coin and continues to do so until it should land "heads" when it comes to the ground. M3 - Article. Cañas, Luis: El falso dilema del prisionero. Y1 - 1998. The St. Petersburg paradox is a situation where a naive decision criterion which takes only the expected value into account predicts a course of action that presumably no actual person would be … The St. Petersburg Paradox is the name now given to the problem rst proposed by Daniel Bernoulli in 1738. Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which Is Not and Never Wasl RobertW Vivian School o/Economic and Business Sciences, University a/the Witwatersrand ABSTRACT It has been accepted for over 270 years that the expectedmonetary value (EMV) of the St Petersburg giune is infinite. According to Daniel Bernoulli’s solution to the St. Petersburg paradox, the utility of the coin landing heads on the \((n+1)\)-th flip isn’t twice that of landing on the \(n\)-th flip, because… when the payouts get very large, it becomes less and less likely you’ll actually be paid the amount promised. 1.. IntroductionDaniel Bernoulli (1700–1782) is widely known as the perspicacious solver of a very popular paradox, named after the journal where it was published, the Commentarii Academiae Scientiarum Imperialis Petropolitanae.However, in Gerard Jorland’s words, ‘the paradox in the St. Petersburg problem is that there is a paradox’ (Jorland, 1987, p. 157). Beberapa Kemungkinan . Nella teoria della probabilità e nella teoria delle decisioni, il paradosso di San Pietroburgo descrive un particolare gioco d'azzardo basato su una variabile casuale con valore atteso infinito, cioè con una vincita media di valore infinito. Originally published in Papers of the Imperial Academy of Sciences in Petersburg by Daniel Bernoulli, the St. Petersburg paradox is a thought experiment that pushes traditional behavioral economics to the test. a. TY - JOUR. Daniel Bernoulli yayınlanan önce, 1728 yılında, bir matematikçi Cenevre , Gabriel Cramer , zaten belirten içinde (aynı zamanda Petersburg Paradox motive) Bu fikrin bölümlerini bulmuştu matematikçiler parayı miktarıyla orantılı olarak, sağduyulu insanlar ise yapabilecekleri kullanımla orantılı olarak tahmin ederler. This contradiction is known as St. Petersburg Paradox. A fair coin will be tossed until a head appears. In other words, the random number of coin tosses, n, A Little History The SPP was so named afterthe eponymous Russian city, where Daniel Bernoulli, a mathematicianand Nicholas Bernoulli’s cousin, published his classical solution to the problem in … For example, offer of participating in a gamble in which a person has even chance (that is, 50-50 odds) of winning or losing Rs. Das Erwartungswert-Kriterium bei Entscheidungen unter Unsicherheit Unsicherheit über die Folgen zu treffender Entscheidun­ gen ist ein prägendes Merkmal des täglichen Lebens. For a similar example of counterintuitive infinite expectations, see the St. Petersburg paradox. Section 3 describes the St Petersburg paradox, the first well-documented example of a situation where the use of ensembles leads to absurd conclusions. The problem was originally presented by Daniel Bernoulli in 1738 in the Commentaries of the Imperial Academy of Science of Saint Petersburg (hence the name). If the first heads appears on the nth toss, you win 2, dollars. Historique. Examples Of St. Petersburg Paradox 1934 Words | 8 Pages. Expected utility hypothesis-Wikipedia. The St Petersburg Paradox has thus been enormously influential. An account of the origin and the solution concepts proposed for the St. Petersburg Paradox is provided. PY - 1998. Note EX = 1. Die Auswahl unter mehreren Investitionsalteniativen, die Ent­ scheidung für oder gegen die Teilnahme an einer Lotterie bzw. DANIEL BERNOULLI - 227 If somebody in Groningen has to choose a famous local mathematician from the past as subject of a talk, the choice is not hard. Also, we show the insu ciency of the historical solution, via the construction of a Menger’s Super-Petersburg Paradox, when not using bounded utility functions. Le paradoxe de Saint-Pétersbourg est généralement formulé en termes de paris sur le résultat de tirages au sort équitables. Paradox in the theory of probability published by Daniel Bernoulli in 1730 in the Commentarii of the St Petersburg academy. There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount. the mathematicians estimate money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it. The explanation offered by Bernoulli and Cramer to account for the St. Petersburg paradox formed the theoretical basis of the insurance business. U(xi) = ln(xi). Daniel Bernoulli and the St. Petersburg paradox. Named from its resolution by Daniel Bernoulli, one-time resident of the eponymous Russian city, who published his arguments in the Commentaries of the Imperial Academy of Science of Saint Petersburg (Bernoulli 1738). you pay a fixed fee to enter, and then a fair coin will be tossed repeatedly until a "tail" first appears, ending the game. 2.2.6 The Bernoulli Hypothesis Daniel Bernoulli, the 18th century Swiss mathematician evinced great interest in the problem known as St. Petersburg paradox and tried to resolve this. Introduction Leonard Jimmie Savage published The Foundations of Statistics in 1954. Un article de Wikipédia, l'encyclopédie libre . This is what is known as the St. Petersburg Paradox, named due to the 1738 publication of Daniel Bernoulli Commentaries of the Imperial Academy of Science of Saint Petersburg. Bernoulli, Daniel: 1738, Exposition of a New Theory on the Measurement of Risk, Econometrica vol 22 (1954), pp23-36. The St Petersburg paradox has been of academic interest for more than 300 years. The St. Petersburg paradox or St. Petersburg lottery is a paradox related to probability and decision theory in economics. Daniel Bernoulli and the St. Petersburg Paradox . Nicholas Bernoulli described the game to his brother Daniel, who was at the time working in St. Petersburg. AU - Dehling, H.G. Das St. Petersburg-Paradoxon Jürgen Jerger, Frerburg 1. Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was . Today we will discuss a famous problem known as the St. Petersburg Paradox. Some Probabilities . Daniel Bernoulli resolved this paradox by saying, and I quote: The determination of the value of an item must not be based on the price, but rather on the utility it yields…. The St. Petersburg Paradox The St. Petersburg game is played by flipping a fair coin until it comes up tails, and the total number of flips, n, determines the prize, which equals $2 n.Thus if the coin comes up tails the first time, the prize is $2 1 = $2, and the game ends. « Que sais-je? It has been accepted for over 270 years that the expected monetary value (EMV)of the St Petersburg game is infinite. Let's begin by calculating probabilities associated with this game. The St Petersburg Game The background to the St Petersburg game5 is now6 well-known and it is not . This is the St. Petersburg Paradox. The St. Petersburg Paradox and the Quantification of Irrational Exuberance a – p. 2/25. The probability that a fair coin lands heads up is 1/2. There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount. In the book, he offered a solution to the St. Petersburg paradox using the economic theory of risk premium, risk aversion, and utility. The introduction of St. Petersburg Paradox by Daniel Bernoulli in 1738 is considered the beginnings of the hypothesis. Savage on St. Petersburg Paradox（Kawayama・Yamazaki） 1. The St Petersburg Game The background to the St Petersburg game5 is now6 well-known and it is not . First published Wed Nov 4, 1998; substantive revision Mon Jun 17, 2013. Noun . Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was June 2003 South African Journal of Economic and Management Sciences (SAJEMS) 6(5233) For example, offer of participating in a gamble in which a person has even chance (that is, 50-50 odds) of winning or losing Rs. And like many good paradoxes it involves a game of chance. This article reviews some of the history of attempts to re-solve the St. Petersburg paradox and we recount some related Tom Cover On the Super Saint Petersburg Paradox Una visión más amplia de las decisiones racionales, Alianza Editorial, Madrid, 2008; Enlaces externos. Daniel is a son of Johann (Jean) I, who was a younger brother of Jakob (Jacques), the author of Ars Conjectandi.Despite Johann's objections Daniel became a mathematician himself, and Daniel spent several years in St. Petersburg, as a professor of mathematics. Ce paradoxe a été énoncé en 1713 par Nicolas Bernoulli [1].La première publication est due à Daniel Bernoulli, « Specimen theoriae novae de mensura sortis », dans les Commentarii de l'Académie impériale des sciences de Saint-Pétersbourg [2] (d'où son nom). 1000 is a fair game. The Bernoulli family is famous for a number of distinguished mathematicians. A resolution of the St Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. EP - 227. This notebook contains an exploration of the Saint Petersberg paradox, first proposed by Daniel Bernoulli around 1738. Daniel Bernoulli toonde grote belangstelling voor het probleem dat bekend staat als de St. Petersburg-paradox en probeerde dit op te lossen. Después de esto Nicolaus estuvo aún un tiempo intentando encontrar la solución al problema que él mismo se había planteado, pero finalmente en el año 1715 optó por consultar a su primo Daniel, al que reconocía una capacidad matemática superior a la suya. Daniel Bernoulli evinced great interest in the problem known as St. Petersburg paradox and tried to resolve this. The term expected utility was first introduced by Daniel Bernoulli who used it to solve the St. Petersburg paradox, as the expected value was not sufficient for its resolution.He introduce the term in his paper “Commentarii Academiae Scientiarum Imperialis Petropolitanae” (translated as “Exposition of a new theory on the measurement of risk”), 1738, where he solved the paradox. Ce paradoxe de Saint-Pétersbourg avait été soulevé par Pierre Raymond de Montmort auprès de Nicolas Bernoulli en 1713. On the Super Saint Petersburg Paradox Tom Cover Stanford February 24, 2012 Tom Cover On the Super Saint Petersburg Paradox The St. Petersburg Paradox Daniel Bernoulli (1738): X = 2k;with prob. Bernoulli … The St. Petersburg game is played by flipping a fair coin until it comes up tails, and the total number of flips, n, determines the prize, which equals $2 n. Thus if the coin comes up tails the first time, the prize is $2 1 = $2, and the game ends. St. Petersburg paradox refers to the problem why most people are unwilling to participate in a fair game or bet. Daniel Bernoulli and the St. Petersburg Paradox LATEX le: StPetersburgParadox Š Daniel A. Graham, June 19, 2005 Suppose you are o ered the chance to play the following game. The St Petersburg paradox was first put forward by Nicolaus Bernoulli in 1713 [13, p. 402]. So it is easy to answer the question, 'How much should the reasonable man, Paul, be prepared to pay to play the St Petersburg game?' The St Petersburg Paradox has thus been enormously influential. Expected value shows what the player should average for each trial given a large amount of trials. • Émile Borel, Probabilité et certitude, Presses universitaires de France, coll. It should not have been since in reality there is no paradox. Research output: Contribution to journal › Article › Academic › peer-review. Daniel is a son of Johann (Jean) I, who was a younger brother of Jakob (Jacques), the author of Ars Conjectandi.Despite Johann's objections Daniel became a mathematician himself, and Daniel spent several years in St. Petersburg, as a professor of mathematics. Ironically, he posed this paradox while his cousin Nikolaus II Bernoulli (brother of Daniel Bernoulli) was actually in St. Petersburg with Daniel. The player gets a payoff of 2" where n is the number of times the coin is tossed to get the first head. It is based on a theoretical lottery game that leads to a random variable with infinite expected value(i.e., infinite expected payoff) but nevertheless seems to be worth only a very small amount to the participants. The St Petersburg paradox has been of academic interest for more than 300 years. Suppose, as did Bernoulli, that the utility of each prize in the St. Petersburg paradox is given by. SP - 223. In 1728 he proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli. Daniel Bernoulli resolved this paradox by saying, and I quote: The determination of the value of an item must not be based on the price, but rather on the utility it yields…. Setiap lemparan koin adalah acara independen dan … » (n 445) (1 éd. By Robert William Vivian. It has been accepted for over 270 years that the expected monetary value (EMV)of the St Petersburg game is infinite. b. See the associated course materials for some background on the economic theory of risk aversion and decision-making and to download this content as a Jupyter/Python notebook. In 1738, J. Bernoulli investigated the St. Petersburg paradox, which works as follows. The probability that a fair coin lands heads up is 1/2. Por aquel entonces Daniel Bernoulli se encontraba en San Petersburgo, atraído junto con otros gr… Since the origins of this paradox with Nicholas Bernoulli, [2], the St. Petersburg Paradox and other probability distributions whose expectation is a diverging series have attracted atten- tion from academia. Download PDF (720 KB) Abstract. called the St. Petersburg paradox. This is the St. Petersburg Paradox. Mari kita mulai dengan menghitung probabilitas yang terkait dengan game ini. If it comes up heads on the first toss he will pay The St. Petersburg Paradox, When EV Isn't Enough. You have the opportunity to play a game in which a fair coin is tossed repeatedly until it comes up heads. The Bernoulli family is famous for a number of distinguished mathematicians. St. Petersburg paradox refers to the problem why most people are unwilling to participate in a fair game or bet. Daniel Bernoulli and the St. Petersburg Paradox Herold G. Dehling Mathernatisch Instituut, Rijksuniversite/t Groningen, Blauwborgje 3, 9747 AC Groningen 1. Petersburg Paradox posed in 1713 by his cousin Nicholas Bernoulli (it is common to note that Gabriel Cramer, another Swiss mathematician, also provided effectively the same solution ten years before Bernoulli). Bevor Daniel Bernoulli im Jahre 1728 veröffentlicht, ein Mathematiker aus Genf, Gabriel Cramer hatte bereits Teile dieser Idee (auch motiviert durch die St. Petersburg Paradox) gefunden in die besagt , dass die Mathematiker schätzen das Geld im Verhältnis zu seiner Quantität und die Menschen mit gesundem Menschenverstand im Verhältnis zu dem, was sie davon verwenden können. The purpose of this article is to demonstrate that contrary to the accepted view, the St Petersburg game does not lead to a paradox at all. Portrait of Daniel Bernoulli (1700-1782) Wikipedia Image Bernoulli introduced his problem in a journal of the Imperial Academy of Science of Saint Petersburg, after which it came to be known as the Saint Petersburg Paradox. However, the problem was invented by Daniel's cousin, Nicolas Bernoulli. La formulación original de la paradoja aparece en una carta enviada por Nicolaus Bernoulli a Pierre de Montmort, fechada el 9 de septiembre de 1713. Le paradoxe de Saint -Pétersbourg ou loterie de Saint-Pétersbourg est un paradoxe lié à la théorie des probabilités et de la décision en économie. Table 2 The EMV of the St Petersburg game played 2 k times 4,8 ... to the EMV arrived at by summing the contributions to the EMV up to the Tk term. Here, / Dehling, H.G. It’s a great game — you’re guaranteed to win money. He referred to St. Petersburg Paradox retrospectively and discussed the solution by Daniel Bernoulli. The expected utility hypothesis stems from Daniel Bernoulli 's (1738) solution to the famous St. Petersburg Paradox posed in 1713 by his cousin Nicholas Bernoulli (it is common to note that Gabriel Cramer, another Swiss mathematician, also provided effectively the … So, if the sequence of tosses 2*. There is a huge volume of literature that mostly concentrates on the psychophysics of the game; experiments are scant. Get PDF (720 KB) Abstract. The Paradox challenges the old idea that people value random ventures according to its expected return. This article demonstrates if two fundamental precepts of Austrian economics are applied this becomes clear. 1950), 136 p. The St. Petersburg Paradox is a famous foleye1@nku.edu ykasturirad1@nku.edu 84 Copyright © SIAM Unauthorized reproduction of this article is prohibited probability paradox discussed originally in a series of letters in 1713 by Nicholas Bernoulli [1] [2]. In it, the gambler flips a coin until he receives his first head. Nicolas Bernoulli’s discovery in 1713 that games of hazard may have infinite expected value, later called the St. Petersburg Paradox, initiated the development of expected utility in the following three centuries. The existence of a utility function means that most people prefer having £98 cash to gambling in a lottery where they could win £70 or £130 each with a chance of 50% - although the lottery has the higher expected prize of £100. Although the problem is phrased di erently today, this was the birth of the St. Petersburg paradox. This is what is known as the St. Petersburg Paradox, named due to the 1738 publication of Daniel Bernoulli Commentaries of the Imperial Academy of Science of Saint Petersburg. Nicholas Bernoulli described the game to his brother Daniel, who was at the time working in St. Petersburg. Suppose you play the following game at a casino: The game master starts with $1 on the table, and tells you to flip a coin. The Paradox posed the following St. Petersburg paradox verwijst naar het probleem waarom de meeste mensen niet willen deelnemen aan een eerlijk spel of weddenschap. In the bet, a fair coin is tossed until it shows heads. The Saint Petersburg paradox, is a theoretical game used in economics, to represent a classical example were, by taking into account only the expected value as the only decision criterion, the decision maker will be misguided into an irrational decision. This paradox was presented and solved in Daniel Bernoulli ’s “Commentarii Academiae... Daniel Bernoulli a manifesté un grand intérêt pour le problème connu sous le nom de paradoxe de Saint-Pétersbourg et a tenté de le résoudre. Paradoxe de Saint-Pétersbourg - St. Petersburg paradox. Das Paradoxon hat seinen Namen von seiner Analyse von Daniel Bernoulli , einem ehemaligen Einwohner der gleichnamigen russischen Stadt , der seine Argumente in den Kommentaren der Kaiserlichen Akademie der Wissenschaften von Sankt Petersburg ( Bernoulli 1738 ) veröffentlichte. Es wurden mehrere Resolutionen zum Paradox vorgeschlagen. The St. Petersburg paradox refers to a gamble of infinite expected value, where people are likely to spend only a small entrance fee for it. The St. Petersburg Paradox. JO - Nieuw Archief voor Wiskunde .