Antoine Gombaud: Chevalier de Méré

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The Art of Statistics: Learning From Data by David Spiegelhalter

Antoine Gombaud: Chevalier de Méré, Bayesian statistics, Carmen Reinhart, complexity theory, computer vision, correlation coefficient, correlation does not imply causation, dark matter, Edmond Halley, Estimating the Reproducibility of Psychological Science, Hans Rosling, Kenneth Rogoff, meta analysis, meta-analysis, Nate Silver, Netflix Prize, p-value, placebo effect, probability theory / Blaise Pascal / Pierre de Fermat, publication bias, randomized controlled trial, recommendation engine, replication crisis, self-driving car, speech recognition, statistical model, The Design of Experiments, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Malthus

Game 2: Throw two fair dice at most twenty-four times, and win if you get a double-six. Which was his better bet? Following good empirical statistical principles, the Chevalier de Méré decided to play both games numerous times and see how often he won. This took a great deal of time and effort, but in a bizarre parallel universe in which there were computers but no probability theory, the good Chevalier (real name Antoine Gombaud) would not have wasted his time collecting data on his successes – he would simply have simulated thousands of games. Figure 8.1 displays the results of such a simulation, showing how the overall proportion of times that he wins each game changes as he ‘plays’ more and more. Although Game 2 looks the better bet for a while, after around 400 games of each it becomes clear that Game 1 is better, and in the (very) long run he can expect to win around 52% of Game 1, and only 49% of Game 2.


pages: 266 words: 86,324

The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow

Albert Einstein, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Atul Gawande, Brownian motion, butterfly effect, correlation coefficient, Daniel Kahneman / Amos Tversky, Donald Trump, feminist movement, forensic accounting, Gerolamo Cardano, Henri Poincaré, index fund, Isaac Newton, law of one price, pattern recognition, Paul Erdős, Pepto Bismol, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, Ronald Reagan, Stephen Hawking, Steve Jobs, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, V2 rocket, Watson beat the top human players on Jeopardy!

His sister Gilberte called it “the time of his life that was worst employed.”9 Though he put some effort into self-promotion, his scientific research went almost nowhere, but for the record, his health was the best it had ever been. Often in history the study of the random has been aided by an event that was itself random. Pascal’s work represents such an occasion, for it was his abandonment of study that led him to the study of chance. It all began when one of his partying pals introduced him to a forty-five-year-old snob named Antoine Gombaud. Gombaud, a nobleman whose title was chevalier de Méré, regarded himself as a master of flirtation, and judging by his catalog of romantic entanglements, he was. But de Méré was also an expert gambler who liked the stakes high and won often enough that some suspected him of cheating. And when he stumbled on a little gambling quandary, he turned to Pascal for help. With that, de Méré initiated an investigation that would bring to an end Pascal’s scientific dry spell, cement de Méré’s own place in the history of ideas, and solve the problem left open by Galileo’s work on the grand duke’s dice-tossing question.


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Fermat’s Last Theorem by Simon Singh

Albert Einstein, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, Augustin-Louis Cauchy, Fellow of the Royal Society, Georg Cantor, Henri Poincaré, Isaac Newton, John Conway, John von Neumann, kremlinology, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, Rubik’s Cube, Simon Singh, Wolfskehl Prize

This exchange of letters with Pascal, the only occasion when Fermat discussed ideas with anyone but Mersenne, concerned the creation of an entirely new branch of mathematics – probability theory. The mathematical hermit was introduced to the subject by Pascal, and so, despite his desire for isolation, he felt obliged to maintain a dialogue. Together Fermat and Pascal would discover the first proofs and cast-iron certainties in probability theory, a subject which is inherently uncertain. Pascal’s interest in the subject had been sparked by a professional Parisian gambler, Antoine Gombaud, the Chevalier de Méré, who had posed a problem which concerned a game of chance called points. The game involves winning points on the roll of a dice, and whichever player is the first to earn a certain number of points is the winner and takes the prize money. Gombaud had been involved in a game of points with a fellow-gambler when they were forced to abandon the game half-way through, owing to a pressing engagement.


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Radical Uncertainty: Decision-Making for an Unknowable Future by Mervyn King, John Kay

"Robert Solow", Airbus A320, Albert Einstein, Albert Michelson, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, autonomous vehicles, availability heuristic, banking crisis, Barry Marshall: ulcers, battle of ideas, Benoit Mandelbrot, bitcoin, Black Swan, Bonfire of the Vanities, Brownian motion, business cycle, business process, capital asset pricing model, central bank independence, collapse of Lehman Brothers, correlation does not imply causation, credit crunch, cryptocurrency, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, Donald Trump, easy for humans, difficult for computers, Edmond Halley, Edward Lloyd's coffeehouse, Edward Thorp, Elon Musk, Ethereum, Eugene Fama: efficient market hypothesis, experimental economics, experimental subject, fear of failure, feminist movement, financial deregulation, George Akerlof, germ theory of disease, Hans Rosling, Ignaz Semmelweis: hand washing, income per capita, incomplete markets, inflation targeting, information asymmetry, invention of the wheel, invisible hand, Jeff Bezos, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Snow's cholera map, John von Neumann, Kenneth Arrow, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, market bubble, market fundamentalism, Moneyball by Michael Lewis explains big data, Nash equilibrium, Nate Silver, new economy, Nick Leeson, Northern Rock, oil shock, Paul Samuelson, peak oil, Peter Thiel, Philip Mirowski, Pierre-Simon Laplace, popular electronics, price mechanism, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, railway mania, RAND corporation, rent-seeking, Richard Feynman, Richard Thaler, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Coase, sealed-bid auction, shareholder value, Silicon Valley, Simon Kuznets, Socratic dialogue, South Sea Bubble, spectrum auction, Steve Ballmer, Steve Jobs, Steve Wozniak, Tacoma Narrows Bridge, Thales and the olive presses, Thales of Miletus, The Chicago School, the map is not the territory, The Market for Lemons, The Nature of the Firm, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, Thomas Davenport, Thomas Malthus, Toyota Production System, transaction costs, ultimatum game, urban planning, value at risk, World Values Survey, Yom Kippur War, zero-sum game


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The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling by Adam Kucharski

Ada Lovelace, Albert Einstein, Antoine Gombaud: Chevalier de Méré, beat the dealer, Benoit Mandelbrot, butterfly effect, call centre, Chance favours the prepared mind, Claude Shannon: information theory, collateralized debt obligation, correlation does not imply causation, diversification, Edward Lorenz: Chaos theory, Edward Thorp, Everything should be made as simple as possible, Flash crash, Gerolamo Cardano, Henri Poincaré, Hibernia Atlantic: Project Express, if you build it, they will come, invention of the telegraph, Isaac Newton, Johannes Kepler, John Nash: game theory, John von Neumann, locking in a profit, Louis Pasteur, Nash equilibrium, Norbert Wiener, p-value, performance metric, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Richard Feynman, Ronald Reagan, Rubik’s Cube, statistical model, The Design of Experiments, Watson beat the top human players on Jeopardy!, zero-sum game

In the decades that followed, other researchers chipped away at the mysteries of probability, too. At the request of a group of Italian nobles, Galileo investigated why some combinations of dice faces appeared more often than others. Astronomer Johannes Kepler also took time off from studying planetary motion to write a short piece on the theory of dice and gambling. The science of chance blossomed in 1654 as the result of a gambling question posed by a French writer named Antoine Gombaud. He had been puzzled by the following dice problem. Which is more likely: throwing a single six in four rolls of a single die, or throwing double sixes in twenty-four rolls of two dice? Gombaud believed the two events would occur equally often but could not prove it. He wrote to his mathematician friend Blaise Pascal, asking if this was indeed the case. To tackle the dice problem, Pascal enlisted the help of Pierre de Fermat, a wealthy lawyer and fellow mathematician.


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Wonderland: How Play Made the Modern World by Steven Johnson

Ada Lovelace, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Berlin Wall, bitcoin, Book of Ingenious Devices, Buckminster Fuller, Claude Shannon: information theory, Clayton Christensen, colonial exploitation, computer age, conceptual framework, crowdsourcing, cuban missile crisis, Drosophila, Edward Thorp, Fellow of the Royal Society, game design, global village, Hedy Lamarr / George Antheil, HyperCard, invention of air conditioning, invention of the printing press, invention of the telegraph, Islamic Golden Age, Jacquard loom, Jacques de Vaucanson, James Watt: steam engine, Jane Jacobs, John von Neumann, joint-stock company, Joseph-Marie Jacquard, land value tax, Landlord’s Game, lone genius, mass immigration, megacity, Minecraft, moral panic, Murano, Venice glass, music of the spheres, Necker cube, New Urbanism, Oculus Rift, On the Economy of Machinery and Manufactures, pattern recognition, peer-to-peer, pets.com, placebo effect, probability theory / Blaise Pascal / Pierre de Fermat, profit motive, QWERTY keyboard, Ray Oldenburg, spice trade, spinning jenny, statistical model, Steve Jobs, Steven Pinker, Stewart Brand, supply-chain management, talking drums, the built environment, The Great Good Place, the scientific method, The Structural Transformation of the Public Sphere, trade route, Turing machine, Turing test, Upton Sinclair, urban planning, Victor Gruen, Watson beat the top human players on Jeopardy!, white flight, white picket fence, Whole Earth Catalog, working poor, Wunderkammern

He also demonstrated the multiplicative nature of probability when predicting the results of a sequence of dice rolls: the chance of rolling three sixes in a row is one in 216: 1⁄6 x 1⁄6 x 1⁄6. Written in 1564, Cardano’s book wasn’t published for another century. By the time his ideas got into wider circulation, an even more important breakthrough had emerged out of a famous correspondence between Blaise Pascal and Pierre de Fermat in 1654. This, too, was prompted by a compulsive gambler, the French aristocrat Antoine Gombaud, who had written Pascal for advice about the most equitable way to predict the outcome of a dice game that had been interrupted. Their exchange put probability theory on a solid footing and created the platform for the modern science of statistics. Within a few years, Edward Halley (of comet legend) was using these new tools to calculate mortality rates for the average Englishman, and the Dutch scientist Christiaan Huygens and his brother Lodewijk had set about to answer “the question . . . to what age a newly conceived child will naturally live.”


How I Became a Quant: Insights From 25 of Wall Street's Elite by Richard R. Lindsey, Barry Schachter

Albert Einstein, algorithmic trading, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, asset allocation, asset-backed security, backtesting, bank run, banking crisis, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business cycle, business process, butter production in bangladesh, buy and hold, buy low sell high, capital asset pricing model, centre right, collateralized debt obligation, commoditize, computerized markets, corporate governance, correlation coefficient, creative destruction, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, discounted cash flows, disintermediation, diversification, Donald Knuth, Edward Thorp, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, full employment, George Akerlof, Gordon Gekko, hiring and firing, implied volatility, index fund, interest rate derivative, interest rate swap, John von Neumann, linear programming, Loma Prieta earthquake, Long Term Capital Management, margin call, market friction, market microstructure, martingale, merger arbitrage, Myron Scholes, Nick Leeson, P = NP, pattern recognition, Paul Samuelson, pensions crisis, performance metric, prediction markets, profit maximization, purchasing power parity, quantitative trading / quantitative finance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Richard Stallman, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, sorting algorithm, statistical arbitrage, statistical model, stem cell, Steven Levy, stochastic process, systematic trading, technology bubble, The Great Moderation, the scientific method, too big to fail, trade route, transaction costs, transfer pricing, value at risk, volatility smile, Wiener process, yield curve, young professional