Léo Gerville-Réache
11 articles published in Tangente
History and CultureN°218Jun 12, 2024The two envelopes
A paradox can sometimes resemble an urban legend. First, its precise origins may be difficult to pin down; second, over time it may become distorted, change form, and proliferate. Such is the case with the two-envelope paradox.
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Math for everyoneN°86May 16, 2023Mathematical modelling of a football match
How can you estimate your favourite team's chances of winning the next FIFA World Cup? To some extent, mathematics and artificial intelligence make this possible. Here is an example from the 2018 tournament.
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Math for everyoneN°86May 16, 2023From training to athletic performance
Modeling the relationship between performance and training is a delicate statistical problem. Seeking a mathematical model that links these two sets of data means thinking about sport and the potential effects of an athlete's efforts on their results.
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Math for everyoneN°200Jun 15, 2021Martin Gardner's challenge
Can a game in which one player's gain is the other's loss benefit both players? That was the question Martin Gardner posed in 1980 with his "Loser Takes All" problem. More than forty years on, the paradox remains as relevant as ever!
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Math for everyoneN°195Jul 14, 2020When game theory takes the stage
Toward the end of the Second World War, the celebrated mathematician John von Neumann and the economist Oskar Morgenstern broke new ground by providing a mathematical foundation for the strategic behavior of players and economic agents.
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Math for everyoneN°193Mar 23, 2020What if we replayed the match?
Predicting the result of a football match from statistics alone is impossible. Yet methods have been developed to refine such predictions. Goals often seem to come down to chance—but might analysing how the match unfolded provide a more reliable way to assess the teams?
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History and CultureN°189Jul 13, 2019Shuffling an infinite deck of cards
Shuffling a fifty-two-card deck is easy enough. But suppose the deck contained infinitely many cards: could it still be "shuffled"? The answer is entirely up to you! Welcome to the world of paradoxes that play with infinity…
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Games and ChallengesN°182May 11, 2018The very delicate principle of indifference
The principle of indifference invites us to reflect on the subtle blend of knowledge and ignorance. The probabilities it generates are sometimes surprising, but always consistent. By analyzing a problem's data, it dictates the probabilities that should rationally be assigned.
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History and CultureN°180Jan 28, 2018Behaving rationally in the face of risk
Faced with a lottery offering two different prizes, people adopt different strategies. Why do some participants prefer a potential prize that is not the largest? Their choices depend on how each person conceives of probability—whether as a one-off event or one that will be repeated.
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History and CultureN°175Mar 26, 2017D'Alembert and heads or tails: a historical controversy
A coin tossed twice has a one-in-four chance of landing heads both times. D'Alembert had his doubts. Why? To say he was wrong is to challenge a law formulated by Laplace. Yet Laplace failed to see that his own rule lent credence to D'Alembert's doubts!
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Math for everyoneN°172Sep 15, 2016A few classic paradoxes
Paradoxes are fun to explore and require no specialist knowledge. They help us better understand rationality, truth, probability, uncertainty and information… along with the many theories built around them. Prepare to be surprised by a few spectacular classics.
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