Gary Gordon and Elizabeth McMahon
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164038
- eISBN:
- 9781400881338
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164038.003.0014
- Subject:
- Mathematics, History of Mathematics
This chapter considers two fundamental questions for detecting and correcting errors made while playing the card game SET®. The game is played with a special deck of eighty-one cards, and the ...
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This chapter considers two fundamental questions for detecting and correcting errors made while playing the card game SET®. The game is played with a special deck of eighty-one cards, and the objective is to find three cards that form a set. Over the course of a game, a player may make a mistake by taking three cards that do not form a set—a common occurrence which this chapter examines by first introducing coordinates for the cards and then uses these coordinates to define a Hamming weight for any subset of cards. The chapter then uses the facts about Hamming weight to describe a variant of the game, called the EndGame, which leads to error detection. Afterward, the chapter produces a perfect, single-error-correcting linear code solely from SET® cards. It concludes with additional topics that demonstrate the deep connections between the simple card game and advanced mathematics.Less
This chapter considers two fundamental questions for detecting and correcting errors made while playing the card game SET®. The game is played with a special deck of eighty-one cards, and the objective is to find three cards that form a set. Over the course of a game, a player may make a mistake by taking three cards that do not form a set—a common occurrence which this chapter examines by first introducing coordinates for the cards and then uses these coordinates to define a Hamming weight for any subset of cards. The chapter then uses the facts about Hamming weight to describe a variant of the game, called the EndGame, which leads to error detection. Afterward, the chapter produces a perfect, single-error-correcting linear code solely from SET® cards. It concludes with additional topics that demonstrate the deep connections between the simple card game and advanced mathematics.
Ken Binmore
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780195300574
- eISBN:
- 9780199783748
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195300574.003.0006
- Subject:
- Economics and Finance, Microeconomics
This chapter develops the idea of a mixed strategy using the entry into a sealed-bid auction as a non-trivial example. Reaction curves are first illustrated for the case of pure strategies and then ...
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This chapter develops the idea of a mixed strategy using the entry into a sealed-bid auction as a non-trivial example. Reaction curves are first illustrated for the case of pure strategies and then applied to computing mixed Nash equilibria. The Hawk-Dove Game is equivalent either to the Prisoner's Dilemma or Chicken, depending on parameter values. The mixed-strategy reaction curves are plotted in each case. The interpretation of mixed Nash equilibria as polymorphic equilibria in a game played by a large population is considered. The matrix algebra necessary for handling mixed strategies is reviewed and illustrated with O'Neill's Card Game. Convexity ideas are reviewed and applied to the geometric representation of mixed strategies. Cooperative and noncooperative payoff regions are introduced and illustrated using Chicken and the Battle of the Sexes. Correlated equilibria are introduced after a discussion of self-policing agreements, cheap talk, and preplay randomization. The possibility of correlation without a referee using techniques from cryptography is discussed.Less
This chapter develops the idea of a mixed strategy using the entry into a sealed-bid auction as a non-trivial example. Reaction curves are first illustrated for the case of pure strategies and then applied to computing mixed Nash equilibria. The Hawk-Dove Game is equivalent either to the Prisoner's Dilemma or Chicken, depending on parameter values. The mixed-strategy reaction curves are plotted in each case. The interpretation of mixed Nash equilibria as polymorphic equilibria in a game played by a large population is considered. The matrix algebra necessary for handling mixed strategies is reviewed and illustrated with O'Neill's Card Game. Convexity ideas are reviewed and applied to the geometric representation of mixed strategies. Cooperative and noncooperative payoff regions are introduced and illustrated using Chicken and the Battle of the Sexes. Correlated equilibria are introduced after a discussion of self-policing agreements, cheap talk, and preplay randomization. The possibility of correlation without a referee using techniques from cryptography is discussed.
Howard Erskine-Hill
- Published in print:
- 1996
- Published Online:
- October 2011
- ISBN:
- 9780198121770
- eISBN:
- 9780191671296
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198121770.003.0004
- Subject:
- Literature, Poetry, 19th-century Literature and Romanticism
When Pope published the five-canto version of The Rape of the Lock, on 4 March 1714, a reader who remembered the Miscellany poem would at once have noted three changes. A system of spirits had been ...
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When Pope published the five-canto version of The Rape of the Lock, on 4 March 1714, a reader who remembered the Miscellany poem would at once have noted three changes. A system of spirits had been added to the fable, apparent as early as Canto I, line 2.0. In keeping with this metaphysical expansion an underworld sequence, the visit to the Cave of Spleen, now dominated the aftermath of the rape with some ninety-three lines of further narrative. And now, immediately before the rape, another new narrative sequence, the card-game at Hampton Court, casts its own new light on the central act of the poem. The card-game repeatedly incites to political identification. Pope uses the contemporary pack in the style of Rouen, to suggest different monarchs and monarchies. Pope's Dunciad of 1728 and 1729 are visionary dream-poems, partly in that they are filled with the idea and rituals of royalty. Three levels of royalty, however, mingle entrancingly in Pope's dream-world.Less
When Pope published the five-canto version of The Rape of the Lock, on 4 March 1714, a reader who remembered the Miscellany poem would at once have noted three changes. A system of spirits had been added to the fable, apparent as early as Canto I, line 2.0. In keeping with this metaphysical expansion an underworld sequence, the visit to the Cave of Spleen, now dominated the aftermath of the rape with some ninety-three lines of further narrative. And now, immediately before the rape, another new narrative sequence, the card-game at Hampton Court, casts its own new light on the central act of the poem. The card-game repeatedly incites to political identification. Pope uses the contemporary pack in the style of Rouen, to suggest different monarchs and monarchies. Pope's Dunciad of 1728 and 1729 are visionary dream-poems, partly in that they are filled with the idea and rituals of royalty. Three levels of royalty, however, mingle entrancingly in Pope's dream-world.
Jonathan Weed
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691171920
- eISBN:
- 9781400889136
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171920.003.0017
- Subject:
- Mathematics, History of Mathematics
War is a card game so simple that only a child could love it. In this game, the deck is divided into piles, one for each player. At the beginning of each round, each player reveals the top card of ...
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War is a card game so simple that only a child could love it. In this game, the deck is divided into piles, one for each player. At the beginning of each round, each player reveals the top card of her deck. Then, whoever has the best card wins all the revealed cards and places them at the bottom of her deck. War is usually played between two players, but this chapter considers a multiplayer version, called Multinational War. The game works exactly as it does with two players, except it tends to take longer. The tools of computational complexity are used to analyze the questions: Does War have any interesting strategic properties? Is there genuinely a game to play? The chapter establishes that finding the best strategy in Multinational War is a hard problem, and shows that, in this sense, playing Multinational War strategically is at least as hard as playing other classic games.Less
War is a card game so simple that only a child could love it. In this game, the deck is divided into piles, one for each player. At the beginning of each round, each player reveals the top card of her deck. Then, whoever has the best card wins all the revealed cards and places them at the bottom of her deck. War is usually played between two players, but this chapter considers a multiplayer version, called Multinational War. The game works exactly as it does with two players, except it tends to take longer. The tools of computational complexity are used to analyze the questions: Does War have any interesting strategic properties? Is there genuinely a game to play? The chapter establishes that finding the best strategy in Multinational War is a hard problem, and shows that, in this sense, playing Multinational War strategically is at least as hard as playing other classic games.
Hugh Gaston Hall
- Published in print:
- 1990
- Published Online:
- October 2011
- ISBN:
- 9780198151579
- eISBN:
- 9780191672743
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198151579.003.0012
- Subject:
- Literature, European Literature, 17th-century and Restoration Literature
Like a number of his contemporaries in Court circles, the salons, and the early Académie-Française, Jean Desmarets wrote numerous short poems. In the first years of the Regency of Anne of Austria he ...
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Like a number of his contemporaries in Court circles, the salons, and the early Académie-Française, Jean Desmarets wrote numerous short poems. In the first years of the Regency of Anne of Austria he also devised educational card-games for Louis XIV. Desmarets published three collections of his verse: a section of his Œuvres poëtiques and La Comparaison includes a few uncollected pieces, poems reprinted from Œuvres poëtiques, and extracts from Les Promenades de Richelieu and Clovis. Desmarets was, however, a reputable poet in the minor genres and his reputation lasted into the third quarter of the century. That it was owed partly to his fame as a performer, novelist, and playwright — and doubtless partly also to his connections at Court and in the Richelieu family — seems likely. Most of these poems are now mainly of biographical and period interest, but some retain considerable charm.Less
Like a number of his contemporaries in Court circles, the salons, and the early Académie-Française, Jean Desmarets wrote numerous short poems. In the first years of the Regency of Anne of Austria he also devised educational card-games for Louis XIV. Desmarets published three collections of his verse: a section of his Œuvres poëtiques and La Comparaison includes a few uncollected pieces, poems reprinted from Œuvres poëtiques, and extracts from Les Promenades de Richelieu and Clovis. Desmarets was, however, a reputable poet in the minor genres and his reputation lasted into the third quarter of the century. That it was owed partly to his fame as a performer, novelist, and playwright — and doubtless partly also to his connections at Court and in the Richelieu family — seems likely. Most of these poems are now mainly of biographical and period interest, but some retain considerable charm.
Osvaldo Jiménez, Ugochi Acholonu, and Dylan Arena
- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780199896646
- eISBN:
- 9780190256142
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:osobl/9780199896646.003.0016
- Subject:
- Psychology, Developmental Psychology
This chapter examines motivational aspects that cause students to play educational games and learn their featured content, with particular emphasis on a card game called Tug-of-War. It begins with an ...
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This chapter examines motivational aspects that cause students to play educational games and learn their featured content, with particular emphasis on a card game called Tug-of-War. It begins with an overview of help-seeking in technical environments before turning to a discussion of an initial way to measure motivation to learn: by focusing on the type and amount of help students seek from others in the classroom while playing the game. It then describes the design and development of Tug-of-War and how it has improved learning outcomes with respect to traditional academic measures.Less
This chapter examines motivational aspects that cause students to play educational games and learn their featured content, with particular emphasis on a card game called Tug-of-War. It begins with an overview of help-seeking in technical environments before turning to a discussion of an initial way to measure motivation to learn: by focusing on the type and amount of help students seek from others in the classroom while playing the game. It then describes the design and development of Tug-of-War and how it has improved learning outcomes with respect to traditional academic measures.
Bruce R. Smith
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780198735526
- eISBN:
- 9780191822506
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198735526.003.0005
- Subject:
- Literature, Shakespeare Studies, 16th-century and Renaissance Literature
This final chapter of Shakespeare | Cut investigates the fetishization of cutting up Shakespeare in contemporary culture, but locates its origins at the very beginning of the twentieth century. A ...
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This final chapter of Shakespeare | Cut investigates the fetishization of cutting up Shakespeare in contemporary culture, but locates its origins at the very beginning of the twentieth century. A chronological survey from 1900 to 2016, the chapter encompasses burlesques, Vorticism, Modernism, Post-modernism, and Post-post-modernism, the still more radical cutwork in Shakespeare scissions since the turn of the millennium. Hamlet provides a convenient reference point for charting these developments. The chapter concludes with consideration of some possible reasons for contemporary fascination with cutwork: fragmentation in Western culture since the demise of Modernism, the speeding up of contemporary life, fascination with violence in the twenty-first century, and a realization that cuts and cutting are fundamental to all acts of perception and creativity. The book has a surprise ending.Less
This final chapter of Shakespeare | Cut investigates the fetishization of cutting up Shakespeare in contemporary culture, but locates its origins at the very beginning of the twentieth century. A chronological survey from 1900 to 2016, the chapter encompasses burlesques, Vorticism, Modernism, Post-modernism, and Post-post-modernism, the still more radical cutwork in Shakespeare scissions since the turn of the millennium. Hamlet provides a convenient reference point for charting these developments. The chapter concludes with consideration of some possible reasons for contemporary fascination with cutwork: fragmentation in Western culture since the demise of Modernism, the speeding up of contemporary life, fascination with violence in the twenty-first century, and a realization that cuts and cutting are fundamental to all acts of perception and creativity. The book has a surprise ending.
