Mathematics of Games

Name: Mathematics of Games
Price: 6.74 USD
Availability: InStock
ISBN: 9780486449760

ISBN-10: 0486449769

ISBN-13: 9780486449760

Edition: 2006

Authors: John D. Beasley

List price: $9.95

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Description:

Just how random is a card shuffle or a throw of the dice? Is bluffing a valid poker strategy? How can you tell if a puzzle is unsolvable? How large a role does luck play in games like golf and soccer? This book examines each of these issues and many others, along with the general principles behind such classic puzzles as peg solitaire and Rubik's cube, showing how simple mathematical analysis can throw unexpected light on games of every type--games of chance, games of skill, games of chance and skill, and automatic games. Lucid, instructive, and full of surprises, it will fascinate mathematicians and gamesters alike. 1989 ed.

Book details

List price: $9.95
Copyright year: 2006
Publisher: Dover Publications, Incorporated
Publication date: 1/30/2006
Binding: Paperback
Pages: 176
Size: 5.25" wide x 8.25" long x 0.50" tall
Weight: 0.440
Language: English




Introduction



The luck of the deal


Counting made easy


4-3-3-3 and all that


Shuffle the pack and deal again



The luck of the die


Counting again made easy


The true law of averages


How random is a toss?


Cubic and other dice


The arithmetic of dice games


Simulation by computer



To err is human


Finding a hole in the ground


Finding a hole in the defence


A game of glorious uncertainty



If A beats B, and B beats C


The assessment of a single player in isolation


The estimation of trends


Interactive games


Grades as measures of ability


The self-fulfilling nature of grading systems


The limitations of grading


Cyclic expectations



Bluff and double bluff


I've got a picture


An optimal strategy for each player


Scissors, paper, stone


You cut, I'll choose


The nature of bluffing


Analysing a game



The analysis of puzzles


Black and white squares


Divisibility by three


Positions with limited potential


Systematic progress within a puzzle


Systematic progress between puzzles



Sauce for the gander


A winning strategy at nim


Nim in disguise


All cul-de-sacs lead to nim


Grundy analysis in practice


Some more balancing acts


Playing to lose



The measure of a game


Nim with personal counters


Games of fractional measure


General piles


The nature of a numeric game


The measure of a feeble threat


Infinite games



When the counting has to stop


The symptoms of a hard game


When you know who, but not how


The paradox underlying games of pure skill



Round and round in circles


Driving the old woman to bed


Turing games


Turing's paradox


The hole at the heart of mathematics


Further reading


Index