Mathematics of Games

ISBN-10: 0486449769

ISBN-13: 9780486449760

Edition: 2006

Authors: John D. Beasley

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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.
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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

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
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