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The mathematics of games 游戏中的数学

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The mathematics of games 游戏中的数学

最 低 价:¥81.00

定 价:¥89.95

作 者:John D. Beasley 著

出 版 社:Oversea Publishing House

出版时间:2006-1-1

I S B N:9780486449760

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内容简介

If playing games is naoural for humans yzing games is equmlyy naural for mathematicians. Even the simplest of games involves the fundamentals of mathematics, such as figuring out the best move or the odds of a certain-Chance event.This entertaining and wide-ranging guide demonstrates how isimpte mathematical a nalysis can throw unexpected light on games of every type games of chance, games of skill, games of chance and skill, and automatic games.
Just how random is a card shuffle or a throw of the dice.J Is bluffing a valid poker strategy? How can you tell ira 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. Lucid, instructive.and full of surDrises, it will fascinate mathematicians and gamesters alike.

作者简介

目录

1.Introduction
2.The luck of the deal
Counting made easy
4-3-3-3 and all that
Shuffle the pack and deal again
3.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
4.To err is human
Finding a hole in the ground
Finding a hole in the defence
A game of glorious uncertainty
5.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
6.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
7.The analysis of puzzles
Black and white squares
Divisibility by three
Positions with limited potential
Systematic progress within a puzzle
Systematic progress between puzzles
8.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
9.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
1O.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
11.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

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