The Mathematics of Games

by Beasley, John D.

• ISBN13: 9780486449760
• ISBN10: 0486449769
• eBook ISBN(s): 9780486151625
• Format: Paperback
• Copyright: 2006-01-30
• Publisher: Dover Publications
• More Book Details

Summary

This book examines how simple mathematical analysis can throw unexpected light on games of every type games of chance, games of skill, games of chanceandskill, and automatic games. Discusses classic puzzles as peg solitaire and Rubik's cube. Lucid, instructive, and full of surprises, it will fascinate mathematicians and gamesters alike. 1989 edition.

Table of Contents

1. Introduction	1	(5)
2. The luck of the deal
Counting made easy	6	(3)
4-3-3-3 and all that	9	(2)
Shuffle the pack and deal again	11	(6)
3. The luck of the die
Counting again made easy	17	(2)
The true law of averages	19	(3)
How random is a toss?	22	(1)
Cubic and other dice	23	(1)
The arithmetic of dice games	24	(4)
Simulation by computer	28	(3)
4. To err is human
Finding a hole in the ground	31	(5)
Finding a hole in the defence	36	(6)
A game of glorious uncertainty	42	(5)
5. If A beats B, and B beats C...
The assessment of a single player in isolation	47	(2)
The estimation of trends	49	(2)
Interactive games	51	(3)
Grades as measures of ability	54	(2)
The self-fulfilling nature of grading systems	56	(3)
The limitations of grading	59	(2)
Cyclic expectations	61	(3)
6. Bluff and double bluff
I've got a picture	64	(2)
An optimal strategy for each player	66	(2)
Scissors, paper, stone	68	(1)
You cut, I'll choose	69	(2)
The nature of bluffing	71	(1)
Analysing a game	72	(5)
7. The analysis of puzzles
Black and white squares	77	(5)
Divisibility by three	82	(3)
Positions with limited potential	85	(3)
Systematic progress within a puzzle	88	(2)
Systematic progress between puzzles	90	(9)
8. Sauce for the gander
A winning strategy at nim	99	(2)
Nim in disguise	101	(5)
All cul-de-sacs lead to nim	106	(2)
Grundy analysis in practice	108	(6)
Some more balancing acts	114	(4)
Playing to lose	118	(2)
9. The measure of a game
Nim with personal counters	120	(2)
Games of fractional measure	122	(3)
General piles	125	(4)
The nature of a numeric game	129	(2)
The measure of a feeble threat	131	(2)
Infinite games	133	(4)
10. When the counting has to stop
The symptoms of a hard game	137	(4)
When you know who, but rot how	141	(4)
The paradox underlying games of pure skill	145	(4)
Round and round in circles
Driving the old woman to bed	149	(4)
Turing games	153	(4)
Turing's paradox	157	(2)
The hole at the heart of mathematics	159	(3)
Further reading	162	(5)
Index	167