The Mathematics of Games

by John D. Beasley

Book Overview

"Mind-exercising and thought-provoking."-- New Scientist If playing games is natural for humans, analyzing games is equally natural for mathematicians. Even the simplest of games involves the... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0486449769
• ISBN13: 9780486449760
• Release Date: January 2006
• Publisher: Dover Publications
• Length: 169 Pages
• Weight: 0.50 lbs.
• Dimensions: 0.4" x 5.3" x 8.5"

Customer Reviews

Automatic Games Caught My Attention

I learned a new family game from John D. Beasley's "The Mathematics of Games." The game is called driving-the-old-women-to-bed. It brings a lot of fun to my family. My family even derives "new" games from the original game by changing the rules. One rule we change is the amount of cards a trick can win. The other rule is that we play two stacks of card together, which is 52(2) + 4 (jokers) = 108 cards, instead of 52 + 2 (jokers) = 54 cards. The jokers require the next player either to play 5 plain cards or to play a court card. Driving-the-old-women-to-bed is "... an automatic game with no opportunity for skills ... which is why... so suitable for family play." Zachary, my son, would jump up onto the table if the game excited him. There are interesting ideas for mathematicians as well: (a) How long is a game likely to last? (b) Can a game get into an infinite loop? (c) If it cannot, can we hope to prove this? The first two questions are solved by the statistics generated by the computer simulation. For the third question, the author provides merely a hint, which is "...a process cannot repeat indefinitely is to show that some property is irreversibly changes by it." The statistics also brings out an interesting characteristic of the game: half-life. About 50% of the games terminate within a further 20 tricks. The book is about the analysis of games. Generally speaking, there are four classes of games: (1) games of pure chance (card and dice games), (2) games of mixed chance and skill (ball games such as golf and soccer), (3) games of pure skill (puzzle such as Rubik's cube), and (4) automatics games. Following are the most interesting overviews, analysis of the games, and mathematical ideas I found on the book: (a) The definition of hard game: "...the amount of computation needed to analyze a specific `instance' of it ... increases with the amount of numerical information needed to define this instance. If the increase is merely linear, the game is relatively easy; if it follows some...polynomial of low degree, the game may not be...bad; if it is exponential, the game is...difficult; and if it is worse than exponential, the game is hard..." (b) Once a game of pure skill has been fully analyzed, it is competitively dead. It is only the ignorance of players that keeps games such as chess alive at championship level. (c) "Turing game...features a line of coins...with a robot which runs up and down turning them over...The robot is extremely simple; in each state, it can only examine the current coin, turn it over if required, and move one step to the left or right...The outcome of the game is completely determined by the actions of the robot in each state and by the initially orientations of the coins..." (d) "...the line initially contains two rows of heads, separated by a single tail...the robot starts within the right hand row...the overall effect is to form a new row whose length is the sum of the lengths of the original r