strategy

In the game of Nim one player always has a winning strategy — it depends on an unusual way of adding numbers.

In many sports a particular tactical conundrum arises. The team captain has to choose the best order in which to use a group of players or set-plays in the face of unknown counter choices by the opposition. Do you want to field the strongest players first to raise morale or play them last to produce a late run for victory? John D. Barrow shows that randomness holds the answer.

Combinatorial Game Theory is a powerful tool for analysing mathematical games. Lewis Dartnell explains how the technique can be used to analyse games such as Twentyone and Nim, and even some chess endgames.
Backgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.

Chomp is a simple two-dimensional game, played as follows.
Cookies are set out on a rectangular grid. The bottom left cookie is poisoned.
Two players take it in turn to "chomp" - that is, to eat one of the remaining cookies, plus all the cookies above and to the right of that cookie.

Steven J. Brams uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.

This is a game played between a team of 3 people (Ann, Bob and Chris, say), and a TV game show host. The team enters the room, and the host places a hat on each of their heads. Each hat is either red or blue at random (the host tosses a coin for each team-member to decide which colour of hat to give them). The players can see each others' hats, but no-one can see their own hat.

Dr. John Haigh, a mathematics lecturer from the University of Sussex, has found the ultimate strategy for winning at Monopoly: use the help of a computer!

How do you choose a partner? Is it an irrational choice or is it made rationally, based on a mathematical model which analyses the best potential partner you are likely to meet?
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