strategy
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.
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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.
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Chomp is a simple two-dimensional game, played as follows. |
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.
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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. |
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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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