Mathematicians in search of romantic success

In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.

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.

What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? John Haigh uses Game Theory to find the answers, and looks at his World Cup predictions from last issue.

Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.

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.

Some birds, including sparrows and herring gulls, lay their eggs so that the last one to come out is a shade or two lighter than the others. You might suppose that laying eggs requires some effort and that the colour of the last egg is a sign of an exhausted mother. But this practice might be of evolutionary advantage.