game theory

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

Disputes over property are all too common. It's quite easy to share a cake, but how do you share out indivisible goods, such as houses or cars, without causing resentment? Here are two easy methods.

A 1 in 14 million chance to win the lottery, a 5% risk of cancer, a 50:50 chance of heads on a coin — we deal with probabilities all the time, but do they actually mean anything? We explore the philosophy of probability and ask whether the probabilities that come up in physics differ from those in every day life.

Are there objective chances in the world?

Is poker a game of psychology and cunning rather than strategy? We investigate the maths of bluffing.

Would you stake your fortune on a 100 to 1 outsider? Probably not. But what if, somewhere in a parallel universe, the straggling nag does come in first? Would the pleasure you feel in that universe outweigh the pain you feel in the one in which you've lost? Questions not dissimilar to this one occupy physicists and for entirely respectable reasons.

In the previous article we explored how a clever argument involving gambling makes the idea that there are parallel universes more credible. But does it really?

How do you best allocate students to universities, doctors to hospitals, or kidneys to transplant patients? It's a tough problem that has earned this year's Memorial Prize in Economics.

Andy Murray and Laura Robson made a good team at London 2012, bringing home silver in the mixed doubles. But how do you make sure that the competing pair is the best you can pick from the team?

Is it rational to believe in a god? The most famous rational argument in favour of belief was made by Blaise Pascal, but what happens if we apply modern game theory to the question?