# strategy

Whether you are a bird hunting caterpillars or a neuron processing information, the marginal value theorem helps you maximise your bang per buck.

Here's a game: pick a positive natural number and if yours is the smallest number no one else has picked, you win. What's the best strategy?

*non-game*enjoyed by thousands of people up and down the UK every week.

How to never lose when playing tic-tac-toe the other way around.

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.

**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.