Chapters authored
‘Chance all’ – A Simple 3D6 Dice Stopping Game to Explore Probability and Risk vs Reward
‘Chance all’ is a simple 3D6 dice game that explores a player’s attitude to risk vs reward. Strategies for playing the game are explored ranging from zero risk to more complex forms of risk, based on an appreciation of the odds; those strategies more likely to win are identified. In addition, the game may be an indirect measure of an individual’s bias towards risk vs reward and how that bias alters through the game as the likelihood of winning and losing changes. It can be used as a simple introductory teaching tool for the Gaussian distribution to examine chance and probability, in evolution and computing science, together with psychological aspects of gameplay.
Part of the book: Game Theory
Lanchester’s Fighting Strength as a Battle Outcome Predictor Applied to a Simple Fire and Manoeuvre Wargame
Lanchester’s equations developed a mathematical understanding of the process of combat, leading to the concept of ‘fighting strength’, the product of fighting efficiency and numbers of troops squared. In this paper we demonstrate that ‘fighting strength’ is a key predictor of outcomes using a simple fire and manoeuvre wargame, set on a Mobius Strip. Lanchester’s equations are solved showing ‘saddle points’, where beneath defeat is certain and above which victory is certain. The influence of tactics is explored using experimental design. The probability of loss in the game with consecutive dice rolls is solved. ‘Fighting strength’ predicted the final result in 33 out of 34 wargames with asymmetric forces. In addition Lanchester’s equations also provide solutions for the % number of casualties in the wargames and the length of time each battle was fought. Based on initial pre-combat fighting efficiencies and numbers of troops between two opponents, a table of likely military strategies are presented to account for the differing ‘fighting strengths’ that best describe possible strategies that can succeed.
Part of the book: Recent Advances in Monte Carlo Methods