Purposive contradiction, intervening duality and the nature of probability

This paper first presents the familiar matching pennies game in an unfamiliar constrained gaming form which can give explicit representation to the fairness or otherwise of the coin. Then the intervening duality idea is introduced and shown to make it possible, among other things, to give formal representations to games in which two individuals play using a coin which both believe to be fair relative to a system, yet potentially systematically advantageously biased towards themselves.